Calculate the sample standard deviation of the data shown. Round to two decimal places. \begin{tabular}{|c|} \hline $\mathrm{x}$ \\ \hline 14 \\ \hline 21 \\ \hline 11 \\ \hline 24 \\ \hline 10 \\ \hline 20 \\ \hline 27 \\ \hline 12 \\ \hline \end{tabular} sample standard deviation = Submit Question

Step 1 ：Given the data set \(x = [14, 21, 11, 24, 10, 20, 27, 12]\)

Step 2 ：Calculate the mean of the data set: \(\bar{x} = \frac{\sum x}{n} = 17.375\)

Step 3 ：Calculate the squared differences from the mean: \((x_i - \bar{x})^2 = [11.390625, 13.140625, 40.640625, 43.890625, 54.390625, 6.890625, 92.640625, 28.890625]\)

Step 4 ：Calculate the variance, which is the mean of these squared differences: \(\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n-1} = 41.69642857142857\)

Step 5 ：Calculate the standard deviation, which is the square root of the variance: \(\sigma = \sqrt{\sigma^2} = 6.46\)

Step 6 ：Round the standard deviation to two decimal places: \(\sigma = \boxed{6.46}\)