Measures of Spread

  • The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the "variation" in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation. Key words: Variability, standard deviation

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  • In this activity, students will perform an ANOVA to determine if the longevity of male fruitflies is related to their reproductive cycle. The dataset contains longevity (in days) of male fruitflies in 5 groups: Alone, 1 Interested Female, 8 Interested Females, 1 Uninterested Female, 8 Uninterested Females. Questions about the exercise and links to Excel and TI-83 instructions are given. The data exist in Excel, TI-83, and text formats.
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  • In this activity, students will calculate the correlation between GPA and SAT scores on 1000 students. The dataset contains high school GPA, college GPA, and SAT score for each student. Questions about the exercise and a link to Excel instructions are given. The data exist in Excel and text formats.
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  • In this activity, students will perform a two-way ANOVA to determine if there is a difference in the amount of pressure (in Mpa) it takes to break two different types of laminated composites under wet or dry conditions. Questions about the exercise and links to Excel and TI-83 instructions are given. The data exist in Excel, TI-83, and text formats.
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  • In this activity, students will calculate the correlation between the ratio of doctors to people and the average lifespan for 40 countries. The dataset contains the name of the country, the number of citizens per doctor, and the average female lifespan (in years). Questions about the exercise and a link to Excel instructions are given. The data exist in Excel data format and text format.
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  • This tutorial explains in detail how to calculate correlation with a TI-83 graphing calculator.
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  • This site contains lessons which include steps, examples, and a calculator, on standard deviation, Pearson's r, t-test, one-way ANOVA, and Tukey's Post Hoc Test.
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  • This pdf file gives definitions for average, standard deviation, and relative standard deviation, and works through a short problem as an example.
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  • This page introduces various measures of central tendency and spread with an example on leaf size. Two descriptive statistics calculators are provided which compute mean, median, minimum, maximum, 1st & 3rd quartiles, standard deviation, and the 95% confidence interval for the mean and tests for normality. Users type in individual data points or copy and paste the entire data set. Key Words: Five Number Summary; Mode; Interquartile Range; Variance; Range; Normal Distribution.
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  • This online, interactive lesson on set estimation provides examples, exercises, and applets concerning estimation of the normal model, estimation in the Bernoulli Model, estimation in the two-sample normal model, and Bayesian set estimation.

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