# Sample Variance & Standard Deviation | Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.7

## Solution:

We know, based on our answer in Exercise 1.1, that the sample mean is $\displaystyle \overline{x}=3.787$.

To compute for the sample variance, we shall use the formula

$\displaystyle s^2=\sum _{i=1}^n\frac{\left(x_i-\overline{x}\right)^2}{n-1}\:$

The formula states that we need to get the sum of $\displaystyle \left(x_i-\overline{x}\right)^2$, so we can use a table to solve $\displaystyle \left(x_i-\overline{x}\right)^2$ for every sample.

The table above shows that

$\displaystyle \sum _{i=1}^{15}=13.197$

Therefore, the variance is

$\displaystyle s^2=\sum _{i=1}^n\frac{\left(x_i-\overline{x}\right)^2}{n-1}=\frac{13.197}{15-1}=0.9426\:$

The standard deviation is just the square root of the variance. That is

$\displaystyle s=\sqrt{s^2}=\sqrt{0.9426}=0.971$