# Sample Variance & Standard Deviation | Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.8

### Solution:

We know, based on our answer in Exercise 1.2, that the sample mean is $\displaystyle \overline{x}=20.768$.

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.

Note: You can refer to the solution of Exercise 1.7 on how to use a table to solve for the variance.

The variance is $s^2=\frac{1}{20-1}[\left(18.71-20.768\right)^2+\left(21.41-20.768\right)^2$ $\displaystyle +...+\left(21.12-20.768\right)^2]$ $\displaystyle s^2=2.5345$

The standard deviation is just the square root of the variance. That is $\displaystyle s=\sqrt{s^2}=\sqrt{2.5345}=1.592$