The following sample of 16 measurements was selected from

Step 1 of 4:

We have 16 samples selected from the population

\(\begin{array}{|l|l|} \hline \mathrm{X} & x^{2} \\ \hline 91 & 8281 \\ \hline 80 & 6400 \\ \hline 99 & 9801 \\ \hline 110 & 12100 \\ \hline 95 & 9025 \\ \hline 106 & 11236 \\ \hline 78 & 6084 \\ \hline 121 & 14641 \\ \hline 106 & 11236 \\ \hline 100 & 10000 \\ \hline 97 & 9409 \\ \hline 82 & 6724 \\ \hline 100 & 10000 \\ \hline 83 & 6889 \\ \hline 115 & 13225 \\ \hline 104 & 10816 \\ \hline \Sigma x=1567 & \Sigma x^{2}=155867 \\ \hline \end{array}\)

\(\begin{aligned} \text { Mean } & =\frac{\Sigma x_{i}}{n} \\ & =\frac{1567}{16} \\ & =97.9375 \end{aligned}\)

\(\begin{aligned} \text { Variance } & =\frac{\Sigma x^{2}-\frac{(\Sigma x)^{2}}{n}}{n-1} \\ & =\frac{155867-\frac{(1567)^{2}}{16}}{16-1} \\ & =\frac{155867-153468.0625}{15} \\ & =159.9291 \end{aligned}\)

\(\begin{aligned} \sigma & =\sqrt{159.9291} \\ & =12.6431 \end{aligned}\)