To calculate the variance of the weekly salaries of the sample of employees at the local bank, follow these steps:
1. List the given weekly salaries:
- Anja: [tex]$245
- Raz: $[/tex]300
- Natalie: [tex]$325
- Mic: $[/tex]465
- Paul: $100
2. Calculate the mean (average) of these salaries:
Mean, [tex]\(\bar{x}\)[/tex], is given by:
[tex]\[
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
\][/tex]
where [tex]\( x_i \)[/tex] are the salaries and [tex]\( n \)[/tex] is the number of employees.
[tex]\[
\bar{x} = \frac{245 + 300 + 325 + 465 + 100}{5} = \frac{1435}{5} = 287
\][/tex]
3. Calculate the squared differences from the mean for each salary:
- For Anja: [tex]\((245 - 287)^2 = (-42)^2 = 1764\)[/tex]
- For Raz: [tex]\((300 - 287)^2 = (13)^2 = 169\)[/tex]
- For Natalie: [tex]\((325 - 287)^2 = (38)^2 = 1444\)[/tex]
- For Mic: [tex]\((465 - 287)^2 = (178)^2 = 31684\)[/tex]
- For Paul: [tex]\((100 - 287)^2 = (-187)^2 = 34969\)[/tex]
4. Sum these squared differences:
[tex]\[
1764 + 169 + 1444 + 31684 + 34969 = 70030
\][/tex]
5. Calculate the variance using the formula:
[tex]\[
s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1} = \frac{70030}{5-1} = \frac{70030}{4} = 17507.5
\][/tex]
Therefore, the variance of the weekly salaries is [tex]\(17507.5\)[/tex].
