To find the variance of the weekly salaries of the employees at the local bank, we need to follow these steps:
1. Calculate the Mean (Average) Salary:
The mean salary is the sum of all salaries divided by the number of employees.
[tex]\( \text{Mean Salary (\(\bar{x}\)[/tex])} = \frac{\[tex]$245 + \$[/tex]300 + \[tex]$325 + \$[/tex]465 + \[tex]$100}{5} = \$[/tex]287.0 \)
2. Calculate the Squared Differences from the Mean:
For each salary, subtract the mean salary and then square the result:
- For Anja: [tex]\((245 - 287)^2 = (-42)^2 = 1764.0\)[/tex]
- For Raz: [tex]\((300 - 287)^2 = (13)^2 = 169.0\)[/tex]
- For Natalie: [tex]\((325 - 287)^2 = (38)^2 = 1444.0\)[/tex]
- For Mic: [tex]\((465 - 287)^2 = (178)^2 = 31684.0\)[/tex]
- For Paul: [tex]\((100 - 287)^2 = (-187)^2 = 34969.0\)[/tex]
So the squared differences are [tex]\([1764.0, 169.0, 1444.0, 31684.0, 34969.0]\)[/tex].
3. Sum of Squared Differences:
Add up all the squared differences:
[tex]\( 1764.0 + 169.0 + 1444.0 + 31684.0 + 34969.0 = 70030.0 \)[/tex]
4. Calculate the Variance:
Finally, divide the sum of squared differences by the number of salaries minus one (n-1), where [tex]\( n \)[/tex] is the number of employees.
[tex]\( \text{Variance} = \frac{70030.0}{5 - 1} = \frac{70030.0}{4} = 17507.5 \)[/tex]
The variance for the weekly salaries of the employees is [tex]\( 17507.5 \)[/tex].
