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

Answer:

$\sigma_x = 5.68$

Explanation:

Given

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

Required

The standard deviation

First, calculate the mean

$\bar x =\frac{\sum x}{n}$

So, we have:

$\bar x = \frac{4+ 14+ 6+ 2+ 7+ 12 +2+17}{8}$

$\bar x = \frac{64}{8}$

$\bar x = 8$

The standard deviation is:

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

So, we have:

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

$\sigma_x = \sqrt{\frac{226}{7}}$

$\sigma_x = \sqrt{32.2857}$

$\sigma_x = 5.68$