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For the following set of data, find the sample standard deviation, to the nearest thousandth.
70,39,114,39,52,108,101

For the following set of data, find the sample standard deviation, to the nearest thousandth. $\newline$ $70,39,114,39,52,108,101$

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Identify discrete and continuous random variables

Full solution

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

\newline

70,39,114,39,52,108,101

List data set: List the given data set. $\newline$ The data set provided is: $70, 39, 114, 39, 52, 108, 101$ .
Calculate mean: Calculate the mean (average) of the data set. $\newline$ To find the mean, sum all the data points and divide by the number of data points. $\newline$ Mean = $(70 + 39 + 114 + 39 + 52 + 108 + 101) / 7$ $\newline$ Mean = $523 / 7$ $\newline$ Mean $\approx 74.714$
Calculate deviations: Calculate the deviations from the mean for each data point. This involves subtracting the mean from each data point. Deviations: $(70 - 74.714)$ , $(39 - 74.714)$ , $(114 - 74.714)$ , $(39 - 74.714)$ , $(52 - 74.714)$ , $(108 - 74.714)$ , $(101 - 74.714)$
Square deviations: Square each deviation to get the squared deviations. $\newline$ Squared deviations: $(70 - 74.714)^2$ , $(39 - 74.714)^2$ , $(114 - 74.714)^2$ , $(39 - 74.714)^2$ , $(52 - 74.714)^2$ , $(108 - 74.714)^2$ , $(101 - 74.714)^2$
Sum squared deviations: Sum the squared deviations. $\newline$ Sum of squared deviations = $(70 - 74.714)^2 + (39 - 74.714)^2 + (114 - 74.714)^2 + (39 - 74.714)^2 + (52 - 74.714)^2 + (108 - 74.714)^2 + (101 - 74.714)^2$ $\newline$ Sum of squared deviations $\approx 22.449 + 1277.571 + 1538.449 + 1277.571 + 517.571 + 1111.449 + 689.571$ $\newline$ Sum of squared deviations $\approx 5434.631$
Calculate variance: Divide the sum of squared deviations by the sample size minus one to get the variance. $\newline$ Since we have $7$ data points, we divide by $6$ ( $n-1$ ). $\newline$ Variance = $5434.631 / 6$ $\newline$ Variance $\approx 905.772$
Find standard deviation: Take the square root of the variance to find the sample standard deviation. $\newline$ Sample standard deviation = $\sqrt{905.772}$ $\newline$ Sample standard deviation $\approx 30.096$

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