Question

Consider the following data:

5 8 2 1 7 1

Determine the standard deviation by filling in the table as part of your calculation.

Answer 1

Option b) Standard deviation is
`\sigma =√(8)\approx 2.83` is correct

Explanation:

Given data is

x
`\bar{x}`
`x-\bar{x}`
`(x-\bar{x})^2`

5 4 1 1

8 4 4 16

2 4 -2 4

1 4 -3 9

7 4 3 9

1 4 -3 9

____________________

`\sum (x-\bar{x})^2=48`

_______________________

Standard deviation
`\sigma =\sqrt{\frac{\sum (x-\bar{x})^2}{n}}` where n= number of samples=6

Standard deviation
`\sigma=\sqrt{(48)/(6)}`

`\sigma=√(8)`

Therefore Standard deviation is
`\sigma=√(8)\approx 2.83`

Therefore Option b) is correct