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Roman SL · Answer 1 · 2023-11-07T21:28:32+0000

The standard population formula is:

$\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_{}-\mu)^2}{n}}$

where

x is the data points

μ is the mean of the data

and n is the number of data points

The mean is computed as follows:

$\mu=(\Sigma x)/(n)$

In this case, the mean is:

$\mu=(121+101+97+121+124+112)/(6)=(676)/(6)=112.67$

Then, the standard deviation of the population is:

$\begin{gathered} \sigma=\sqrt[]{((121-112.67)^2+(101-112.67)^2+(97-112.67)^2+(121-112.67)^2+(124-112.67)^2+(112-112.67)^2)/(6)} \\ \sigma=\sqrt[]{(69.39+136.19+245.55+69.39+128.37+0.045)/(6)} \\ \sigma=\sqrt[]{108.22} \\ \sigma=10.4 \end{gathered}$

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