Two towns both average 20°C, but one is mild year-round while the other bakes in summer and freezes in winter. The average hides that difference; the standard deviation reveals it by measuring how far the days spread from the middle.
Center isn't the whole story
Two data sets can share the same mean yet look completely different. Measures of spread describe how far the values scatter. The range is simply the largest value minus the smallest; the standard deviation measures the typical distance of a value from the mean.
A small standard deviation means values cluster tightly around the mean; a large one means they spread widely. It is the square root of the average squared distance from the mean (the variance).
{4, 5, 6} and {1, 5, 9} both average 5, but the second has a far larger range (8 vs. 2) and standard deviation — it's more spread out.0 rolls
7 is the most likely sum — there are more ways to make it.
Roll many times and watch how outcomes spread around the average.
- Take the data set {3, 7, 7, 12}.
- Identify the largest and smallest values.
- Subtract to get the range.
What you should see: Largest 12, smallest 3, so the range is 12 − 3 = 9.