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) $8195.1
B) $8422.8
C) $7588.1
D) $7967.5

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) $8195.1
B) $8422.8
C) $7588.1
D) $7967.5

Quizplus · Accepted Answer

To calculate the standard deviation, we need to first find the mean. We can do this by finding the midpoint of each salary range and multiplying by the corresponding frequency, then adding up all of these products and dividing by the total number of employees:

$\frac{9,500(19) + 12,500(14) + 17,500(12) + 22,500(16) + 27,500(19)}{80} = 17,125$

Next, we need to find the variance. We can do this by finding the deviation from the mean for each salary range, squaring each deviation, multiplying by the corresponding frequency, adding up all of these products, and dividing by the total number of employees:

$\frac{(5,625,000 - 17,125^2)(19) + (2,250,000 - 17,125^2)(14) +  (225,000 - 17,125^2)(12) + (1,225,000 - 17,125^2)(16) + (6,025,000 - 17,125^2)(19)}{80} \approx 57,611,282.28$

Finally, we take the square root of the variance to find the standard deviation:

$\sqrt{57,611,282.28} \approx \$7,588.1$

Therefore, the answer is C.

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