What it shows
A histogram with positive skew. Most observations fall toward the low end, and a thin tail extends to the right. Incomes and waiting times often have this shape.
The bars are the expected counts for 1,000 observations from a gamma distribution, with the same distribution’s density drawn as a dashed curve.
How to read it
The peak is in the second and third bins (174 and 178), just above zero.
From there the counts fall slowly; the last bins on the right hold 4, 3 and 2.
The skew is named for the tail, not the peak. A long tail to the right is right skew, or positive skew.
The numbers behind it
- Gamma distribution, shape 2, scale 1. n = 1,000, bins of width 0.5 from 0 to 8.
- Counts, left to right: 90, 174, 178, 152, 119, 88, 63, 44, 30, 21, 14, 9, 6, 4, 3, 2.
- 0.30% of the distribution lies above 8.
Ways to use it in teaching
Pair it with the left-skewed histogram, its mirror image, and ask which way the mean moves in each.
Collect examples from students of variables in their own field likely to have this shape.
It gives a concrete case of a clearly non-normal variable, useful before discussing when skew matters for an analysis (usually through the residuals or the sampling distribution, not the raw variable) and what a log transformation does.
For the summary statistics behind this kind of chart, see our plain-language guide to descriptive statistics.
Sources
Standard formulas for the normal, gamma and uniform distributions.
