Test Scores: Variance & Maximum Mark

[Ted123]

Say we have a sample of test scores, all marked between 0 and 100.

Does the sample variance have to be less than or equal to the maximum mark 100 or can it exceed this?

 

[micromass]

It can exceed it: say your test scores are 0 and 100. Then the sample mean is 50. The sample variance equals

$$\frac{1}{n-1}\sum_{i=1}^n{(X_i-\overline{X_n})^2}=5000$$.

You probably mean the sample standard deviation... In this example, it is 70. I don't think it can exceed 100...