Answer:
17507.5
Step-by-step explanation:
Given :
Weekly Salary
Anja $245
Raz $300
Natalie $325
Mic $465
Paul $100
Formula given :
[tex]S^2 =\frac{(x_1-\bar x)^2+(x_2-\bar x)^2+....+(x_n-\bar x)^2}{n-1}[/tex]
Where [tex]\bar x[/tex] is mean
n = no. of observations
To find: What is the variance for the data?
Solution:
Now to find mean :
[tex]Mean = \frac{\text{Sum of all observations}}{\text{Total no. of observations}}[/tex]
[tex]Mean = \frac{245+300+325+465+100}{5}[/tex]
[tex]Mean = \frac{1435}{5}[/tex]
[tex]Mean = 287[/tex]
So, [tex]\bar x = 287[/tex]
[tex]x_1 = 245[/tex]
[tex]x_2 = 300[/tex]
[tex]x_3 = 325[/tex]
[tex]x_4 = 465[/tex]
[tex]x_5 = 100[/tex]
n = 5
Substitute the values in the formula :
[tex]S^2 =\frac{(245-287)^2+(300-287)^2+(325-287)^2+(465-287)^2+(100-287)^2}{5-1}[/tex]
[tex]S^2 =\frac{70030}{4}[/tex]
[tex]S^2 =17507.5[/tex]
Hence the variance of the data is 17507.5
