Without Calculating the Standard Deviation, Compare the Standard Deviation for the Following

Essay

Without calculating the standard deviation, compare the standard deviation for the following three data sets. (Note: All data sets have a mean of 30.) Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula s $= \sqrt { \frac { \sum ( x - \bar { x } ) ^ { 2 } } { n - 1 } }$ .

$\begin{array}{cccccccccc}\text { Set A: } 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\\text { Set B: } 20 & 25 & 25 & 30 & 30 & 30 & 30 & 35 & 35 & 40 \\\text { Set C: } 20 & 20 & 20 & 25 & 25 & 35 & 35 & 40 & 40 & 40\end{array}$