Question

The table below shows the scores on a math test.

David
75
Aaron
75
Ashley
60
Gina
75
Andrew
75
Kei
95
Monica
100
Anna
60
Lucas
75
Jennifer
65

Find the standard deviation. Round to the nearest tenth when necessary.
a.
157.25
c.
9.1
b.
12.5
d.
12.3


Please select the best answer from the choices provided

Answer 1

With the use of a calculator with statistical functions, the standard deviation was found to be 12.54

Answer 2

1572.5

Explanation:

David : 75

Aaron : 75

Ashley : 60

Gina : 75

Andrew : 75

Kei : 95

Monica : 100

Anna : 60

Lucas : 75

Jennifer : 65

First calculate the mean

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

So,
`Mean = (75+75+60+75+75+95+100+60+75+65)/(10)`

`Mean = 75.5`

Standard deviation =
`\sum (x_i-\mu)^2`

So, Standard deviation =
`(75-75.5)^2+(75-75.5)^2+(60-75.5)^2+(75-75.5)^2+(75-75.5)^2+(95-75.5)^2+(100-75.5)^2+(60-75.5)^2+(75-75.5)^2+(65-75.5)^2`

Standard deviation =
`1572.5`

Hence the standard deviation is 1572.5