Year 5 - September 2016
Visit from Helen Sharp
Children were privileged to have Helen Sharp present a session on gravity and its effect on humans. She delved into how gravity was discovered and how it works in our universe. Children thoroughly enjoyed the session, which sparked many thoughtful questions.
Children participated in a child protection sports workshop, which involved self-defence.
Maths this week featured interpreting negative numbers in context. Children were practising this skill by playing ‘Arctic Expedition’, a board game that featured a range of questions involving negative numbers and applying their knowledge of them. Many children expressed interest in playing again, as they enjoyed it so much!


This accommodation is assured, so that you don’t need to worry about discovering somewhere to stay after accepting a spot right here, all of that is organised for you earlier than you arrive. Islands students are entitled to different help to that of students from the relaxation of the UK. Ultimately, we’re most interested in a candidate’s potential to suppose imaginatively, deeply and in a structured manner about the patterns of mathematics. If a sensible part varieties part of any of your science A‐levels used to satisfy your provide, we expect you to cross it. Our programs have restricted formal prerequisites, so it is the experience quite than outright knowledge which must be made up.
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And even “gentle science” disciplines like sociology rely on refined statistical regression methods to attract out insights in regards to the workings of our human world. Learn the talents that will set you up for success in polynomial operations and complicated numbers; equations; transformations of capabilities and modeling with functions; exponential and logarithmic relationships; trigonometry; and rational capabilities. Learn eighth grade math aligned to the Eureka Math/EngageNY curriculum —functions, linear equations, geometric transformations, and more. Learn seventh grade math aligned to the Eureka Math/EngageNY curriculum—proportions, algebra fundamentals, arithmetic with adverse numbers, likelihood, circles, and more. Whether you’re on the lookout for a solid grounding in maths and statistics or wish to specialize in aspects of pure or utilized mathematics, an OU maths course will help you stand out from the gang.
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- Boaler was the chief author of the 2021 California Math Framework , which aimed to enhance instructional fairness by reshaping the state’s math curriculum.
Section 1 deals with the formulation of linear programming models, describing how mathematical models of suitable real-world issues may be constructed. Section 2 seems at graphical representations of two-dimensional models, considers some theoretical … The integrated pathway of courses covers the identical topics as the standard pathway . Math 1, Math 2, and Math three every contain elements of algebra, geometry, and statistics, so the content is more interwoven. We’ve added 500+ learning alternatives to create one of many world’s most complete free-to-degree online learning platforms. Learn to use R programming to apply linear models to research data in life sciences.
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Due to the chaotic nature of the atmosphere, weather forecasts, even with ever improving numerical weather prediction models, eventually lose all skill.
Meteorologists have a strong desire to better understand this process as they try to trace forecast error back to observational gaps and to provide a means for improvement.
Root mean square error (rms, or its square, the variance distance) is often used to measure differences between simulated and observed fields. In this case, scientists measured the distance between a model forecast field within its grid and the verifying analysis field that represents all real-world observations.
However, one must consider that atmospheric features, like fronts and pressure systems are three dimensional weather features in space that computer models displace and also structurally distort as the numerical forecast moves away from initiation. Variance or rms error metrics do not quantify the displacement and distortion of weather systems.
In a recently published paper in Advances in Atmospheric Sciences, a team of scientists with the National Oceanic and Atmospheric Administration (NOAA), the Massachusetts Institute of Technology (MIT), and the University of Connecticut set out to find a general approach to assess the positional and structural components of the total difference between two fields.
Essentially, meteorologists want to assess the accuracy of many different weather features within a model forecast compared to a verifying analysis based on real-world observations.
Sai Ravela from MIT, a co-author of this study, previously developed a Field Alignment method. In this case, his approach aligns the model forecast field with the observationally based analysis in a smooth fashion so their difference is minimized (Step 1 in schematic diagram, see also example map).
Next, small scale errors from uncertain origins are removed from all three fields (the original and aligned forecast as well as the verifying analysis, or proxy for observations) through a process called spatial filtering or smoothing (Step 2).
The total variance distance, or difference, is then partitioned into three unique components (Step 3).
Positional error, which is the variance distance between the smoothed original model forecast and smoothed aligned forecast fields, and structural error that is the variance distance between the smoothed aligned forecast and the smoothed verifying analysis fields, are two sides of the right angle triangle in Fig. 1, and fine scale noise, which are the uncertain small-scale errors removed from the original model forecast and verifying analysis, or observation fields (see smoothing arrows orthogonal to the triangle in Fig. 1).
This method outputs the three orthogonal error components as scalar fields, as well as a vector field (Fig. 2) indicating the large-scale displacement of the forecast compared to the observational analysis field.
Interestingly, throughout all regions and lead times that the team studied, more than half of the total error variance is associated with the misplacement of weather features.
Therefore, displacement is more pronounced than distortion in forecast fields: only about 25% error variance is associated with structural inaccuracies of the partially predictable features, such as fronts and low pressure systems. The rest of the error variance remains unexplained or unpredictable variability, or noise.
“How noise grows in error variance as a function of forecast lead time, and whether a positional-structural-noise decomposition of the spread among an ensemble of perturbed forecasts captures forecast error components is the subject of ongoing studies,” said Dr. Jankov from NOAA, the lead author of the study.


A toy robot pattern has been added to the Stitching Cards collection. The design makes a wonderful card for young boys. Robot: www.stitchingcards.com/product.php/869/ The robot design comes with a numbered diagram, a colour illustration, a pricking pattern and step-by-step instructions for the stitching. It is delivered by download to your computer. Pattern size 152 mm… Read More »
Primary school teachers looking for a fun maths project for the Christmas term will find it at the String Art Fun website. The string art maths projects are suitable for Key Stage 2 Maths (8 – 11 years old). They include numbered patterns and maths questions sheets.
Designs can be created with pencils and ruler or drawing pins (thumb tacks) and string / wool.
There is a free maths project featuring a Christmas pudding with holly.


Once the data file is loaded it is displayed with the data in a spreadsheet. A Plot button will initiate graphic plots of X versus the other variables. The Curve fit button is for creating a polynomial curve fit of each dependent variable (Y, Z, etc) as a function of the independent variable (X) based on the user specified degree of the polynomial (maximum = 5). The coefficients of the curve fit (such as a0, a1, etc) are displayed below the data grid for each of the dependent variable Y, Z, etc. The Interpolate button will prompt user to specify the X value and the calculated values of Y, Z, and etc T will be displayed in the data grid in a different color from that of the main data. When plotting is initiated, the independent variable X will be plotted on the horizontal axis. The dependant variables Y, Z, etc are plotted on the vertical axes. The left vertical axis will be Y values. The remaining variables (Z, R, S and T) will be plotted on vertical axes located on the extreme right side. The scales of the various axes (minimum, maximum and increments) are displayed for user to change if desired. Similarly the Titles and sub-titles for each plot will also be specified by the user. The graphs are plotted in a separate screen. The graph screen can be copied (to clipboard), saved or printed using the Copy, Save and Print buttons.
Typical plots of one independent variable X (Flow rate) versus three dependant variables (Head, Efficiency and NPSH) are shown in the screen shot below.


Experienced technical skills
- Standard methods of theoretical physics at the level of the Landau-Lifshitz course
(7-year teaching experience) and basic methods of quantum field theory.
- Wide range of mathematical methods including partial differential equations (published textbook), asymptotic methods, functional analysis,
random processes, combinatorics, point and space groups, numerical methods.
- Advanced methods of statistical physics including series expansions, exact enumeration, exactly solvable models, scaling theory, mean-field theory,
variational approach, Monte-Carlo methods, ALPS for spin models.
- Computational quantum mechanics: SCF calculations, geometry optimization, structure prediction, vibronic couplings, exact analytical diagonalization, GTO and STO basis sets,
MOPAC for semiempirical calculations,
TINKER and LAMMPS for classical molecular mechanics,
Firefly and Gaussian for ab-initio calculations with GTO,
VASP for ab-initio calculations with plane waves,
ALPS for state of the art calculations of model systems (e.g. Hubbard model).


Click here to read the Math department goals.
This document will take you to the Math standards for grades 5-12. The bolded standards are the prioritized standards in each grade. A committee of grade 5-12 Math teachers collaborated to choose the priority standards and to ensure they were cohesive and built upon previous knowledge and skills in each grade. The priority standards are the more rigorous standards that will take more class time for students to achieve. The supporting standards are the remaining standards that must be taught in order to reach the priority standards.


Previously the Opponent’s Batting Average (OBA) or Batting Average Against (BAA) was calculated using the formula documented here: http://en.wikipedia.org/wiki/Batting_average_against
However, I have had feedback from a few teams asking to verify how the calculation was being made. To simplify things we have changed OBA to simply be:
hits / ab
The simple calculation should help clear up any questions on how OBA is being calculated.
If you have questions or comments we would love to hear them! Please post a comment below or let us know through the support form.


The first comparison that compares group 1 to teams 2, 3, 4 assigns three/4 to group 1 and -1/four to groups 2, 3, 4. Likewise, the second comparability that compares group 2 to teams 1, 3, 4 assigns three/4 to group 2 and -1/4 to groups 1, 3, 4 and so forth for the third comparability. Note that you could substitute three for three/four and 1 for 1/four and you’ll get the identical check of significance, however the distinction coefficient would be completely different.
Level of raceNew variable 1 New variable 2 New variable three Level 1 v. MeanLevel 2 v. MeanLevel 3 v. Mean Below we present how to create x1 x2 and x3 based mostly on the desk above and use them in the regression command. As you see within the example under, the regressioncoding is accomplished by assigning “1” to group 1 for the primary comparison , a “1” to group 2 for the second comparison , and “1” to group three for the third comparison .
The third comparability is coded reflecting that group 3 is compared to group four. For contrast coding, we see that the first comparison comparing teams 1 and a pair of are coded -1 and 1 to compare these groups, and 0 otherwise. The second comparability evaluating teams 1,2 with group 3 are coded -.5 -.5 1 and zero, and the final comparability comparing teams 1,2,3 with group four are coded -.333 -.333 -.333 and 1.
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Note that the contrasts are listed out in three groups separated by commas that can assist you see every set of comparisons. For distinction coding, the coding more naturally reflects the comparisons being made. The first comparability is coded reflecting that group 1 is compared to group 2. The second comparability is coded reflecting that group 2 is compared to group 3, and the third comparison is coded reflecting that group three is in contrast with group four. Below we show tips on how to create the variables for the regression evaluation primarily based on the above desk and enter them into the regression command. For distinction coding, we see that the primary comparison evaluating group 1 with groups 2, 3 and four is coded 1 -.333 -.333 -.333 reflecting the comparability of group 1 vs. all other teams. The second comparison is coded zero 1 -.5 -.5 reflecting that it compares group 2 with teams three and 4.


How to Calculate a commercial CAP Rate.
What is CAP rate ? It is a rate of return that you get yearly on the commercial property. For example:
Purchase price$ 1,000,000.
Net Operating Income , NOI = 100.000.
100,000/1,000,000 = 10% CAP Rate.
The difference on borrowing rate and CAP rate is what you make on your investment at the end of the day. If you borrower at 6%, and your CAP rate is 10%, then you will make 4% net.
Loan amount that you can get based on the cap rate :
NOI / 1.25 and then divide that by the borrowing rate. For example :
100,000/1.25 = 80,000 / .06 =$1,333,333. That means you can borrow up to $1,333,333 to buy that property unless you require to put a down payment and which makes the loan allowed lower.


Yesterday I went to a refresher training for the Voyager program I teach. Last year I was unable to teach the Math part in small groups and I really hope to do that this year. I'm thinking of having an hour and half block to teach the Voyager program. During the hour and a half, the students would rotate to three stations: Reading, Math, and Computer. Both the reading and math have an online component so they would be using Ticket to Read or VMath Live on the computer. However, I do not know when we'll be going to special area, lunch, and recess so the schedule I mapped out yesterday may not happen, but as a teacher, we all know we have to remain flexible!
I thought I would share with you what I used to track my student's MAP data last year. I just modified it so that it's up to date for this school year. I left off a year so that it can be used year after year.
Math MAP Analysis: Click here to view this.
Reading MAP Analysis: Click here to view this.
These are great for determining small group instruction. I plan to use this to group my students for differentiated math group instruction on Fridays. I will also look at where my students fall for Reading to determine mini lessons with guided reading. I hope you find this helpful!
UPDATE: I found a picture of one that I filled out for one of my students last year. This one also has their MAP scores from the previous grade. The ones I attached are cuter (I think!). Hopefully this is helpful :)
I am off to lay out for my last day of summer then I have big plans to paint my nails! Whoo hoo...I am kind of excited about going back. I know I'll be regretting this in a few months though. I'm also loving that college football is around the corner! On a totally random note, we just bought this (not exact brand) for my husband to wear to the games we go to. I'd love to find a girls version. I have a jersey (as you can see in my header), but Alshon Jeffrey signed it! I went to Steve Spurrier's Ladies Clinic this year and he signed my jersey, so my hubby says I can no longer wear it!
Wow, this is sad how quickly I got off topic. This just goes to show how spaztastic my brain is lately. Yes, I totally believe in spaztastic being a real word. I will continue to use it :) Hope everyone is enjoying their summer or start to the school year. See you soon!


Michael PorterORG Ware County Board of Education Title BIO Mike Porter is Director of Technology for the Ware County Schools in Waycross, GA. The system has approximately 6000 students in 10 school buildings. He has a BS in mathematics and completed graduate studies in applied math and computer science. He has programmed and worked with personal computers since 1981 beginning with the Apple II and then IBM XT. Over the next few years, he began networking computers and installing and using servers. He holds several technology certifications including CCNA and CNE. A classroom teacher and math dept chair for his first 14 years in education, he has been the director of technology for the Ware County Schools for the last 15 years. His department manages over 2000 computers, 11 networks, 25 servers, 15 high definition codecs for video conferencing, and the Student Information System (SIS) for Ware County.
Sessions and Presentations
Time 11/02/10 08:45AM-10:00AM


Around A.D. 1175, Leonardo of Pisa was born in Pisa, Italy. Now better known as Fibonacci, he is now known as the greatest mathematician in Europe during the middle ages. He brought the Arabic-Hindu numbering system to Europe and developed the decimal system, both of which became the foundation of the mathematics that are used today. To the financial trader, the Fibonacci retracement method based on the contributions of this great mathematician are significant.
The most important numbers found in trading are percentages: 38.2%, 50%, and 61.8%. These percentages are considered to be trend retracement points, and are what the Fibonacci retracement method focuses on. If the retracement goes to the 61.8% mark, there is a new trend starting. If the retracement goes to the 38.2% mark, then there has been a failed reversal and the current trend will likely continue. If the retracement goes to the 50% mark, there are other signals that have to come into play and some different strategies are used.
The Fibonacci retracement numbers have become more popular recently as traders have begun to see the value in utilizing these numbers that consistently predict new trends. If you take the time to study the Fibonacci retracements and check them against the current numbers and then follow them, you will see that most of the predictions are accurate, sometimes right on the money.
As with any of the systems out there, Fibonacci retracement numbers should not be the only source you consult when making trading and investment decisions because it’s never a good idea to rely solely on one system, even if the system is a good one. However, it can be an extremely useful tool to combine along with other indicators so help strengthen your trading system. Every trader, from individuals to large investment firms, can benefit from using Fibonacci retracement as a part of their financial trading.Tags: Fibonacci Retracement


Mathematics plays a crucial role in the game of poker, providing players with winning strategies and practical tips. By understanding the mathematical concepts underlying the game, such as probability theory, expected value calculations, and game theory, players can make informed decisions that maximize their chances of success. This article explores the significance of mathematics in poker and how it can be applied to gain an edge over opponents.
The Importance of Probability and Statistics in Poker
Poker, a game of skill and strategy, has long captivated the minds of players around the world. While many may think of poker as a game of luck, those who truly understand its intricacies know that mathematics plays a crucial role in determining success at the table. In particular, probability and statistics are fundamental concepts that can greatly enhance a player’s understanding of the game.
Probability is the branch of mathematics that deals with the likelihood of events occurring. In poker, understanding probability is essential for making informed decisions. For example, knowing the probability of being dealt certain starting hands can help players determine whether to fold, call, or raise. By calculating the odds of completing a hand based on the cards already on the table, players can make more accurate assessments of their chances of winning.
Statistics, on the other hand, involves analyzing data to draw meaningful conclusions. In poker, statistical analysis can provide valuable insights into opponents’ playing styles and tendencies. By keeping track of how often an opponent raises, calls, or folds, players can gain a better understanding of their opponents’ strategies. This information can then be used to exploit weaknesses and maximize profits.
Furthermore, statistics can also shed light on the overall profitability of different poker strategies. Through careful analysis, players can determine which approaches yield the best long-term results. Whether it’s aggressive play, tight play, or a combination of both, statistics can provide empirical evidence to support strategic decision-making.
Transitional phrase: With a solid foundation in probability and statistics, players can employ various winning strategies and practical tips to improve their performance at the poker table.
One such strategy is known as pot odds. Pot odds refer to the ratio of the current size of the pot to the cost of a contemplated call. By comparing this ratio to the odds of completing a hand, players can determine whether a call is mathematically profitable in the long run. If the pot odds are greater than the odds of completing a hand, making the call would be considered a +EV (positive expected value) play.
Another important concept in poker is implied odds. Implied odds take into account potential future bets that can be won if a particular hand improves. By factoring in these additional winnings, players can make more informed decisions about whether to continue with a hand that may not currently have favorable pot odds but could yield significant profits in the long run.
Transitional phrase: In addition to understanding probability and employing winning strategies, there are also practical tips that players can utilize to improve their game.
One such tip is bankroll management. Properly managing one’s bankroll is crucial for long-term success in poker. By setting aside a specific amount of money for playing poker and sticking to it, players can avoid going on tilt and risking more than they can afford to lose. This disciplined approach helps maintain focus and prevents emotional decision-making.
Furthermore, maintaining a consistent playing style can also be advantageous. While it may be tempting to switch between aggressive and passive play, doing so can make it easier for opponents to read your hands. By staying consistent, players can keep their opponents guessing and maintain an element of unpredictability.
In conclusion, mathematics plays a vital role in the game of poker. Probability and statistics provide the foundation for making informed decisions and analyzing opponents’ strategies. By understanding concepts such as pot odds and implied odds, players can employ winning strategies to maximize their profits. Additionally, practical tips like bankroll management and consistency can further enhance a player’s chances of success. With a solid grasp of these mathematical principles and strategic approaches, players can elevate their game and increase their chances of coming out on top at the poker table.
Mastering Expected Value: Calculating Pot Odds and Implied Odds
Poker is a game of skill, strategy, and calculation. While luck certainly plays a role, the most successful poker players rely on their ability to make informed decisions based on mathematical principles. One such principle that every aspiring poker player should understand is expected value (EV). By mastering EV, players can calculate pot odds and implied odds, two crucial concepts that can greatly improve their chances of winning.
Expected value is a mathematical concept that represents the average outcome of a particular decision over the long run. In poker, it allows players to determine whether a specific play will be profitable or not. To calculate EV, one must consider both the probability of each possible outcome and the potential payoff associated with each outcome.
Pot odds are a way for players to assess the potential profitability of a hand by comparing the current size of the pot to the cost of making a particular bet. By calculating pot odds, players can decide whether it is mathematically correct to call, raise, or fold. The formula for pot odds is simple: divide the size of the pot by the cost of the bet. If the resulting ratio is greater than the probability of winning the hand, it is a favorable play.
For example, if the pot contains $100 and your opponent bets $20, the pot odds would be 5:1 ($100/$20). If you believe you have a 25% chance of winning the hand, your probability of winning is 3:1. Since the pot odds are higher than your probability of winning, calling the bet would be a profitable play in the long run.
Implied odds take into account future bets that may be won if certain cards are drawn. Unlike pot odds, which only consider the current size of the pot, implied odds factor in potential future gains. This concept is particularly relevant in situations where players have strong drawing hands, such as flush or straight draws.
To calculate implied odds, players must estimate the potential future bets they can win if their hand improves. For example, if you have a flush draw with one card to come and your opponent makes a bet that is less than the size of the pot, calling the bet may be justified if the potential future winnings outweigh the immediate cost of the call.
By understanding both pot odds and implied odds, players can make more informed decisions at the poker table. However, it is important to note that these calculations are based on probabilities and expected values, not certainties. Even with favorable odds, there is always a chance of losing. Therefore, it is crucial for players to manage their bankroll wisely and avoid making reckless bets solely based on mathematical calculations.
In conclusion, mastering expected value is an essential skill for any serious poker player. By calculating pot odds and implied odds, players can make more informed decisions and increase their chances of winning in the long run. However, it is important to remember that poker is a game of skill and luck, and no amount of mathematical calculation can guarantee success. So while mathematics can certainly improve your game, ultimately, it is up to the player’s judgment and decision-making abilities to come out on top.
Using Game Theory to Optimize Decision-Making in Poker
Using Game Theory to Optimize Decision-Making in Poker
When it comes to poker, mathematics plays a significant role in determining the outcome of each hand. From calculating probabilities to making strategic decisions based on expected value, understanding game theory can greatly improve your chances of winning at the poker table.
Game theory is a mathematical framework that helps analyze decision-making in competitive situations, such as poker. It provides players with a systematic approach to making optimal choices by considering all possible outcomes and their associated probabilities.
One key concept in game theory is Nash equilibrium, named after mathematician John Nash, who won the Nobel Prize in Economics for his work in this field. Nash equilibrium refers to a state where no player can improve their outcome by unilaterally changing their strategy. In other words, it’s a stable point where both players are playing optimally given their opponent’s strategy.
To apply game theory to poker, players must first understand the concept of expected value (EV). EV represents the average amount of money a player expects to win or lose on each bet over the long run. By calculating the EV of different actions, players can make informed decisions that maximize their overall profitability.
For example, let’s say you have a pair of kings in Texas Hold’em, and the flop reveals two more kings. You’re confident that you have the best hand, but you want to extract the most value from your opponents. To determine whether to bet or check, you need to consider the EV of each action.
If you decide to bet, you might scare away weaker hands, reducing the potential winnings. On the other hand, if you check, your opponents may catch up with better hands, decreasing your chances of winning. By calculating the EV of betting versus checking, you can determine the optimal play that maximizes your long-term profits.
In addition to expected value calculations, game theory also helps players understand bluffing and counter-bluffing strategies. Bluffing is a crucial aspect of poker, as it allows players to win pots even with weaker hands. However, bluffing too often can be easily exploited by observant opponents.
Game theory provides insights into optimal bluffing frequencies and helps players determine when to bluff based on their opponent’s likely range of hands. By analyzing the probabilities and expected payoffs of different bluffing strategies, players can make informed decisions that maximize their chances of success.
Furthermore, game theory also considers the concept of mixed strategies, where players randomize their actions to prevent opponents from exploiting predictable patterns. Mixing strategies makes it more challenging for opponents to discern whether a player is bluffing or playing a strong hand, adding an element of unpredictability to the game.
In conclusion, understanding game theory is essential for optimizing decision-making in poker. By calculating expected values, considering Nash equilibrium, and employing strategic bluffing techniques, players can improve their overall profitability at the poker table. While luck will always play a role in individual hands, incorporating mathematical principles into your gameplay will undoubtedly increase your chances of long-term success. So next time you sit down at the poker table, remember to think strategically and let mathematics guide your choices.
Applying Mathematical Concepts to Bluffing and Bet Sizing Strategies
Applying Mathematical Concepts to Bluffing and Bet Sizing Strategies
In the game of poker, bluffing is an essential skill that can greatly enhance a player’s chances of winning. However, successful bluffing requires more than just intuition and gut feeling; it also involves a deep understanding of mathematical concepts. By applying these concepts to bluffing and bet sizing strategies, players can make informed decisions that will increase their odds of success.
One fundamental mathematical concept in poker is probability. Probability allows players to calculate the likelihood of certain outcomes based on the cards they have been dealt and the community cards on the table. This knowledge is crucial when deciding whether to bluff or not. For example, if a player has a weak hand but there is a high probability of them improving their hand with the upcoming community cards, bluffing may be a viable option. On the other hand, if the probability of improving their hand is low, bluffing would be a riskier move.
Another important mathematical concept in poker is expected value (EV). EV is a measure of the average amount a player can expect to win or lose on each bet over the long run. By calculating the EV of different betting options, players can determine the most profitable course of action. When bluffing, it is crucial to consider the potential gains and losses associated with the bluff. If the expected value of the bluff is positive, meaning that the potential winnings outweigh the potential losses, then it may be a good time to bluff.
Bet sizing is another aspect of poker where mathematical concepts come into play. The size of a bet can influence how opponents perceive a player’s hand strength. It is important to strike a balance between making a bet large enough to scare opponents away and making a bet small enough to entice opponents to call. To achieve this balance, players must consider pot odds and implied odds. Pot odds refer to the ratio of the current size of the pot to the cost of a contemplated call. Implied odds, on the other hand, take into account potential future bets and winnings. By carefully calculating pot odds and implied odds, players can determine the optimal bet size that maximizes their expected value.
Moreover, understanding game theory can provide valuable insights into bluffing and bet sizing strategies. Game theory is a branch of mathematics that studies strategic decision-making in competitive situations. In poker, game theory helps players analyze the actions of their opponents and make decisions based on the best response to those actions. By considering the range of possible hands their opponents could have and the likelihood of certain actions leading to positive outcomes, players can apply game theory principles to their bluffing and bet sizing strategies.
In conclusion, applying mathematical concepts to bluffing and bet sizing strategies can significantly improve a player’s performance in poker. By understanding probability, expected value, bet sizing, and game theory, players can make informed decisions that increase their chances of success. Bluffing becomes more calculated and effective when backed by mathematical analysis, while bet sizing becomes optimized for maximum profitability. So, next time you sit at the poker table, remember to bring your math skills along with your poker face.
Analyzing Hand Ranges and Range Equity in Poker Mathematics
Analyzing Hand Ranges and Range Equity in Poker Mathematics
In the game of poker, understanding your opponent’s hand range is crucial to making informed decisions and maximizing your chances of winning. This concept involves assessing the possible combinations of cards that your opponent could have based on their actions and the information available to you. By analyzing hand ranges and calculating range equity, players can gain a significant edge over their opponents.
To begin with, let’s define what a hand range is. In poker, a hand range refers to the set of possible hands that an opponent may have at any given moment. It is not just about determining the specific hand they hold but rather considering all the different combinations of hands that are consistent with their actions and the current state of the game. By narrowing down the potential hands, you can make more accurate predictions and better decisions.
One way to analyze hand ranges is by observing your opponent’s betting patterns and tendencies. For example, if an opponent raises preflop, it indicates that they likely have a strong starting hand. Conversely, if they call or limp into the pot, their range might be wider, including both strong and weak hands. By paying attention to these patterns, you can start to narrow down their possible holdings.
Another important factor to consider when analyzing hand ranges is the position of your opponent. Players who act earlier in the betting round have less information than those who act later. Therefore, their ranges tend to be broader, as they have less knowledge about the strength of other players’ hands. On the other hand, players who act later have more information and can narrow down their opponent’s range accordingly.
Once you have determined your opponent’s hand range, the next step is to calculate range equity. Range equity refers to the percentage of the pot that you expect to win on average against your opponent’s entire range of hands. It takes into account the likelihood of each hand within their range and the probability of winning with your own hand.
To calculate range equity, you can use various mathematical tools and techniques. One commonly used method is Monte Carlo simulation, which involves running thousands of random simulations to estimate the probabilities of different outcomes. By inputting your opponent’s range and your hand into a poker software or using online calculators, you can obtain an approximate value for your range equity.
Understanding range equity allows you to make better decisions in terms of bet sizing and strategy. For example, if you have a strong hand with high range equity, it may be profitable to bet aggressively and try to extract maximum value from your opponent. Conversely, if your hand has low range equity, it might be more prudent to play cautiously and minimize losses.
In conclusion, analyzing hand ranges and calculating range equity are essential skills in poker mathematics. By studying your opponent’s betting patterns, considering their position, and using mathematical tools, you can gain valuable insights into their likely holdings. Understanding range equity enables you to make informed decisions and maximize your chances of success at the poker table. So, next time you sit down to play, remember to analyze hand ranges and utilize this powerful tool in your arsenal.


In the second period of the 2021 College Scholastic Ability Test (CSAT), which took place on the 3rd, the math section that students in the humanities and social sciences usually take was similar to last year, and the family type that students in the science and natural sciences usually take was more difficult than last year.
In an online briefing held by the Korean Council for University Education Counseling and Counseling, Cho Man-ki, a teacher at Pangyo High School in Gyeonggi Province, said, “The level of difficulty must have been a little less burdensome for students as it was set at a level similar to last September’s mock test and last year’s CSAT.” “The blank reasoning or fractal questions that students felt the most pressure on the previous year’s CSAT were not presented this year.” In particular, he said, “Middle and lower-level students would feel difficult, but students in the upper-middle class would have felt flat compared to the September mock test or last year’s CSAT.” However, Type 20 questions, which can be solved only by knowing the relationship between differential and integral, and Type 30 questions, which have to be checked by dividing the absolute value, and the defined functions, and the differential and continuity, were selected as new types and high-level questions.
On the other hand, some experts said that the exam was more difficult than last year’s College Scholastic Ability Test and September’s mock test in September this year. Kim Jung-hwan, a teacher at Hyehwa Girls’ High School in Daegu, who is a member of the College Entrance Counseling Team, said, “As the process of solving questions for middle-level students has been somewhat prolonged, it may have been difficult for middle-level students to arrange time, and the geometric questions have been asked as calculus questions, so the top students must have felt somewhat difficult.” In particular, among the 20s, 21s, 29s and 30s, 토토사이트 which are so-called “killer questions,” which are presented to give discrimination against the top ranks, the calculation was complicated due to calculus-related problems, and the 28th question that needs to be applied was considered difficult. Teacher Kim said, “(A type of high-level questions) Not only did the number of high-level questions increase by one or two, but the solving process itself must have felt difficult because students spent more time than usual.”
Unlike in previous years, this year’s CSAT math section was the first test to be applied to the 2015 revised curriculum. As a result, geometry and vectors were excluded from the required range of questions, instead of math I, calculus probability, and statistics. In the case of Math Type B, the test was given in the probability and statistics of Mathematics I Mathematics II, and the aesthetic I, which was presented last year, was excluded. Oh Seok-seok, a teacher at Somyeong Girls’ High School in Gyeonggi Province, who was in charge of the general review of the CSAT’s math section for 2021, said, “The revised curriculum has reduced the contents by about 10 percent, but rather than making it easier, we can see that the questions that require in-depth thinking and application skills in the curriculum have been presented with discrimination due to their difficulty.” He also commented, “In both type A and type B, the ratio of EBS-linked questions is relatively low, so the difficulty of feeling can be formed high.”
Admission companies also analyzed that “Math A type has a high level of difficulty in feeling, and Type Na was easy compared to the mock test in June and September and last year’s CSAT.”
Lee Young-deok, head of the Daesung Institute for Education Development, said, “Mathematics Ga and B type were all similar to last year’s CSAT, and the overall level of difficulty felt is likely to have been similar to last year due to the increased difficulty of the remaining questions except killer questions.” Lim Sung-ho, CEO of Jongno Academy, said, “Mathematics A type has many difficult problems, so there will be a considerable difference in the level of difficulty between the upper and middle classes,” adding, “In Mathematics B type, the questions of the index and trigonometric functions newly added to the test range this year were also relatively plain.


Qualifying examination for the degree of
“Statistical Data Analyst, 3RD Grade License”
| ◆Accreditation Criteria:
Criteria to qualify for the license includes the ability to express data in easy-to-understand tables and figures, the aptitude to organize, calculate and interpret fundamental statistics, and the proficiency to collect, validate and summarize survey data. The details of the criteria are listed in detail below.
| ◆Contents of the qualifying examination:
● Data expression by tables or figures
Characterization of data as histograms, scatter diagrams and correlation
tables. Includes expression of time-series data based on figures, linear
regressions, auto-regressions, etc.
● Interpretation and calculation of a variety of basic statistics
Calculation of the mean, median, mode, variance, and standard deviation.
Includes the coefficient of variation, ratio, correlation coefficient and
rank correlation coefficient, etc.
● Validity, interpretation and summary of survey data
Survey data including market research, brand research, and customer satisfaction.
Basic summary of survey data including contingency table and data representation


Patricia "Trish" Killingsworth, M.Ed.
Assistant Director of Production
Ms. Killingsworth has 32 years experience in education including 20 years teaching mathematics in elementary and middle school. The remaining 12 years of experience were in professional development in mathematics, coordinating the elementary mathematics program for the Little Rock School District, and teaching pre-service and graduate courses in mathematics for the University of Arkansas at Little Rock (UALR). She joined BestQuest after retiring from the Little Rock School District. She has won several awards including a Superintendent's Citation, the AP&L Outstanding Teacher of the Year, and the Presidential Award for Excellence in Mathematics Teaching. Her experiences include the facilitation of hundreds of workshops and in-services in mathematics with teachers across the country for local, state and national organizations.
She is a member of the National Council of Teachers of Mathematics, the Arkansas Council of Teachers of Mathematics, the Society of Presidential Award Recipients, Delta Kappa Gamma and numerous other organizations. She earned her BS degree at West Texas State University in Canyon, TX and her Masters degree from the University of Central Arkansas in Conway, AR.
Ms. Killingsworth was the Curriculum Coordinator for Algebra'scool and now serves as the Assistant Project Director for Math'scool.


This innovative resource is designed to help early years practitioners feel more confident about teaching early Mathematics using stories and rhymes to demonstrate concepts in ways that are both fun and meaningful to children. Storytelling as a creative springboard for Maths activities, including outdoors, will also encourage those who feel they could never tell a story, applying it as an effective tool for teaching and learning.
Developing Early Maths through Story contains 14 chapters, each containing sections for different activities. The introduction will include straightforward advice on 'how to use the book' to ensure the best possible outcome, and some theoretical background; touching on schemas and open-ended activities.
Each section includes:-
A brief outline of a traditional story
Opportunities for adult-directed learning
Follow-up activities suitable for children from 3-5 (for all kinds of early years settings, including the home)
Scope for outdoor activities and for using natural materials
Where relevant, suggestions for using ICT
Further activity suggestions for younger children and babies.
This is also a perfect resource for parents and carers who want to explore or extend the learning of Maths at home with their children, in a very accessible and enjoyable way
About the author
Marion Leeper is an early years teacher and storyteller who has used story and small world play to teach Maths throughout a twenty-year teaching career. She has published a series of articles on storytelling and schemas for Early Years Educator magazine, with s strong focus on story and mathematical thinking. Marion is based in Cambridge.


Updated: Sep 2, 2022
Want to save time when ordering extrusions for your next catheter project? This article will help you calculate the diameter of your next coiled catheter.
Many neuro and peripheral catheters are made by a process of reflowing or laminating polymers and reinforcement materials over a mandrel. The reinforcement material we'll consider in this article is a coil. A coil winder is used to wind a wire over a catheter mandrel. Then a polymer jacket is sized to slide over the coil during assembly. Heat shrink tubing is then slid over the jacket. During the catheter reflow process, the jacket melts and is compressed by the heat-shrink. This causes the jacket to reduce in diameter and increase in wall thickness.
Conservation of Area
For starters, let's think of the cross section of a reflowed catheter without a coil. There's a mandrel, liner, and polymer jacket. During the catheter reflow process the jacket melts and is compressed by the heat shrink tubing. This reduces inner and outer diameter of the jacket. Since no material is lost during the catheter reflowing process, the cross-sectional area of the jacket must be the same before and after reflowing. We can use this to calculate the relationship between the pre and post reflowed jacket diameters.
Keep in mind that the final ID of the jacket would be the liner OD, or the diameter of the mandrel plus twice the liner thickness.
Enter the coil
Now let's add a coil. The conservation of
area method is invalidated because the coil is not a uniform tube. In fact, the jacket is no longer a uniform tube.
The reflowed jacket has a helical void in it because of the space the coil takes up inside of it. Instead of thinking of a conservation of area, we can use a conservation of volume to equate the pre and post lamination conditions. Again, we assume that we're not losing any material during catheter reflow. Let's cut a section of coiled catheter into a unit length and work out the volumes of each component. We'll use 1 inch for the length unit and use inches for all the diameter and volume calculations too.
Finding the volume of the jacket is straightforward. We just multiply the cross-sectional area of the jacket (first equation) by the length. Since the length is 1, it's unchanged. For the coil volume it's the same plan. We'll multiply the area of the coil wire by the length of the coil wire in a unit length of catheter. Visualize un-wrapping the coil wire along the coiled length. The result forms a right triangle.
The height of the triangle (a) is 1 unit (the same unit as the rest of your calculations). For the base of the triangle (b), think of how many times the cylinder would turn if you unwrapped the coil. The number of turns can be represented by the length of the cylinder (1 unit) divided by the pitch of the coil. We multiply the number of turns by the coil mean diameter and Pi to find this leg of the triangle.
Great, we have the length of each leg, now we just apply the Pythagorean theorem to get the wire length. Note that this number expresses how much coil wire is required per length of catheter. So, if you wanted to know how much total wire a catheter would take, you just multiply this number by the length of the catheter.
To find the volume of coil wire in a unit length, we now multiply the cross-sectional area of the wire by the length of the wire. If using a round wire you'd use the equation for the area of a circle. If you're using flat wire, you'd multiply the wire width by the thickness. Add the volume of the coil to the volume of the jacket and that gets us the total volume before and after reflowing! Let's remember the equation for the area of a pipe and assume that the area is equal to the volume since the length is 1. Solving for OD we get:
Using this method, you can calculate the OD and wall thickness of polymer jackets for reflow. It should save you a few prototype iterations when designing a new catheter. Additionally, you can fine-tune the OD of the device by varying the coil pitch. If reflowing a braided shaft, the volume of the braid can be calculated similarly based on the braid angle, number of wires, and cross section of the wire. Of course, these calculations should only be used as a starting point. Fine-tune your catheter OD with prototypes and testing. Good luck!


How many 1 inch squares can be cut from an 18"x24" piece
1 acre = 4,840 square yards 1 chain = 22 yards 1 sq chain = 22 times 22 sq yd = 484 sq yd 1 acre = 10 sq chains = 4,840 square yards Another way to figure it out First, keep in mind that an acre is a unit of area , whereas the inch, foot, yard, rod, chain, and mile are all units … of length .... 17/05/2012 · For those of you that have many fat quarters in your life and are having fun making Nickel Quilts this is how I cut up my fat quarters to make the best use of them. You are able to get twelve 5? squares from every fat quarter and a 2 1/2? strip.
How many 1 inch squares can be cut from an 18"x24" piece
When you are laying out your blocks in a random pattern, you can get a general idea of how many blocks of each fabric you’ll need to cut out by dividing your total blocks amount by …...Firstly, we should rule out the case when the 5th square doesn't touch the edge(s) of the big one. This is obviously impossible, because if the first four squares occupy all the edges, it means their areas add up to the area of the big square, so there is no place for the fifth one.
Squares in Rectangles nrich.maths.org
31/12/2012 · best way to cut 10 inch squares with out waste with out wasting fabric how many thickness would you cut and how would you fold it i know its layer cakes but i will be doing fabric by the yard and cutting it into the squares 12/29/2012 2:10:20 PM FarmChick Kansas. Good morning! I'd cut my fabric in 10" strips either across the fabric or lengthwise. Then, starting at the selvedge side, cut how to cut a standing 4x4 post Perimeter of Square = 4 ? Length. 3. Area of Rectangle and Square. Let's find the area of the rectangle below. To find the area of the rectangle, we find out how many one-centimetre squares we can fit into the rectangle. Area of the rectangle = 4 ? 2 = 8 cm 2 We need 8 one-centimetre squares to make a rectangle 4 cm long and 2 cm wide. The area of the rectangle is 8 cm 2. Area of Rectangle. How to cut richness in food
To Prove or Not to Prove nrich.maths.org
- Square (Geometry) Math is Fun - Square
- Square (unit) Wikipedia
- How to Cut Fabric Squares with a Rotary Sew Many Ways
- How many 10x10 squares can you get out of 1 yard of fabric?
Cut 2 pieces of cardboard cut to 3.5" squares Check Choose a piece of ribbon and cut to 20 inches or so Place the cardb... 11 1 INGREDIENTS: 12x12 piece of paper, Ruler, 3.5" square …
- Cut 2 pieces of cardboard cut to 3.5" squares Check Choose a piece of ribbon and cut to 20 inches or so Place the cardb... 11 1 INGREDIENTS: 12x12 piece of paper, Ruler, 3.5" square …
- One day I decided to cut 2 charms from all of my many many fat quarters and scraps so I now have a whole tub of scrappy charms to do something with. I like the idea someone did of putting a border around each charm and putting them together. I may try that.
- Remember that however many squares you cut, that is now many HSTs you will end up with. So, if you cut 2 squares and sew them up according to this method, you will end up with 2 identical HSTs. If you cut 50 squares and assemble them according to this method, you will end up with 50 HSTs.
- If you are reading this, your browser is not set to run Java applets. Try IE11 or Safari and declare the site https://www.cut-the-knot.org as trusted in the Java setup.
You can find us here:
- Australian Capital Territory: Emu Ridge ACT, Majura ACT, Charnwood ACT, Scullin ACT, Anembo ACT, ACT Australia 2694
- New South Wales: Taree NSW, Castle Doyle NSW, Moonee Beach NSW, Brewongle NSW, Ashford NSW, NSW Australia 2062
- Northern Territory: Galiwinku NT, East Arnhem NT, Katherine NT, Barrow Creek NT, Desert Springs NT, Darwin NT, NT Australia 0845
- Queensland: Darra QLD, Hughenden QLD, Hatton Vale QLD, Point Lookout QLD, QLD Australia 4031
- South Australia: Mitchellville SA, Stepney SA, Big Bend SA, Monteith SA, Solomontown SA, Pike River SA, SA Australia 5083
- Tasmania: Acton TAS, Miena TAS, Mathinna TAS, TAS Australia 7046
- Victoria: Speewah VIC, Dimboola VIC, Moora Moora VIC, Point Leo VIC, Nulla Vale VIC, VIC Australia 3008
- Western Australia: Salmon Gums WA, The Vines WA, Donnelly River WA, WA Australia 6047
- British Columbia: Zeballos BC, Burnaby BC, Enderby BC, New Denver BC, Campbell River BC, BC Canada, V8W 9W2
- Yukon: Nesketahin YT, Sulphur YT, Brewer Creek YT, Braeburn YT, Champagne YT, YT Canada, Y1A 6C3
- Alberta: Stirling AB, Strathmore AB, Hanna AB, Milo AB, Hardisty AB, Penhold AB, AB Canada, T5K 9J9
- Northwest Territories: Deline NT, Colville Lake NT, Inuvik NT, Kakisa NT, NT Canada, X1A 4L1
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- Manitoba: Grand Rapids MB, Somerset MB, Selkirk MB, MB Canada, R3B 9P4
- Quebec: Nicolet QC, Saint-Pie QC, Grenville QC, La Sarre QC, Vaudreuil-Dorion QC, QC Canada, H2Y 3W7
- New Brunswick: Doaktown NB, Grand Falls NB, Campobello Island NB, NB Canada, E3B 1H4
- Nova Scotia: Canso NS, Kentville NS, Canso NS, NS Canada, B3J 6S7
- Prince Edward Island: Darlington PE, Lorne Valley PE, Souris PE, PE Canada, C1A 6N3
- Newfoundland and Labrador: Makkovik NL, Channel-Port aux Basques NL, Pinware NL, Baie Verte NL, NL Canada, A1B 8J2
- Ontario: Camden East ON, Savant Lake ON, Tarbutt and Tarbutt Additional ON, Midhurst, Mattice ON, Farrell Corners ON, Etwell ON, ON Canada, M7A 9L9
- Nunavut: Nueltin House NU, Wager Inlet (Wager Bay) NU, NU Canada, X0A 6H8
- England: Scunthorpe ENG, Halifax ENG, Torquay ENG, Worcester ENG, Ellesmere Port ENG, ENG United Kingdom W1U 4A8
- Northern Ireland: Bangor NIR, Belfast NIR, Craigavon (incl. Lurgan, Portadown) NIR, Belfast NIR, Craigavon (incl. Lurgan, Portadown) NIR, NIR United Kingdom BT2 5H5
- Scotland: Edinburgh SCO, Edinburgh SCO, East Kilbride SCO, Cumbernauld SCO, Glasgow SCO, SCO United Kingdom EH10 6B1
- Wales: Wrexham WAL, Newport WAL, Cardiff WAL, Cardiff WAL, Barry WAL, WAL United Kingdom CF24 4D2


A main topic of my studies is Lattice Polytope.
I'm also interested in other related combinatorial objects.
Key Words :
- Ehrhart polynomial, δ-vector (h*-vector), Cayley decomposition,
(regular, unimodular) triangulation, reflexive polytope, mutation of lattice polytopes, dimer models, graph theory...
- Toric geometry
- toric (Fano) variety, Fano polytope, Newton-Okounkov body, mutation, mirror symmetry for Fano manifolds,
toric Mori theory, primitive collection, primitive relation...
- Commutative or Computational algebra
- toric ring, toric ideal, Gröbner basis, Cohen-Macaulay, Gorenstein, level, Stanley-Reisner ring,
divisorial ideals, F-signatures...
and so on...
Current interest :
- Toric degenerations and mutation of Grassmannians
- Combinatorial mutation of lattice polytopes
- Hibi rings and their algebraic properties
- Characterization of h*-vectors
- Equivariant Ehrhart theory
last updated : 18, October, 2023


This book contains a collection of original research articles and review articles that describe novel mathematical modeling techniques and the application of those techniques to models of cell motility in a variety of contexts. The aim is to highlight some of the recent mathematical work geared at understanding the coordination of intracellular processes involved in the movement of cells. This collection will benefit researchers interested in cell motility as well graduate students taking a topics course in this area.
This volume contains extended abstracts outlining selected presentations delivered by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2018 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), dedicated to the mathematical theory and applications of the multiple scale systems, the systems with hysteresis and general trends in the dynamical systems theory. The workshop was jointly organized by the Centre de Recerca Matemàtica (CRM), Barcelona, and the Collaborative Research Center 910, Berlin, and held at the Centre de Recerca Matemàtica in Bellaterra, Barcelona, from May 28th to June 1st, 2018. This was the ninth workshop continuing a series of biennial meetings started in Ireland in 2002, and the second workshop of this series held at the CRM. Earlier editions of the workshops in this series were held in Cork, Pechs, Suceava, Lutherstadt and Berlin. The collection includes brief research articles reporting new results, descriptions of preliminary work, open problems, and the outcome of work in groups initiated during the workshop. Topics include analysis of hysteresis phenomena, multiple scale systems, self-organizing nonlinear systems, singular perturbations and critical phenomena, as well as applications of the hysteresis and the theory of singularly perturbed systems to fluid dynamics, chemical kinetics, cancer modeling, population modeling, mathematical economics, and control.The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active research areas.


WARNING: CRUDE LANGUAGE
California children who failed math last year are now in summer school, attempting to pass math so they can be promoted before the fall semester begins. In an effort to make math more interesting for the students, California teachers have revised their lesson plans to make the concepts studied more relevant and applicable to the children in their everyday lives. Here are a few sample questions from the new lesson plan:
1. Lajames has an AK-47 with a 200-round clip. He usually misses 6 of every 10 shots and he uses 13 rounds per drive-by shooting. How many mofos can Lajames ice on a drive-by before he gotta reload?
2. Raul has 2 ounces of cocaine. If he sells an 8 ball to Antonio for $320 and 2 grams to Juan for $85 per gram, what be the street value of the rest of his shit?
3. Dwayne pimps 3 hos. If the price is $85 per trick, how many tricks per day must each ho turn to support Dwayne’s $800/day crack habit?
4. Leroy gets $2000 for a stolen BMW, $1500 for a Corvette, and $1000 for a 4×4. If he steals 1 BMW, 2 Corvettes, and 3 4×4’s, how many more Corvettes must he steal to make the 10K for his brother’s bail?
5. Pedro got 6 years for homicide. He also got $10,000 for the hit. If his common-law wife spends $100 of his hit money per month, how much money will be left when he gets out?
6. Tyrone knocked up 4 girls in the gang. There be 20 girls in the gang. What be the percentage of bitches Tyrone knocked up?
7. Lafawnda is a lookout for the gang. Lafawnda has a boa constrictor that eats 5 rats a week, and each rat costs $4. If Lafawnda makes $700 a week as a lookout, how long can she feed her boa constrictor on one week’s income?
8. Marvin steals Juan’s skateboard. As Marvin skates away at 15 mph, Juan loads his 357 Magnum. If it take Juan 20 seconds to load his piece, how far away will Marvin be when he get whacked?


This is the total number of eligible participants randomly selected from the sampling frame of the total population in the survey. The desired sample size is determined by the necessary statistical quality for the survey results. [Note: The total sample size will inevitably be greater than the actual number of completed interviews due to varying response rates and other sources of survey error.]
One type of inaccuracy caused by making inferences about the target population based on the sample. The sampling error is an estimate of how a sample statistic is expected to differ from the population parameter.
This is the list of eligible participants included in the target population. The sample is chosen from the sampling frame.
This is the total unweighted count of all completed interviews, also referred to in iPOLL as the population size.
A statistic which describes the sample. (e.g. If you want to do a survey of New York City Marathon runners, including their finishing times, the average finishing time of the those surveyed would be an example of a sample statistic. Not to be confused with population parameter, which would calculate the average finishing time of all the runners, not just a sample of them.)
A method of selecting elements (or units) from the target population in a way that is representative. Types of sampling include: Simple random sampling, stratified sampling, systematic sampling, and multi-stage cluster sampling.
This term refers to materials and information that has previously been documented. For example, a poll, a press release, a business report.
Simple Random Sample (SRS)
The most common sampling method where each element in the population has an equal chance of being selected.
The document from which survey information was gathered.
A statistic that shows the dispersion of scores in a distribution of scores. It is a measure of the average amount the scores in a distribution deviate from the mean. The more widely spread out the scores are, the larger the standard deviation will be.
Standard Error (of the Mean)
A statistic indicating how much the mean score of a single sample is likely to differ from the mean score of the population. It answers the question, "How good an estimate of the population mean is the sample mean?" (Not to be confused with sampling error)
A number that describes some characteristic of a variable. (e.g. the mean, the standard deviation)
A method of sampling where groups that might not otherwise be equally represented are first divided proportionately into categories ("strata"); then, a sample is randomly selected from each of these categories. (e.g. If you wanted to do a study on hospitals, you'd separate them by size-small, medium-sized, and large hospitals. From there, you would draw samples from each category so that they'd all be equally represented.
This notation pertains to the entire release, report, or study from which the question was taken.
The topic classification(s) that best describe the question. The scheme for this categorization was developed by the Roper Center and contains over 100 subject categories.
In cases where responses are not based on the entire sample, a description of the portion of the sample whose responses are being reported appears here (e.g. women, or those who favor a given policy).
The name of the survey firm or other organization which conducted the research.
A method of sampling where units are selected from the sampling frame by every "nth" unit. (e.g. You have a directory of 100,000 names and you want a sample of 1,000 names. Divide 100,000 by 1,000 to get 100. You will select every 100th name from the directory. Randomly select a number between 1 and 100, say 42, and select every 42nd name in groups of 100 (42, 142, 242, 342, 442.) to complete your sample.


The strength of Epps’ 3D Academy described in last week’s post is based on the notion that relevance, context and authenticity in learning really do matter. Epps explains:
"We see this as a great opportunity for students to use a 3D skill set to give them a better [and more relevant] understanding of math and science concepts. And what better concepts are there to visualize than the very concepts that they’re weakest in? If they can design it, they’re going to have to understand it. It’s a win-win: the student has now mastered a specific weakness in math or science and the teacher now has a tool that she can use with other students."
|Students designing and testing stereoscopic 3D content in North Carolina
Here’s how Epps strategy works: imagine a middle school math student who still struggles with fractions. Working closely with her math teacher, Epps anticipates crafting a design-build project that fortifies the student’s own math skills, while at the same time provides the teacher with a 3D visualization tool that can help instruct other struggling students. In designing this project, according to Epps, our young middle schooler “will soon acquire a better-than-average understanding of fractions that will get her past this unfortunate hurdle in math skills.” (Social studies applications are also possible. During middle school “I made pyramids, burial chambers, and a simulation of the launch and orbit of the Sputnik satellite,” Ben Dibble recalls.)
Asking your students to design stereoscopic 3D learning objects can also leverage improved student performance in critically important science skills. Creating a visual model of the human cell can contribute directly to mastery of learning by students who struggle to understand abstract concepts that they ordinarily cannot see. Asking students to create stereoscopic 3D learning objects that require precise measurement, metric conversion, and tool calibration skills will go a long way toward cementing some of the most critical prerequisite skills in understanding science. 3D design projects also provide a powerful seedbed for improving other building blocks of science achievement, such as tentative explanation, putting raw data into graphical form, and, of course, technical writing.


1) Natural Numbers
A. Playing with numbers;
I. Finding missing numbers by using addition, subtraction, multiplication
II. Finding missing numbers based on the properties of numbers,
III. Solving arithmetic problems using order of operation.
B. Divisibility of numbers;
I. Checking and showing divisibility of numbers,
II. Finding the divisor and a multiple based on properties of numbers.
I. Properties of exponents,
II. Finding ones in some exponents.
2) Fractions and decimals
A. Using properties of decimal number system to create decimals;
I. Converting fraction to decimal and decimal to fraction,
II. Conversion of units: weight, length.
3) Acting on fractions
A. Solving problems on fractions and decimals using addition, subtraction,
multiplication and division;
B. Word problem solving;
I. Analyze, solving and checking word problems with fractions and decimals,
II. Finding the fraction of a given number,
III. Solving word problems with distance, speed, time, money and weight.
A. Breakdown given polygons according to properties;
B. Angles in polygon;
I. Using the property of the sum of angles in the triangle to find external
and internal angles,
II. Areas and perimeter of polygons,
III. Solving practical problems using knowledge of areas and perimeters of
5) Algebraic expressions
A. Writing and reading algebraic expression;
I. Creation of algebraic expression to different pictures for instance to
perimeter of figure,
II. Transformation of algebraic expression.
B. Creating equation and inequities to word problems;
C. Solving equations with one or more variables.
A. Prism model and it properties;
B. Surface area and volume of prism in word problems.
7) Rational number
A. Repeating decimal;
I. Converting from repeating decimal to fraction,
II. Solving word problem with repeating decimal.
B. Power and ratios of rational numbers;
C. Mathematical operation;
D. Analyzing and solving word problems with rational numbers.
A. Percentages in economic and finance;
B. Percentages in real life;
I. Sales, diagrams,
II. Creating percentages diagram using MS Excel.
9) Flat figures
A. Area and perimeter of flat figures;
B. Breakdown different kind of shapes to the common figures;
C. Geometric construction - symmetry, bisector;
D. Inscribed angle and described angle to find the angles in the circle.
10) Pythagorean Theorem
A. Using Pythagorean theorem in geometric and practical word problems.


Bogged Down in Details
I found some very pretty flowers in Aristotle's garden of ethics. I sat down over some intense hours breaking down the sentences in Book VI (and other places) into a more mathematical structure . . . and was amazed at some of the really beautiful ideas Aristotle had. I have come to a small enlightenment on Aristotle . . . I can now feel him as a human being, as a person. I can now see the fragile child within Aristotle, and I realize he's just like me -- vulgar with a spot of divinity. I can accept him now. Unfortunately I don't have any time to elucidate, nor time to think theoretically about life when all these practical people keep hammering away at me about their tick-tock hallucinationism universe . . . so here's something to think about :
These computations are based on the algorithm from "Computing Special Values of the Myriad Motivations of Ordinary Life". The package applies to Ordinary Life given by the usual series (for Re s>>0),
Assume that Ordinary Life multiplied by a suitable product of Gamma-Detail-factors,
admits a meromorphic continuation to the whole of C. It has, moreover, at most simple poles and is known or conjectured to satisfy a functional equation
or, slightly more generally, a functional equation relating Ordinary Life and a "dual" Ordinary Life-function also known as Mating (i.e. marriage, shacking-up, etc).
To use the formula one has to know the parameters of the functional equation (exponential factor A, sign e, weight w, Gamma-Details-factor parameters l1...ld) and enough coefficients of Gremlin-Goofs an. Note that there is no restriction on the number d of Gamma-Details-factors and they do not have to be distinct. The poles of Ordinary Life have to be known as well, but not necessarily the residues in there. The functions provided allow to perform the following numerical computations with required precision:
- Determine the residues at the poles of Ordinary Life if necessary
- Verify the assumed functional equation numerically
- For a given complex s, compute Ordinary Life results or its k-th derivative for a given k
We are smothered by detail.
Our bodies fill up with knots of anxiety.
Our throats are dry.
We would weep, but our eyes have no tears.
We could cry out, but we have no passion.
Who has done this to us?
We confess the pain we cause ourselves.
We confess the pain we cause others.
May we accept our limitations:
We cannot do everything.
May we affirm our power:
We can do something.
May we open ourselves to larger hope,
In the silence, in the silence.
* The first is a parody of the formula from the Harvard Math Department explained at:
and the second is from the website of Unitarian Universalist Association of Congregations :
The insane SLoodle thing from http://www.sloodle.com/


Softball : CCSS.ELA-Literacy.L.6.4.c Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. Ask students to work in pairs to determine the mean of the data set represented by the Brothers and Sisters dot plot.
Quartile 3. Example.
The dot plots below show the top ten test scores for each of Mrs. Sanderss Period A and Period B math classes. The graph above does not show you the probability of events but their probability density.To get the probability of an event within a given range we will need to integrate. Edit. In each plot I have highlighted the largest of the seven values. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about Compute the sample standard deviation of Data Set I.Form a new data set, Data Set II, by adding 3 to each number in Data Set I. Calculate the sample standard deviation of Data Set II.Form a new data set, Data Set III, by subtracting 6 from each number in Data Set I. Comparing the answers to parts (a), (b), and (c), can you guess the pattern? For example, if a data point is 42, the stem is 4 and the leaf is 2.
So both types of cereal vary over a range of 14 grams. Quartile 1. Find the measures of center - mean, median, and mode - for the Period A data. The answer is to group the data (put it into "bins"). Often, outliers are easy to identify on an individual value plot. The mean of the data in the dot plot is 4. Sampling variability the concept that a data sets values will . b. Histograms is a special type of bar graph. I'd like to create what my statistics book calls a "dot plot" where the number of dots in the plot equals the number of observations.
To find the average you would add up their times (23.4+24.5+27.8 which equals 75.7) and
Draw a dot plot of the distribution of number of green jellybeans for each of the five candy makers. Looking at the dot plots and without calculating the standard deviations, match the data sets to the standard deviations. In this case, each dot corresponds to one data point. consistent with the dot plot shown at the beginning of this section. Explain your reasoning for choosing the order. Syntax: In the dot plot below, the center is near 50. The number of pieces of candy one gets is random. Looking at the dot plot, there are 8 values marked with anXand the mean of the 8 values is shown with the arrow. Draw a dot plot for the table. The number of pieces of candy one gets is random. Example 2.3.
57 times. The median appears clearly on the box plot at the line within the box: 10. Plots can be customized by using themes. The dot plot shows the number of letters in the spellings of the 12 months. Download it once and read it on your Kindle device, PC, phones or tablets. A dot plot represents a data set by creating a column of dots over a category. First, look at the boxes and median lines to see if they overlap. We have detailed all the useful points that help The maximum is the largest value in the dataset and the minimum is the smallest value. To create a dot plot for the data in Example 1 of Box Plots (repeated in range A3:C13 of Figure 1), press Ctrl-m and select the Descriptive Statistics and Normality data analysis tool. 3)The median appears clearly on the dot plot at Median. Each dot represents a value of numeric variable and they are placed in columns. Hi Everyone, Can some one help me to replicate the below chart , I have just two columns, 1. Interpreting Dot Plots and Assessing The Distribution of Your Data Calculate the median and quartiles of a data set. To introduce the idea of variability, consider this example. In this case let's try rounding every value to the nearest 10%: Country Access to Electricity (% of population, nearest 10%) Algeria : 100: Explain your reasoning. In VitaraCharts the play axis can be used to show variability across any other dimension as well by dragging and dropping the appropriate attribute to the Play Axis drop zone. Describe the shape of a dot plot. 70% average accuracy. Setting up the Dot Plot Variance chart A measure of center that represents the value or values that appear the most often in a data set. If you count from left to right (since the values have to be in order to find the median), the 8th and 9th values are both 31. Elements in the product matrix of two matrices are the dot products of the corresponding row vectors and column vectors. For Data Set II the maximum is 47 and the minimum is 33, so the range is R = 47 33 = 14. For the preceding undergraduate expense data, if we just wanted to compare the dollar values and were not concerned with the categories, a dot plot would look like that shown in Figure 1. Next, right-click on the graph, and choose Select Data.
distributions with dot plots and histograms and described the overall shape of a data distribution. Example: if our 5 dogs are just a sample of a bigger population of dogs, we divide by 4 instead of 5 like this: Sample Variance = 108,520 / 4 = 27,130.
1)Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13.
Spread: We can use the range to measure the spread of values in the dataset. Definition The range of a data set is the number R defined by the formula R = x max x min where x max is the largest measurement in the data set and x min is the smallest. The data is available here. As a group, the softball players are shorter than the basketball players. Find the mean absolute deviation of the Period A data.
(Note: Overall range = highest value lowest value. We need to look for a value that will tell us more about the spread or variability of a data set. What do you notice about the mean and standard deviation you and your partner found for the three dot plots? Suppose we are interested in finding the probability of a random data point landing within the interquartile range .6745 standard deviation of the mean, we need to integrate from -.6745 to .6745. To introduce the idea of variability, consider this example.
mvaugha. A Box and Whisker Plot (or Box Plot) is a convenient way of visually displaying the data distribution through their quartiles. 4.4 Measures of Variability: Range, Variance, and Standard Deviation. While mean and median tell you about the center of your observations, it says nothing about the 'spread' of the numbers. Example: Suppose two machines produce nails which are on average 10 inches long. A sample of 11 nails is selected from each machine. without variability. There might be only one "59.6" and one "37.8", etc. The median of the data set is 9 for the data: 4, 5, 9, 1, 10. Use the dot plot to answer the questions given below. The post Find tiny Pokmon with the new Size Variance Feature revealed in Pokmon Legends: Arceus leaks appeared first on Pro Game Guides. Like us on Facebook to see similar stories Please give an overall site rating:
Get Free Access See Review. The mean or average, in this case, will be a misinterpretation of the actual data. Check the value corresponding to that dot.
The mean turns out to be 4.22. There are three main ways that we measure central tendency: mean, median, and mode.
For example, if the data are all the same, they are all placed into a single bar, and there is no variability. A shortcut method of calculating variance and standard deviation requires two quantities: sum of the values and sum of the squares of the values.
Here's an example from mathisfun.com:. Order the candy manufacturers from the one you think has least variability to the one with most variability. The horizontal axis represents a range of values, called an interval, instead of a single value or category. Objectives Content Objectives Understand median as a measure of center. sleep (hrs / night) frequency 0 2 4 6 8 10 12 0 20 40 60 80 without variability.
I'd like to plot a single point on my graph, but it seems like they all need to plot as either a list or equation. This is when mean absolute deviation comes into the picture.
If a number is added to the set that is in the middle of the data, how does this affect the range? They have the same center, but what about their spreads? Now, return to the phrase absolute deviation and circle the first X on the dot plot, probably representing 0. Dot Plots, Measures of Center and Variation Plot each of the data sets below on a separate graph.
When we want to represent variability, we use a box plot instead of a dot plot, because the box plot allow us to observe the range of the data set, that is, the minium and the maximum value. Measures of Variability. (3 points) 2. Range = L S = 11- 8 = 3 Example 2 What are the most appropriate measures to describe the center and the variation? (Supporting) including: dot plots, stem-and-leaf plots, histograms, and box plots 7.
Free! So, the median is 31 + 31 2 = 31 mpg. (Note: Overall range = highest value lowest value.
The mean is the average of all the data. To calculate the variance in a dataset, we first need to find the difference between each individual value and the mean. For a data set with 16 values, this would be the average of the 8th and 9th value. See also Creating Dot Plots in Excel for how to create a dot plot manually using Excels charting capabilities. It is evident that five of the seven weekdays can be considered, in some specific sense, to have the largest variation. Example 1 Find the range of each data set in Table 2.1.
To calculate an "average" square deviation, it is best for the sum of squared deviations to be divided by \(n1\) instead of by \(n\) (\(n\) is the sample size). 6th - 8th grade. The unit of the standard deviation is always the same as the unit of the original data set.
1. R is an open-source programming language mostly used for statistical computing and data analysis and is available across widely used platforms like Windows, Linux, and MacOS. 2)Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 7. Find the measures of variability - range, median, upper quartile, lower quartile, and interquartile range - of the Period A data. You can then click the plus button to add a series.
So both types of cereal vary over a range of 14 grams. To find it, count the number of dots in the dot plot (for example, 30). The range is easy to calculate but it is very much affected by extreme values. This is the average value of the dataset. For childrens cereals: 15 1 = 14) Typical range: Typical adult cereals have between 0 and 6 grams of sugar in a serving, compared to 9 to 13 grams in typical childrens cereals. Data should be of limited tangle or else the width of the dot plot becomes cumbersome. it as a multiple of a measure of variability. Each dot plot variation represents a slightly different method of charting and analyzing data using this visualization. Find the range of each data set in Table 2.3. Explain your reasoning. R is an interpreted language that supports both procedural programming and There are many ways to describe variability or spread including: Range; Interquartile range (IQR) Variance and Standard Deviation Which statements best describe the dot plot or box plot? In the dot plot below, the two distributions both center on 50. The mean can be found by adding all the numbers in a data set and dividing by the number of numbers in the data set. Two vending machines A and B drop candies when a quarter is inserted. 6 Task #3 - Answering Questions from Data group of students was asked, How many children are in your family?.
Describe the center of the dot plot. Broader distributions signify greater variability. The minimum essay score that a student received is 2 points.
Which statements best describe the dot plot or box plot?
The stem values divide the data points into groups. Interpret the median and IQR in a Write the calculated mean on the board. We will write x min and x max for the smallest and largest values, so Range = x max x min . The range represents the difference between the largest and smallest value. Dot plots are created based on a set of given data and analyzed. In the example, there are six dots above the 0 value on the X-axis representing the six observations of the value zero.. Below are dot plots for three different data sets. 1) In this dataset, we can see that the largest value is 5 and the smallest value is 1 so the range can be calculated as 5 1 = 4. The variability would be greater for the data set displayed in Histogram 2. instructional video. How do we make a dot plot of that? Variation range: The extent or width of variation present in a characteristic is immediately recognized in a dot plot or histogram.
Invent some data that fits the conditions. The median appears clearly on the dot plot at the center of the number line: 9.5. It seems that a "dot plot" can have several variations. We construct a box and whisker plot by first identify our five-number summary. Solution: The standard deviations for these three data sets are given in the following table. And there are four measures that a statistician needs to consider. There is no standard notation for range. 2. The dot plot shows the average number of hours students in a class sleep each night. The lines extending parallel from the boxes are known as the whiskers, which are used to indicate variability outside the upper and lower quartiles. Visually compare the shapes of the dot plots. (Supporting) including: dot plots, stem-and-leaf plots, histograms, and box plots 7. The dot plots below show the top ten test scores for each of Mrs. Sanders's Period A and Period B math classes. Use the dot plot shown to find the summary statistics for the data set.
Describe the shape of the dot plot. Search: Dot Plot Worksheets.
Construct box plots and use the IQR to measure variability of a data set. Creating the Dot Plot Variance chart. Finally, look for outliers if there are any. The dot plot is the only display that can be used to show the variability of the data. This product is modeled to practice:7.12 (A) compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreadsFocusing only are the dot plot aspect of CCSS.Math.Content.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Choose the DAIRY GIRL values for the x-values and SPACING for the y-values. All other calculations stay the same, including how we calculated the mean.
The easiest measure of variability to calculate is the range of the data. The steps to find mean, median, mode, range, and interquartile range - Mean: the sum of all numbers divided by the quantity of data points - Median: the middle number of a data set in numerical order - Mode: the number that occurs By understanding how the different types of dot plots operate, you can better decide which one to use for your efforts. Problem Statement: A study of "To what extent does it take you to have breakfast?" You may realize that the element in the product matrix C is the dot product of the corresponding row vector and column vector in matrices A and B, respectively.. Matrix inverse: only square matrices can be inverted, the product of a matrix A 2)Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 7. Variability DRAFT. And these are Range, IQR, SD, and Variance.
Students should have the following skills: Ability to calculate means Ability to read and interpret dot plots Teachers should draw two number lines side by side on the board, with values going from 60 to 90 and counting by twos. Variability in statistics is the degree to which data in a set varies, or how much difference there is in a single set of data. No categorical data can be used. Outliers, which are data values that are far away from other data values, can strongly affect your results. 2 years ago. Mark the location of the mean on each distribution with the balancing symbol. Chapter 7 Dot plots and the mean Dot plots Useful for visualizing one numerical variable. Q. We can express the variance with the following math expression: 2 = 1 n n1 i=0 (xi )2 2 = 1 n i = 0 n 1 ( x i ) 2. 1.5.3 - Measures of Variability. Use technology to find the mean and the standard deviation for the data in the dot plots. The test scores data set has an odd number of items which
All the dots are about the same height. Solution: So as per the above data represented in the dot plot, shows the data of the number of students who received scores for essays on a 6-point scale. One can read a dot plot only by counting how many dots fall into one category. 3.
The class an adult swimming class. 2 years ago. Refer to that if you need to know how to create the data prior to this tutorial.
Check all that apply. The stem value contains all the digits of a data point except the final number, which is the leaf. 2. The difference between the greatest observed value xMAX and the smallest observed value xMIN creates the range of the distribution. Unit 4: Dot Plots and Histogram Vocabulary VOCABULARY Dot Plot- Includes all values from the range of the data and plots a point for each occurrence of an observed value on a number line. Range example You have 8 data points from Sample A. Calculating Mean Absolute Deviation. Check all that apply.
1. One of them finishes in 23.4 seconds, another finishes in 24.5 seconds and the last one finishes in 27.8 seconds. The number of data points should also be limited to n is less than or equal to 100 data points or the plotting becomes tiresome. Divide by n - 1 (if you are working with a data from a sample, which is the most common case); 6. The Wilkinson Dot Plot: This type of chart is a more classic dot plot example. Maximum.
1: Identifyig the Range of a dataset. The larger the standard deviation, the To sum up: Thats a quick and easy way to compare two box-and-whisker plots. On an individual value plot, unusually low or high data values indicate potential outliers. Two vending machines A and B drop candies when a quarter is inserted. (Only Tues and Fri don't show up.) In other words, height explains about half the variability of weight in preteen girls.
Example 1: The table below describes the average number and types of pizzas ordered from a pizza store in a week. Subtract the maximum and minimum values of the box plot to find the number of players on the team: 12 - 7. Develop an idea of the datas variability by looking at the distance between the minimum and maximum bins. The highest value ( H) is 324 and the lowest ( L) is 72. You can modify the theme of a single plot using the theme() method or you can modify the active theme, which will affect all subsequent plots, by calling theme_update(). How to Calculate Variance. Find the mean of the data set. Add all data values and divide by the sample size n . x = i = 1 n x i n. Find the squared difference from the mean for each data value. Subtract the mean from each data value and square the result. ( x i x ) 2. Find the sum of all the squared differences. Refer to the . For childrens cereals: 15 1 = 14) Typical range: Typical adult cereals have between 0 and 6 grams of sugar in a serving, compared to 9 to 13 grams in typical childrens cereals. vary in repeated random sampling. Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13. Save.
Which dot plot shows more variability? has these outcomes: Most values are close to 50, and values further away are rarer.
#first importing data Q1<-read.table("~/Q1.txt", header=T) # Optionally, read in data directly from figshare. The center of the graph is between 6 and 7 letters.
If youre learning about statistics and like the approach I use in my blog, check out my Introduction to Statistics eBook! The steps to find mean, median, mode, range, and interquartile range - Mean: the sum of all numbers divided by the quantity of data points - Median: the middle number of a data set in numerical order - Mode: the number that occurs 3)The median appears clearly on the dot plot at Statistical variability and distributions. Central tendency is defined as the typical value of a set of data. Mathematics. Be prepared to share your data set and reasoning for choice of values. Variability DRAFT. Its the easiest measure of variability to calculate. A dot chart or dot plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles. R = H L R = 324 72 = 252 The range of your data is 252 minutes. Solution:
1)Add the number of dots above each age in the dot plot to find the number of players on the team: 2 + 1 + 3 + 2 + 3 + 2 = 13. Nearly all values will have just one dot. 2. For example, If there are 3 people in a race. The dots have a relatively even spread, with a peak at 8 letters. Based on the dot plot, do you agree with each of the following statements? Hopefully, you can start to see the dot plot taking shape. The box is drawn around the quartile values, and the whiskers extend from each Measures of variation Box and whisker plot.notebook 1 February 06, 2015 May 205:22 PM BoxandWhisker Plots A boxandwhisker plot uses a number line to show the distribution of a set of data. Planting is the most important and labour intensive operation in sugarcane cultivation. Preview this quiz on Quizizz. Number crunching statisticians explore displaying data with dot plots and define the difference between quantitative data and qualitative data. Furthermore, each column represents (relative) frequency of observations in a certain category. Currency Code, 2. Try to The following data are recorded for six trials at each vending machine: Vending Machine A. In fact, it is possible to derive the data set from a discrete dot plot. You can get a sense of variability in a statistical data set by looking at its histogram. That is, find the range, median, mode, and mean. (Self-Publishing Basics 1) - Kindle edition by Murphy, Derek. I am trying to plot a dot-whisker plot of the confidence intervals for 4 different regression models.