To determine the variance for the given data, we will follow these steps:
1. List the weekly salaries:
[tex]\[
245, 300, 325, 465, 100
\][/tex]
2. Calculate the mean (average) salary:
The mean [tex]\(\bar{x}\)[/tex] is calculated by adding all the salaries and dividing by the number of salaries.
[tex]\[
\bar{x} = \frac{245 + 300 + 325 + 465 + 100}{5} = \frac{1435}{5} = 287.0
\][/tex]
3. Determine the deviations from the mean for each salary:
[tex]\[
245 - 287.0 = -42.0
\][/tex]
[tex]\[
300 - 287.0 = 13.0
\][/tex]
[tex]\[
325 - 287.0 = 38.0
\][/tex]
[tex]\[
465 - 287.0 = 178.0
\][/tex]
[tex]\[
100 - 287.0 = -187.0
\][/tex]
4. Square each deviation:
[tex]\[
(-42.0)^2 = 1764.0
\][/tex]
[tex]\[
(13.0)^2 = 169.0
\][/tex]
[tex]\[
(38.0)^2 = 1444.0
\][/tex]
[tex]\[
(178.0)^2 = 31684.0
\][/tex]
[tex]\[
(-187.0)^2 = 34969.0
\][/tex]
5. Sum the squared deviations:
[tex]\[
1764.0 + 169.0 + 1444.0 + 31684.0 + 34969.0 = 70130.0
\][/tex]
6. Divide by the number of salaries minus 1 (to get the sample variance):
[tex]\[
s^2 = \frac{70130.0}{5 - 1} = \frac{70130.0}{4} = 17507.5
\][/tex]
Therefore, the variance for the weekly salaries is:
[tex]\[
s^2 = 17507.5
\][/tex]
So, the correct answer from the given choices is [tex]$17,507.5$[/tex].
