\begin{tabular}{|c|c|}
\hline
Employee & Salary (\$) \\
\hline
Employee 1 & 245 \\
\hline
Anja & 300 \\
\hline
Raz & 325 \\
\hline
Natalie & 465 \\
\hline
Mic & 100 \\
\hline
Paul & \\
\hline
\end{tabular}

What is the variance for the data?

Variance: [tex]$s^2=\frac{(x_1-\bar{x})^2+(x_2-\bar{x})^2+\cdots+(x_n-\bar{x})^2}{n-1}[tex]$[/tex]

A. 118.35
B. 132.32
C. 14,006
D. $[/tex]17,507.5$



Answer :

To find the variance of the given salaries, we will follow a detailed, step-by-step approach:

### Step 1: List the Salaries

We have the following salaries:
- Employee: [tex]$245 - Anja: $[/tex]300
- Raz: [tex]$325 - Natalie: $[/tex]465
- Mic: $100

### Step 2: Calculate the Mean

First, we calculate the mean (average) of the salaries.

[tex]\[ \bar{x} = \frac{245 + 300 + 325 + 465 + 100}{5} \][/tex]

Summing these salaries:

[tex]\[ 245 + 300 + 325 + 465 + 100 = 1435 \][/tex]

Next, we divide the sum by the number of salaries (5):

[tex]\[ \bar{x} = \frac{1435}{5} = 287.0 \][/tex]

### Step 3: Calculate the Squared Differences from the Mean

Next, we for each salary, calculate the squared difference from the mean:

[tex]\[ \left(x_1 - \bar{x}\right)^2 = (245 - 287.0)^2 = (-42)^2 = 1764 \][/tex]
[tex]\[ \left(x_2 - \bar{x}\right)^2 = (300 - 287.0)^2 = (13)^2 = 169 \][/tex]
[tex]\[ \left(x_3 - \bar{x}\right)^2 = (325 - 287.0)^2 = (38)^2 = 1444 \][/tex]
[tex]\[ \left(x_4 - \bar{x}\right)^2 = (465 - 287.0)^2 = (178)^2 = 31684 \][/tex]
[tex]\[ \left(x_5 - \bar{x}\right)^2 = (100 - 287.0)^2 = (-187)^2 = 34969 \][/tex]

### Step 4: Sum the Squared Differences

Sum these squared differences:

[tex]\[ 1764 + 169 + 1444 + 31684 + 34969 = 70030 \][/tex]

### Step 5: Calculate the Variance

Finally, the variance is given by the sum of the squared differences divided by [tex]\(n-1\)[/tex], where [tex]\(n\)[/tex] is the number of salaries (5 in this case).

[tex]\[ s^2 = \frac{70030}{5 - 1} = \frac{70030}{4} = 17507.5 \][/tex]

Therefore, the variance for the given data is:

[tex]\[ \boxed{17507.5} \][/tex]