For the following data set, approximate the sample standard deviation of unused vacation days. $$\begin{array} { c | c }
\text { Days } & \text { Frequency } \
\hline 1 - 2 & 9 \
3 - 4 & 12 \
5 - 6 & 8 \
7 - 8 & 5 \
9 - 10 & 4
\end{array}$$
A) 2.6 days
B) 2.5 days
C) 6.5 days
D) 6.6 days

Question

For the following data set, approximate the sample standard deviation of unused vacation days. $$\begin{array} { c | c } 
\text { Days } & \text { Frequency } \
\hline 1 - 2 & 9 \
3 - 4 & 12 \
5 - 6 & 8 \
7 - 8 & 5 \
9 - 10 & 4
\end{array}$$
A) 2.6 days
B) 2.5 days
C) 6.5 days
D) 6.6 days

Quizplus · Accepted Answer

To approximate the sample standard deviation of unused vacation days, we first find the midpoint of each class by averaging the lower and upper bounds. Then, we multiply each midpoint by the class frequency to find the total for each class, and sum these totals to find the mean. Next, we calculate the squared deviations from the mean for each class, multiply by the class frequencies, sum these values, divide by the total number of observations minus one (for sample standard deviation), and finally take the square root. The closest approximation given the choices is 2.6 days.