Question

4. Calculate the standard deviation for the following data set: Foundations of Technology Engineering byDesi OITEEA . . Data Set = 4, 14, 6, 2, 7, 12 217 ,​

Answer 1

`\sigma_x = 5.68`

Step-by-step explanation:

Given

`x = 4, 14, 6, 2, 7, 12 2,17`

Required

The standard deviation

First, calculate the mean

`\bar x =(\sum x)/(n)`

So, we have:

`\bar x = (4+ 14+ 6+ 2+ 7+ 12 +2+17)/(8)`

`\bar x = (64)/(8)`

`\bar x = 8`

The standard deviation is:

`\sigma_x = \sqrt{(\sum(x - \bar x)^2)/(n-1)}`

So, we have:

`\sigma_x = \sqrt{((4 - 8)^2+ (14 - 8)^2+ (6 - 8)^2+ (2 - 8)^2+ (7 - 8)^2+ (12 - 8)^2+ (2 - 8)^2+ (17 - 8)^2)/(8-1)}`

`\sigma_x = \sqrt{(226)/(7)}`

`\sigma_x = √(32.2857)`

`\sigma_x = 5.68`