Question

the weekly salaries of a sample of employees at the local bank are given in the table below.

employee	weekly salary
raz	$300
natalie	$325
mic	$465
paul	$100

what is the variance for the data?
variance:
$s^2 = \frac{\left(x_1 - \bar{x}\
ight)^2 + \left(x_2 - \bar{x}\
ight)^2 + \dots + \left(x_n - \bar{x}\
ight)^2}{n - 1}$
\bigcirc 118.35

Explanation:

Step1: Calculate the mean ($\bar{x}$)

First, find the sum of the weekly salaries: $245 + 300 + 325 + 465 + 100 = 1435$.
There are $n = 5$ employees, so the mean $\bar{x} = \frac{1435}{5} = 287$.

Step2: Calculate each $(x_i - \bar{x})^2$

• For Anja: $(245 - 287)^2 = (-42)^2 = 1764$
• For Raz: $(300 - 287)^2 = (13)^2 = 169$
• For Natalie: $(325 - 287)^2 = (38)^2 = 1444$
• For Mic: $(465 - 287)^2 = (178)^2 = 31684$
• For Paul: $(100 - 287)^2 = (-187)^2 = 34969$

Step3: Sum the squared differences

Sum: $1764 + 169 + 1444 + 31684 + 34969 = 69930$

Step4: Calculate the variance

Using the formula $s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$, we have $s^2 = \frac{69930}{5 - 1} = \frac{69930}{4} = 17482.5$

Answer:

17482.5