For the following data set, approximate the sample standard deviation of commuting times per day. $$\begin{array} { c | c }
\text { Commute (in min) } & \text { Frequency } \
\hline 50 - 52 & 5 \
53 - 55 & 8 \
56 - 58 & 12 \
59 - 61 & 13 \
62 - 64 & 11
\end{array}$$
A) 3.9 min
B) 6.6 min
C) 2.5 min
D) 55.7 min

Question

For the following data set, approximate the sample standard deviation of commuting times per day. $$\begin{array} { c | c } 
\text { Commute (in min) } & \text { Frequency } \
\hline 50 - 52 & 5 \
53 - 55 & 8 \
56 - 58 & 12 \
59 - 61 & 13 \
62 - 64 & 11
\end{array}$$
A) 3.9 min
B) 6.6 min
C) 2.5 min
D) 55.7 min

Quizplus · Accepted Answer

To approximate the sample standard deviation, first, calculate the midpoint for each class by averaging the upper and lower bounds. Then, multiply each midpoint by the class frequency to find the sum of all values and the sum of the squared values, which are used to calculate the mean and variance. The square root of the variance gives the standard deviation. The choice closest to the calculated value is 3.9 min.

For the Following Data Set, Approximate the Sample Standard Deviation