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Chapter 4 Measures of Variability

Chapter 4 Measures of Variability. Measures of Variability and Dispersion. Two tests were given with the following results: Test 1: 0 80 85 90 95 100 Test 2: 75 75 75 75 75 75. The Range. Simplest and quickest measure of distribution dispersion

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Chapter 4 Measures of Variability

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  1. Chapter 4Measures of Variability

  2. Measures of Variability and Dispersion Two tests were given with the following results: • Test 1: 0 80 85 90 95 100 • Test 2: 75 75 75 75 75 75

  3. The Range • Simplest and quickest measure of distribution dispersion • Range = Difference between highest and lowest scores in a distribution • In equation form: • Provides a crude measure of variation • Outliers severely affect the range R = range H = highest score in a distribution L = lowest score in a distribution 1, 2, 2, 4, 5, 5, 8, 9, 9, 10, 10, 10

  4. The Inter-Quartile Range • Inter-quartile range manages effects of extreme outliers • In equation form: • The larger the size of IQR, the greater the variability IQR = inter-quartile range Q1 = score at the 1st quartile, 25% below, 75% above Q3 = score at the 3rd quartile, 75% below, 25% above

  5. = mean squared = total number of scores The Raw-Score Formula for Variance and Standard Deviation • In equation form: • Variance • Standard deviation = sum of the squared raw scores

  6. Illustration: Using Raw Scores Step 1: Square each raw score and sum both columns Step 2: Obtain the mean and square it Step 3: Insert results from Step 1 and 2 into the formulas N = 6 ΣX2 = 202 = 25

  7. On your own: Measures of Variability • On a 20 item measure of self-esteem (higher scores reflect greater self-esteem), five teenagers scored as follows: 16, 5, 18, 9, 11, 13, 17, 10, 11, 14. Calculate the.. • Range • IQR • Variance • Standard deviation

  8. The Meaning of the Standard Deviation • Standard deviation converts the variance to units we can understand. But, how do we interpret it?

  9. Measuring the Base Line in Units of Standard Deviation when the SD is 5 and is 80

  10. End Day 1

  11. Variance and Standard Deviation of a Frequency Distribution • The table on the right is a simple frequency distribution of the number of courses taken by each full time student in a particular class.

  12. Variance and Standard Deviation of a Grouped Distribution • The table on the right is a grouped frequency distribution of 25 individuals and their ages when first married.

  13. Selecting the Most Appropriate Measure of Dispersion • It is harder to determine the most appropriate measure of dispersion than it is to determine the most appropriate measure of central tendency Not as “tied” to level of measurement • Range can always be used • Regardless of data level or distribution form • Limited in information • Variance and standard deviation are good for interval and some ordinal data

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