What is a Histogram? Definition, Examples and How to Read One
Last updated: October 16, 2026
A histogram is a chart that shows how a set of numbers is distributed: where most values fall, how spread out they are and whether any are unusual. The range of the data is split into equal intervals called bins, and each bar shows how many values land in its bin.
It answers questions a list of numbers can’t answer at a glance: What is a typical value? Are most values close together or spread out? Is the data lopsided? Are there outliers?
The parts of a histogram
- Bins (classes): equal-width intervals that cover the data, such as 10–20, 20–30, 30–40. They sit on the horizontal x-axis in number order.
- Bars: one per bin. The bars touch, because the bins are next to each other on a continuous number line. A gap means an empty bin, not a separator.
- Y-axis: usually the frequency (count) in each bin. It can also show relative frequency (the share of all values) or density.
- Bin width: the size of each interval. It controls how much detail you see, so it is the most important choice when you make a histogram.
Worked example: 20 quiz scores
A teacher records these scores (out of 50) for a class of 20 students:
12, 18, 21, 23, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 41, 44, 46, 49
Step 1: Choose the bins
The scores run from 12 to 49, a range of 37. Bins of width 10 starting at 10 (10–20, 20–30, 30–40, 40–50) cover everything with round, easy-to-read edges. As a check, Sturges’ rule suggests about log₂(20) + 1 ≈ 5 bins for 20 values, so 4 bins is a sensible amount.
Step 2: Decide where boundary values go
A score of exactly 30 could belong to 20–30 or 30–40. The usual convention is that each bin includes its lower edge and excludes its upper edge, written [30, 40). So 30 goes in the 30–40 bin. Whatever rule you pick, use it for every bin.
Step 3: Count the values in each bin
| Score | Values | Frequency | Relative frequency |
|---|---|---|---|
| 10–20 | 12, 18 | 2 | 10% |
| 20–30 | 21, 23, 25, 27, 28 | 5 | 25% |
| 30–40 | 30, 31, 32, 33, 34, 35, 36, 38, 39 | 9 | 45% |
| 40–50 | 41, 44, 46, 49 | 4 | 20% |
| Total | 20 | 100% |
Step 4: Draw the bars
Open this example in the Histogram Maker to change the bin width and watch the shape change.
What the histogram tells us
- Center: the tallest bar is 30–40, so a typical score is in the 30s. (The mean is 32.1 and the median 32.5.)
- Spread: scores range from the 10s to the 40s, with 70% of students between 20 and 40.
- Shape: fairly symmetric, with a slightly longer tail on the low side. Two students scored under 20 and may need extra help.
Bin width changes the picture
The same 20 scores look different with other bin widths. With width 20 there are only two bars (7 and 13), and the shape disappears. With width 5 there are eight bars, and the result starts to look noisy:
There is no single correct bin width. Start with a rule of thumb, try one or two alternatives, and keep the one that shows the overall shape without random bumps. Our histogram maker picks a width automatically with standard rules (Sturges, square-root, Scott, Freedman–Diaconis) and lets you set your own.
How to read the shape of a histogram
Most histograms you meet will look like one of these:
Mean ≈ median. Heights, measurement error.
Long tail right. Mean > median. Incomes, wait times.
Long tail left. Mean < median. Scores on an easy test.
Two peaks. Often two groups mixed together.
Flat. Every range equally likely, like a fair die.
An isolated bar far from the rest. Check it!
Then look at three things:
- Center: where is the middle of the data? For skewed data, the median is a better summary than the mean, because the long tail pulls the mean toward it.
- Spread: how wide is the histogram? A narrow histogram means consistent values; a wide one means lots of variation.
- Unusual features: gaps, a second peak, or isolated bars far from the rest. These are often the most interesting part of the data, or a sign of a data-entry error.
Histogram or bar chart?
They look alike but answer different questions. A histogram shows the distribution of numbers on a number line, so its bars touch and their order is fixed. A bar chart compares separate categories (such as countries or favorite colors), so its bars have gaps and can be sorted any way you like. See histogram vs. bar chart for the tricky cases.
Common mistakes
- Unequal bins with frequency on the y-axis. A bin twice as wide collects about twice as many values and looks more important than it is. Use equal bins, or switch the y-axis to density.
- Too few or too many bins. Too few hide the shape; too many turn it into noise.
- Comparing groups of different sizes by count. Use relative frequency or percent so a class of 60 doesn’t dwarf a class of 20.
- Gaps between bars. In a histogram, a gap should only mean an empty bin.
Quick FAQ
How many values do I need for a histogram?
You can draw one with 10 or so, but the shape only becomes reliable with about 30 or more values. With very small samples, a dot plot or simply listing the values may be clearer.
Can a histogram show negative numbers or decimals?
Yes. Bins can cover any range, such as −10 to 0 or 1.5 to 2.0. The same rules apply.
What is a frequency distribution table?
It’s the table in Step 3: the bins and how many values fall into each. A histogram is a picture of that table. Our tool builds both, and you can copy the table into Excel or Word.