Grouping a list of values into intervals reveals center, spread, and skew at a glance.
A list of 40 commute times is hard to scan for a typical value or unusually long trips. The human eye reads shape more easily than a long sequence of numbers.
A frequency distribution groups values into intervals and counts how many fall in each one. In a histogram, height represents frequency when bins have equal width; when widths differ, area must represent frequency.
Key question
How should continuous data be grouped into intervals so that the overall distribution becomes visible?
What does a frequency distribution do?
| Commute-time interval | Frequency | Relative frequency |
|---|---|---|
| 10–20 minutes | 5 | 12.5% |
| 20–30 minutes | 9 | 22.5% |
| 30–40 minutes | 8 | 20.0% |
| 40–50 minutes | 7 | 17.5% |
| 50 minutes or more | 11 | 27.5% |
Frequency is the number of observations. Relative frequency is the proportion of the full sample. Relative frequencies are more useful when comparing groups of different sizes.
How is a histogram different from a bar chart?
A bar chart compares distinct categories, so gaps between bars are acceptable. A histogram's horizontal axis consists of consecutive numeric intervals, so the bars touch.
| Histogram | Bar chart |
|---|---|
| Continuous numeric data | Categorical data |
| Order fixed by numeric scale | Category order can often change |
| Bin boundaries and widths matter | Bar width usually has no data meaning |
When bin widths differ
If interval widths are unequal, use frequency density on the vertical axis so that bar area—not height alone—represents frequency.
Why do bin settings matter?
Too few bins can hide peaks and gaps. Too many can exaggerate random jaggedness. Even with the same number of bins, shifting the starting boundary can change the picture.
Practical rule
Do not trust a single automatic setting. Try several bin counts and starting points and look for features that persist.
What should you read from a histogram?
Limitation
A histogram groups observations into bins, so individual values are hidden. Use the raw data or another plot to investigate exact values and potential outliers.
Change the number of bins
Start with a small number of bins to see the broad outline, then increase the count to inspect finer structure. Notice when conclusions about peaks, skew, or extremes become unstable.
What to notice
The same data can look different under different bin settings. Base your interpretation on features that remain visible across reasonable choices.