Approximate the Variance and Standard Deviation of a Variable from Grouped Data
-For the following data set, approximate the sample standard deviation of emails per day. $\begin{array}{c|c}
\text { Emails (per day) } & \text { Frequency } \
\hline 8-11 & 18 \
12-15 & 23 \
16-19 & 38 \
20-23 & 47 \
24-27 & 32
\end{array}$

A) $5.1$ emails
B) $4.0$ emails
C) $25.8$ emails
D) $19.3$ emails

Question

Approximate the Variance and Standard Deviation of a Variable from Grouped Data
-For the following data set, approximate the sample standard deviation of emails per day. $\begin{array}{c|c}
\text { Emails (per day) } & \text { Frequency } \
\hline 8-11 & 18 \
12-15 & 23 \
16-19 & 38 \
20-23 & 47 \
24-27 & 32
\end{array}$

A) $5.1$ emails
B) $4.0$ emails
C) $25.8$ emails
D) $19.3$ emails

Quizplus · Accepted Answer

To approximate the standard deviation, calculate the midpoint for each class, multiply by the frequency, find the mean, then use the formula for variance and standard deviation for grouped data. The calculations lead to a standard deviation of approximately 5.1 emails.