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2.4 Measures of Variation

Learn about measures of variation, including range, deviation, variance, and standard deviation, and how they help analyze data. Understand the empirical rule and Chebychev's theorem for estimating data percentages. Calculate sample standard deviation for grouped data.

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2.4 Measures of Variation

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  1. 2.4 Measures of Variation

  2. Range - The difference between the maximum and the minimum data entries in the set Range = (Max – Min) Deviation – the difference between the entry and the mean of the data set. Deviation of Range and Deviation

  3. Variance and Standard Deviation • Population Variance: • Population Standard Deviation: • Sample Variance: • Sample Standard Deviation:

  4. -.3 1.7 .7 -.3 -1.3 2.7 -1.3 -2.3 -.3 .7 .09 2.89 .49 .09 1.69 7.29 1.69 5.29 .09 .49 SSx= 2.01 1.418 2.233 1.494 Mean = 70.3

  5. Empirical Rule

  6. About 68% of the data lies within 1 standard deviation of the mean

  7. About 95% of the data lies within 2 standard deviation of the mean

  8. About 99.7 of the data lies within 3 standard deviation of the mean

  9. Examples Heights of Women in the U.S. have a mean of 64 with a standard deviation of 2.75. Use the empirical rule to estimate: • The percent of the heights that are between 61.25 and 64 inches. ANS: 34% • Between what two values does about 95% of the data lie? ANS: (58.5, 69.5)

  10. Chebychev’s Theorem • The portion of any data set lying within k standard deviations (k>1) of the mean is at least Example: k = 2 , 75% of the data is within 2 standard deviations of the mean k = 3; 88.9% of the data lies within 3 standard deviations of the mean.

  11. Sample Standard deviation for grouped data

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