Question

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

Anja $245
Raz $300
Natalie $325
Mic $465
Paul $100
What is the variance for the data? Variance: the picture ^^

Answer 1

i just took the test and the correct answer is 17,507.5

Answer 2

17507.5

Explanation:

Given :

Weekly Salary

Anja $245

Raz $300

Natalie $325

Mic $465

Paul $100

Formula given :

`S^2 =((x_1-\bar x)^2+(x_2-\bar x)^2+....+(x_n-\bar x)^2)/(n-1)`

Where
`\bar x` is mean

n = no. of observations

To find: What is the variance for the data?

Solution:

Now to find mean :

`Mean = \frac{\text{Sum of all observations}}{\text{Total no. of observations}}`

`Mean = (245+300+325+465+100)/(5)`

`Mean = (1435)/(5)`

`Mean = 287`

So,
`\bar x = 287`

`x_1 = 245`

`x_2 = 300`

`x_3 = 325`

`x_4 = 465`

`x_5 = 100`

n = 5

Substitute the values in the formula :

`S^2 =((245-287)^2+(300-287)^2+(325-287)^2+(465-287)^2+(100-287)^2)/(5-1)`

`S^2 =(70030)/(4)`

`S^2 =17507.5`

Hence the variance of the data is 17507.5