Find the standard deviation of the following data set. Assume the data set is a sample. Round your answer to the nearest hundredth, if necessary.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline 19 & 36 & 27 & 38 & 15 & 27 & 28 & 21 & 33 & 22 & 22 \\
\hline
\end{tabular}
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Step 1 ：First, calculate the mean of the data set: \( \frac{19 + 36 + 27 + 38 + 15 + 27 + 28 + 21 + 33 + 22 + 22}{11} = 26.18 \)

Step 2 ：Next, calculate the squared differences from the mean: \( (19 - 26.18)^2, (36 - 26.18)^2, (27 - 26.18)^2, (38 - 26.18)^2, (15 - 26.18)^2, (27 - 26.18)^2, (28 - 26.18)^2, (21 - 26.18)^2, (33 - 26.18)^2, (22 - 26.18)^2, (22 - 26.18)^2 \)

Step 3 ：Then, calculate the variance, which is the mean of these squared differences: \( \frac{51.58 + 96.40 + 0.67 + 139.67 + 125.03 + 0.67 + 3.31 + 26.85 + 46.49 + 17.49 + 17.49}{11 - 1} = 52.56 \)

Step 4 ：Finally, calculate the standard deviation, which is the square root of the variance: \( \sqrt{52.56} = 7.25 \)

Step 5 ：Round the standard deviation to the nearest hundredth: \( 7.25 \)

Step 6 ：Final Answer: The standard deviation of the data set is \(\boxed{7.25}\)