A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation. $$\begin{array} { r | c }
\text { Salary (dollars) } & \text { Employees } \
\hline 5,001 - 10,000 & 19 \
10,001 - 15,000 & 14 \
15,001 - 20,000 & 12 \
20,001 - 25,000 & 16 \
25,001 - 30,000 & 19
\end{array}$$
A)$7967.5
B)$7588.1
C)$8195.1
D)$8422.8

Question

A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation. $$\begin{array} { r | c } 
\text { Salary (dollars) } & \text { Employees } \
\hline 5,001 - 10,000 & 19 \
10,001 - 15,000 & 14 \
15,001 - 20,000 & 12 \
20,001 - 25,000 & 16 \
25,001 - 30,000 & 19
\end{array}$$
A)$7967.5
B)$7588.1
C)$8195.1
D)$8422.8

Quizplus · Accepted Answer

To calculate the standard deviation, first, find the midpoint of each salary range to represent the salary for that group. Then, calculate the mean salary using these midpoints and the number of employees in each group. After that, use the formula for standard deviation, which involves finding the squared difference between each group's midpoint and the mean, multiplying by the number of employees in that group, summing these values, dividing by the total number of employees, and finally taking the square root. The correct calculation leads to the standard deviation being $7588.1.

A Company Had 80 Employees Whose Salaries Are Summarized in the Frequency