What it shows
A bell-shaped histogram with one peak in the middle and tails that fall away at the same rate on both sides. The bars are not a random sample: each is the count expected from 1,000 observations of a standard normal distribution.
A dashed curve over the bars is the normal density scaled to the same counts. It is one of a set of six histogram shapes drawn to the same layout.
How to read it
Each bar covers a bin 0.5 wide, from −3 on the left to 3 on the right.
The two tallest bars sit either side of zero, at 191 each.
The two halves match bar for bar about zero, which is what symmetric means here.
The numbers behind it
- Normal distribution, mean 0, standard deviation 1. n = 1,000, bins of width 0.5 from −3 to 3.
- Counts, left to right: 5, 17, 44, 92, 150, 191, 191, 150, 92, 44, 17, 5.
- 0.27% of the distribution lies outside the plotted range.
Ways to use it in teaching
Show it first, as the reference shape for the other five histograms in the set.
Have students add up the counts and explain why the total falls a little short of 1,000.
Discuss what would change if the bins were twice as wide.
For how charts like this one are chosen and reported in a results chapter, see our guide to analyzing quantitative results.
Sources
Standard formulas for the normal, gamma and uniform distributions.
