What it shows
The mirror image of the right-skewed histogram. Most observations fall at the high end and the tail extends to the left. Scores on an easy exam often have this shape.
It reflects the same gamma distribution (8 − X), so the bars are expected counts for 1,000 observations, with the density curve drawn over them.
How to read it
The tallest bars are near the right edge, at 178 and 174.
Reading leftward, the counts fall to 3 and then 2 in the first bins.
The long tail is on the left, so this is left skew, also called negative skew.
The numbers behind it
- 8 − X, where X has a gamma distribution with shape 2 and scale 1. n = 1,000, bins of width 0.5 from 0 to 8.
- Counts, left to right: 2, 3, 4, 6, 9, 14, 21, 30, 44, 63, 88, 119, 152, 178, 174, 90.
- 0.30% of the distribution lies below 0.
Ways to use it in teaching
Students often name skew by the side the peak is on; this one peaks on the right and is called left-skewed, which makes it a useful check.
Combine it with the mean, median and mode diagram to show where each measure falls.
Ceiling effects are a natural discussion point: ask where one might produce this shape in students’ own fields.
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.
