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 46 & 32 & 32 & 33 & 27 & 27 & 43 & 26 & 20 & 48 & 24 \\ \hline \end{tabular} Copy Data

Step 1 ：Calculate the mean of the data set: \(\frac{46 + 32 + 32 + 33 + 27 + 27 + 43 + 26 + 20 + 48 + 24}{11} = 32.55\)

Step 2 ：Subtract the mean from each data point and square the result: \((46 - 32.55)^2, (32 - 32.55)^2, (32 - 32.55)^2, (33 - 32.55)^2, (27 - 32.55)^2, (27 - 32.55)^2, (43 - 32.55)^2, (26 - 32.55)^2, (20 - 32.55)^2, (48 - 32.55)^2, (24 - 32.55)^2\)

Step 3 ：Calculate the mean of these squared differences: \(\frac{180.9025 + 0.3025 + 0.3025 + 0.2025 + 30.9025 + 30.9025 + 109.7025 + 42.9025 + 157.5025 + 239.7025 + 73.1025}{11} = 78.7666\)

Step 4 ：Take the square root of the result from the previous step: \(\sqrt{78.7666} = 8.88\)

Step 5 ：\(\boxed{\text{So, the standard deviation of the given data set is approximately 8.88.}}\)