Calculate the standard deviation of the data shown. Use technology.
\begin{tabular}{|r|}
\hline$x$ \\
\hline 23.1 \\
\hline 21.4 \\
\hline 17 \\
\hline 22.1 \\
\hline 28.2 \\
\hline 11.2 \\
\hline 18.7 \\
\hline 12.8 \\
\hline
\end{tabular}

I Round to 2 places.
Submit Question

Step 1 ：Given the data set \(x = [23.1, 21.4, 17, 22.1, 28.2, 11.2, 18.7, 12.8]\)

Step 2 ：Calculate the mean of the data set: \(\bar{x} = \frac{\sum x}{n} = 19.3125\)

Step 3 ：Calculate the squared differences from the mean: \((x - \bar{x})^2 = [14.345156250000011, 4.3576562499999945, 5.34765625, 7.770156250000008, 78.98765624999999, 65.81265625000002, 0.37515625000000086, 42.41265624999999]\)

Step 4 ：Calculate the mean of the squared differences: \(\frac{\sum (x - \bar{x})^2}{n} = 27.426093750000003\)

Step 5 ：Calculate the square root of the mean squared difference to get the standard deviation: \(\sqrt{\frac{\sum (x - \bar{x})^2}{n}} = 5.24\)

Step 6 ：Round the standard deviation to 2 decimal places: \(\boxed{5.24}\)