What it shows
A histogram with three distinct peaks. Each comes from its own normal distribution, and all three share the same spread, so they differ only in their centers and in how many observations each contributes.
As with the rest of the set, the bars are expected counts for 1,000 observations, and the dashed curve is the mixture’s density scaled to the bars.
How to read it
The outer peaks, at −4 and 4, each reach 79.
The middle peak, at 0, reaches 105, because 40% of the observations come from that group against 30% for each of the others.
Between the peaks the counts drop to 5 and 6.
The numbers behind it
- Three normal distributions, each with standard deviation 0.7: 30% with mean −4, 40% with mean 0 and 30% with mean 4.
- n = 1,000, bins of width 0.5 from −6 to 6.
- Counts, left to right: 4, 18, 48, 79, 79, 48, 18, 5, 6, 24, 64, 105, 105, 64, 24, 6, 5, 18, 48, 79, 79, 48, 18, 4.
- 0.13% of the distribution lies outside the plotted range.
Ways to use it in teaching
Discuss what a single mean and standard deviation would tell a reader about these data, and what it would leave out.
A case for plotting data before choosing summary statistics.
Set it beside the bimodal histogram as a pair on mixture distributions.
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.
