Question

Calculate the sample standard deviation of data from Question 1
76,45,64,80,92

Answer 1

`S.D = 15.98`

Explanation:

Given: 76,45,64,80,92

Required: Determine the standard deviation

We start by calculating the mean

`Mean = \frac {\sum x}{n}`

Where x-> 76,45,64,80,92 and n = 5

`Mean = \frac {76+45+64+80+92}{5}`

`Mean = (357)/(5)`

`Mean = 71.4`

Subtract Mean (71.4) from each of the given data

`76 - 71.4 = 4.6\\45 - 71.4 = -26.5\\64 - 71.4 = -7.4\\80 - 71.4 = 8.6\\92 - 71.4 = 20.6`

Determine the absolute value of the above result

`|4.6| = 4.6\\|-26.5| = 26.5\\|-7.4| = 7.4\\|8.6| = 8.6\\|20.6| = 20.6`

Square Individual Result

`4.6^2 = 21.16 \\26.5^2 = 702.25\\7.4^2 = 54.76\\8.6^2 = 73.96\\20.6^2 = 424.36`

Calculate the mean of the above result to give the variance

`Mean = \frac {\sum x}{n}`

`Mean = (21.16 + 702.25 + 54.76 + 73.96 + 424.36)/(5)\\Mean = (1276.49)/(5)\\Mean = 255.298`

Hence, Variance = 255.298

Standard Deviation is calculated by
`√(Var)`

`SD = √(255.298)`

`S.D = 15.9780474402`

`S.D = 15.98 (Approximated)`