Sample Statistics
The Sample Variance
The Problem
The variance is a measure of the variability in the data. The standard deviation is also a measure of how spread out the data are. The main advantage of the variance over the standard deviation is that variances do not involve a square root, which means variances can be easily added — standard deviations cannot.
Because the variance uses the mean in its calculations, it would only make sense to use it if the mean should also have been used. Thus, data that are highly skewed should not use the variance to represent variability. To illustrate calculating the variance, assume that you collected the following 4 data values:
15, 24, 90, 89
Calculate the variance of this sample, s².
Your Answer
In the box below, please enter the sample variance of the data given above, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.
![[Correct!]](images/correct.png "You are correct. Well done!")
You got the correct answer of 1647. Congratulations!
![[Incorrect!]](images/incorrect.png "You are not correct.")
Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.
Assistance
Show Formula
Show Solution
Show the R Code
Show the Excel Code