The salaries of employees of the Moe D. Lawn Landscaping Company are: $$\begin{array} { l l }
\text { cellpadding } = 0 " 0 \text { cellspacing } = " 0 " \text { width } = " 52 \% " \text { border }= "0" \
\text { Salary } & \text { Frequency } \
\$ 25,000 & 5 \
\$ 27,000 & 3 \
\$ 29,000 & 2 \
\$ 39,000 & 2
\end{array}$$ Find the variance rounded to the nearest thousand dollars and the standard deviation rounded to the nearest dollar.
A) variance: $\$ 24,083,000$ standard deviation: $\$ 4,907$
B) variance: $\$ 28,000$ standard deviation: $\$ 812,079,011$
C) variance: $\$ 29,000$ standard deviation: $\$ 28,497$
D) variance: $\$ 5,000$ standard deviation: $\$ 24,083,333$
E) variance: $\$ 812,079,000$ standard deviation: $\$ 28,497$

Question

The salaries of employees of the Moe D. Lawn Landscaping Company are: $$\begin{array} { l l } 
\text { cellpadding } = 0 " 0 \text { cellspacing } = " 0 " \text { width } = " 52 \% " \text { border }= "0"> \
\text { Salary } & \text { Frequency } \
\$ 25,000 & 5 \
\$ 27,000 & 3 \
\$ 29,000 & 2 \
\$ 39,000 & 2
\end{array}$$ Find the variance rounded to the nearest thousand dollars and the standard deviation rounded to the nearest dollar.
A) variance: $\$ 24,083,000$ standard deviation: $\$ 4,907$
B) variance: $\$ 28,000$ standard deviation: $\$ 812,079,011$
C) variance: $\$ 29,000$ standard deviation: $\$ 28,497$
D) variance: $\$ 5,000$ standard deviation: $\$ 24,083,333$
E) variance: $\$ 812,079,000$ standard deviation: $\$ 28,497$

Quizplus · Accepted Answer

First, we need to calculate the mean:
$$	ext{Mean}=\frac{(5	imes25,000)+(3	imes27,000)+(2	imes29,000)+(2	imes39,000)}{12}=\$29,000$$
Next, we can use the formula for variance:
$$	ext{Variance}=\frac{\sum (x-\bar{x})^2}{n-1}$$
where $x$ is the salary, $\bar{x}$ is the mean salary, and $n$ is the sample size. Substituting values, we get:
\begin{align*}
	ext{Variance} &= \frac{(25,000-29,000)^2	imes5+(27,000-29,000)^2	imes3+(29,000-29,000)^2	imes2+(39,000-29,000)^2	imes2}{12-1} \
&= \frac{16,450,000	imes5+4,000,000	imes3+0	imes2+100,000,000	imes2}{11} \
&= 24,083,000
\end{align*}
Finally, the standard deviation can be found as the square root of the variance:
$$	ext{Standard deviation}=\sqrt{24,083,000}\approx4,907$$
Therefore, the answer is (A).

The Salaries of Employees of the Moe D Find the Variance Rounded to the Nearest Thousand Dollars and Company