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Range and standard deviation

The range is the largest value minus the smallest value. It uses only the two extremes. The standard deviation here is the square root of the average of the squared deviations from the mean, that is divided by the count. Some calculators divide by the count minus 1 when they compute a sample standard deviation, and then the number is larger. The example divides by the count, so the calculation is unambiguous.

range=xmax⁡−xmin⁡\text{range} = x_{\max} - x_{\min}spread
σ=∑(x−xˉ)2n\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n}}divided by the count

Symbols

nnnumber of values
σ\sigmastandard deviation

Example

The numbers 12, 4, 19 and 7 have range 19−4=1519 - 4 = 15.

The numbers 2, 4, 4 and 6 have mean 4 and standard deviation 2≈1.414\sqrt{2} \approx 1.414 when we divide by 4.

Dividing by n and dividing by n minus 1 are two different definitions. Here we divide by n.
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Part of Mathematics 2P: Statistics.