Find the standard deviation for the group of data items.
\[
8,8,8,11,14,14,14 \text { 마 }
\]
Answer
\(\boxed{2.78}\) is the standard deviation of the data set
Step 1 ：Calculate the mean of the data set: \(\frac{8 + 8 + 8 + 11 + 14 + 14 + 14}{7} = 11\)
Step 2 ：Subtract the mean from each number and square the result to get the squared deviation: \((8 - 11)^2 = 9\), \((8 - 11)^2 = 9\), \((8 - 11)^2 = 9\), \((11 - 11)^2 = 0\), \((14 - 11)^2 = 9\), \((14 - 11)^2 = 9\), \((14 - 11)^2 = 9\)
Step 3 ：Calculate the mean of these squared deviations: \(\frac{9 + 9 + 9 + 0 + 9 + 9 + 9}{7} = 7.71\)
Step 4 ：Take the square root of the mean squared deviation to get the standard deviation: \(\sqrt{7.71} = 2.78\)
Step 5 ：\(\boxed{2.78}\) is the standard deviation of the data set
