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For the following set of data, find the sample standard deviation, to the nearest thousandth. $\newline$ $59,68,40,56,36,70,20$ $\newline$

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Find values of normal variables

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Q. For the following set of data, find the sample standard deviation, to the nearest thousandth.

\newline

59,68,40,56,36,70,20

\newline

Calculate Mean: List the data set and calculate the mean (average). $\newline$ The data set is: $59, 68, 40, 56, 36, 70, 20$ . $\newline$ To find the mean, add all the numbers together and divide by the number of data points. $\newline$ Mean = $(59 + 68 + 40 + 56 + 36 + 70 + 20) / 7$ $\newline$ Mean = $349 / 7$ $\newline$ Mean = $49.857$
Calculate Squared Deviations: Subtract the mean from each data point and square the result. $\newline$ This will give us the squared deviations from the mean. $\newline$ Squared deviations: $\newline$ $(59 - 49.857)^2 = 83.724$ $\newline$ $(68 - 49.857)^2 = 329.724$ $\newline$ $(40 - 49.857)^2 = 97.724$ $\newline$ $(56 - 49.857)^2 = 37.724$ $\newline$ $(36 - 49.857)^2 = 193.724$ $\newline$ $(70 - 49.857)^2 = 406.724$ $\newline$ $(20 - 49.857)^2 = 889.724$
Add Squared Deviations: Add all the squared deviations together. $\newline$ Sum of squared deviations = $83.724 + 329.724 + 97.724 + 37.724 + 193.724 + 406.724 + 889.724$ $\newline$ Sum of squared deviations = $2039.068$
Calculate Variance: Divide the sum of squared deviations by the number of data points minus one to find the variance. $\newline$ Since we have $7$ data points, we subtract $1$ to get $6$ ( $n - 1 = 7 - 1 = 6$ ). $\newline$ Variance = $2039.068 / 6$ $\newline$ Variance = $339.845$
Calculate Standard Deviation: Take the square root of the variance to find the sample standard deviation. $\newline$ Sample standard deviation = $\sqrt{339.845}$ $\newline$ Sample standard deviation $\approx 18.435$ to the nearest thousandth.

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