Histograms - Displaying Grouped Continuous Data
A histogram looks similar to a bar chart, but it is used for continuous data grouped into intervals called classes. Unlike a bar chart, the bars in a histogram touch each other because the data is continuous – there are no gaps between classes.
Histogram vs. Bar Chart
| Feature | Bar Chart | Histogram |
|---|---|---|
| Data type | Discrete or categorical | Continuous, grouped |
| Gaps between bars | Yes | No |
| X-axis | Categories | Numerical scale (class intervals) |
| Bar width | Equal (and arbitrary) | Equal to class width |
| What bars show | Frequency | Frequency (or frequency density for unequal classes) |
Equal Class Width Histograms
When all classes have the same width, the height of each bar equals the frequency. This is the most common type at introductory level.
Worked Example
Draw a histogram for the following grouped data (class width = 10).
| Height (cm) | Frequency |
|---|---|
| 140 – 150 | 4 |
| 150 – 160 | 9 |
| 160 – 170 | 14 |
| 170 – 180 | 8 |
| 180 – 190 | 5 |
Total students = 4 + 9 + 14 + 8 + 5 = 40.
The tallest bar is the 160–170 cm class with frequency 14 – this is the modal class.
Key Takeaways
- Histograms display grouped, continuous data – bars have no gaps.
- The x-axis is a continuous numerical scale, not a list of categories.
- When classes have equal width, bar height = frequency.
- The class with the tallest bar is called the modal class.
Practice Questions
- Draw a histogram for ages: 0–10 (7), 10–20 (12), 20–30 (18), 30–40 (10), 40–50 (3).
- Using the histogram above, how many people are younger than 20?
- State the modal class in the example histogram.
- Why do the bars in a histogram touch, while bar chart bars do not?
- A histogram shows test scores: 50–60 (8 students), 60–70 (15), 70–80 (22), 80–90 (12), 90–100 (3). How many students scored 70 or above?