Two data sets can have the same mean but differ in variability, meaning how spread out the scores are.
The range uses only the highest and lowest scores, while the standard deviation — roughly the average distance of scores from the mean — takes every score into account.
Two data sets can have the same mean and the same range yet different standard deviations, depending on how the other scores are spread.
On a histogram, the wider, flatter distribution has the larger standard deviation; a tall, sharply peaked one has a smaller standard deviation.
Adding and subtracting one standard deviation from the mean shows the span of scores within one standard deviation of the mean.
Key terms
variability
How spread out the scores in a data set are.
range
The difference between the highest and lowest scores.
standard deviation
Roughly the average distance of scores from the mean; larger means more spread out, smaller means clustered near the mean.
Watch out
The range uses only two scores; the standard deviation uses all of them, so equal ranges do not mean equal standard deviations.