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

Compute the sample variance and standard deviation for the water absorbency data of Exercise 1.2 on page 13.


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


\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