Question

The following are all 5 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.

6,6, 5, 8, 10
Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.

Answer 1

2

Explanation:

Given: 5 quiz scores of a student in a statistics course are 6,6, 5, 8, 10

To find: standard deviation of the population

Solution:

Mean (M) =
`(\sum_(i=1)^(n)x_i)/(n)`

here,
`x_i` denotes number of observations and n denotes number of observations.

Variance =
`(\sum_(i=1)^(n)(x_i-M)^2)/(n-1)`

Standard deviation =
`√(variance)`

`M=(6+6+5+8+10)/(5)=(35)/(5)=7`

Variance =
`(\sum_(i=1)^(n)(x_i-7)^2)/(n-1)`

`=(\left [ (6-7)^2+(6-7)^2+(5-7)^2+(8-7)^2+(10-7)^2 \right ])/(5-1)\\=(1+1+4+1+9)/(4)\\=(16)/(4)\\=4`

Standard deviation =
`√(4)=2`