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

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 sample standard deviation, we first find the midpoint of each class by averaging the lower and upper bounds. Then, we calculate the mean by multiplying each midpoint by its frequency, summing these products, and dividing by the total number of observations. Finally, we use the formula for standard deviation, which involves squaring the difference between each midpoint and the mean, multiplying by the frequency, summing these, dividing by the total number of observations minus one, and taking the square root. The result is approximately 5.1 emails, indicating option A is correct.

For the Following Data Set, Approximate the Sample Standard Deviation