For the following set of data, find the population standard deviation, to the nearest thousandth. $103,107,124,121,123,67,77,107,124$

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

103,107,124,121,123,67,77,107,124

List data set: List the data set and verify the number of data points. $\newline$ The data set given is: $103, 107, 124, 121, 123, 67, 77, 107, 124$ . $\newline$ Count the number of data points to ensure none are missing. $\newline$ There are $9$ data points in total.
Calculate mean: Calculate the mean (average) of the data set. $\newline$ The mean is calculated by adding all the data points together and then dividing by the number of data points. $\newline$ Mean = $(103 + 107 + 124 + 121 + 123 + 67 + 77 + 107 + 124) / 9$ $\newline$ Mean = $953 / 9$ $\newline$ Mean = $105.888\dots$
Subtract and square: Subtract the mean from each data point and square the result. $\newline$ This step is part of calculating the variance, which is the average of the squared differences from the Mean. $\newline$ $(103 - 105.888)^2 = 8.347^2 = 69.672$ $\newline$ $(107 - 105.888)^2 = 1.112^2 = 1.237$ $\newline$ $(124 - 105.888)^2 = 18.112^2 = 328.045$ $\newline$ $(121 - 105.888)^2 = 15.112^2 = 228.472$ $\newline$ $(123 - 105.888)^2 = 17.112^2 = 292.922$ $\newline$ $(67 - 105.888)^2 = -38.888^2 = 1511.111$ $\newline$ $(77 - 105.888)^2 = -28.888^2 = 834.672$ $\newline$ $(107 - 105.888)^2 = 1.112^2 = 1.237$ $\newline$ $(124 - 105.888)^2 = 18.112^2 = 328.045$
Sum squared differences: Sum the squared differences. $\newline$ Add all the squared differences together to get the total sum. $\newline$ Total sum = $69.672 + 1.237 + 328.045 + 228.472 + 292.922 + 1511.111 + 834.672 + 1.237 + 328.045$ $\newline$ Total sum = $3595.413$
Calculate variance: Calculate the variance. $\newline$ Since we are dealing with a population standard deviation, we divide the total sum of squared differences by the number of data points $N$ . $\newline$ $\text{Variance} = \frac{\text{Total sum}}{N}$ $\newline$ $\text{Variance} = \frac{3595.413}{9}$ $\newline$ $\text{Variance} = 399.490$
Calculate standard deviation: Calculate the population standard deviation. $\newline$ The standard deviation is the square root of the variance. $\newline$ Standard deviation = $\sqrt{\text{Variance}}$ $\newline$ Standard deviation = $\sqrt{399.490}$ $\newline$ Standard deviation $\approx 19.987$
Round standard deviation: Round the standard deviation to the nearest thousandth. $\newline$ The standard deviation rounded to the nearest thousandth is $19.987$ .