Question

You used (formula in screenshot) when calculating variance and standard deviation. An alternative formula for the standard deviation that is sometimes convenient for hand calculations is shown below. You can find the sample variance by dividing the sum of squares by n-​1, and the sample standard deviation by finding the square root of the sample variance. Complete parts​ (a) and​ (b) below.

Answer 1

`Varianve = 3.842`

`SD = 1.960`

Explanation:

Given

See attachment for data

First, calculate
`\sum x^2`

`\sum x^2 = 18^2 + 17^2 +20^2 + 19^2 + 20^2 + 16^2 + 16^2 + 15^2 + 18^2+14^2 +19^2 + 19^2+18^2+17^2 + 16^2+20^2+16^2+18^2+14^2+20^2`

`\sum x^2 = 6198`

Calculate
`\sum x`

`\sum x = 18 + 17 +20 + 19 + 20 + 16 + 16 + 15 + 18+14 +19 + 19+18+17 + 16+20+16+18+14+20`

`\sum x = 350`

So, we have:

`SS_x = \sum x^2 -((\sum x)^2)/(n)`

`SS_x = 6198 -(350^2)/(20)`

`SS_x = 6198 -(122500)/(20)`

`SS_x = 6198 -6125`

`SS_x = 73`

Solving (a): The variance

`Varianve = (SS_x)/(n-1)`

`Varianve = (73)/(20-1)`

`Varianve = (73)/(19)`

`Varianve = 3.842`

Solving (b): The standard deviation

`SD = √(Variance)`

`SD = √(3.842)`

`SD = 1.960`