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For the following set of data, find the population standard deviation, to the nearest thousandth. \(\newline103,107,124,121,123,67,77,107,124\newline\) Copy Values for Calculator Open Statistics Calculator Answer Attempt \(\newline1\newline\) out of \(\newline20\newline\) Submit Answer Copyright \(\newline52024\newline\) DeitaMath.com All Rights Reserved. Privacy Policy | Terms of Service

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Interpret measures of center and variabilityright chevron icon

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Q. For the following set of data, find the population standard deviation, to the nearest thousandth. \(\newline103,107,124,121,123,67,77,107,124\newline\) Copy Values for Calculator Open Statistics Calculator Answer Attempt \(\newline1\newline\) out of \(\newline20\newline\) Submit Answer Copyright \(\newline52024\newline\) DeitaMath.com All Rights Reserved. Privacy Policy | Terms of Service
  1. Arrange Data in Ascending Order: Arrange the data set in ascending order.\newlineThe data set in ascending order is: 6767, 7777, 103103, 107107, 107107, 121121, 123123, 124124, 124124.
  2. Calculate Mean: Calculate the mean (average) of the data set.\newlineMean = (67+77+103+107+107+121+123+124+124)/9(67 + 77 + 103 + 107 + 107 + 121 + 123 + 124 + 124) / 9\newlineMean = 953/9953 / 9\newlineMean ≈105.889\approx 105.889
  3. Calculate Variance: Calculate the variance of the data set.\newlineVariance = Σ((each value−mean)2)/number of values\Sigma((\text{each value} - \text{mean})^2) / \text{number of values}\newlineVariance = ((67−105.889)2+(77−105.889)2+(103−105.889)2+(107−105.889)2+(107−105.889)2+(121−105.889)2+(123−105.889)2+(124−105.889)2+(124−105.889)2)/9((67 - 105.889)^2 + (77 - 105.889)^2 + (103 - 105.889)^2 + (107 - 105.889)^2 + (107 - 105.889)^2 + (121 - 105.889)^2 + (123 - 105.889)^2 + (124 - 105.889)^2 + (124 - 105.889)^2) / 9\newlineVariance = ((−38.889)2+(−28.889)2+(−2.889)2+(1.111)2+(1.111)2+(15.111)2+(17.111)2+(18.111)2+(18.111)2)/9((-38.889)^2 + (-28.889)^2 + (-2.889)^2 + (1.111)^2 + (1.111)^2 + (15.111)^2 + (17.111)^2 + (18.111)^2 + (18.111)^2) / 9\newlineVariance = (1512.568+834.568+8.345+1.234+1.234+228.345+292.679+328.012+328.012)/9(1512.568 + 834.568 + 8.345 + 1.234 + 1.234 + 228.345 + 292.679 + 328.012 + 328.012) / 9\newlineVariance = 4535.997/94535.997 / 9\newlineVariance ≈503.999\approx 503.999
  4. Calculate Standard Deviation: Calculate the population standard deviation.\newlineStandard deviation = Variance\sqrt{\text{Variance}}\newlineStandard deviation ≈503.999\approx \sqrt{503.999}\newlineStandard deviation ≈22.453\approx 22.453

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