A histogram is a graph that shows how data are distributed by grouping values into bins (intervals) and showing how many observations fall into each bin.
It’s perfect for visualizing:
- shape (skewed, symmetric, bimodal)
- spread
- clusters
- outliers
Think of it as stacking blocks into intervals to see where the data pile up.
⭐ Key Features of a Histogram
- X‑axis: the bins (ranges of values)
- Y‑axis: frequency (count) or relative frequency (proportion)
- Bars touch because the data are continuous or ordered
- Bin width matters — too wide hides structure, too narrow creates noise
⭐ Examples
Example 1: Test Scores
Suppose 30 students take a math test, and their scores range from 40 to 100.
If we choose bins of width 10 (40–49, 50–59, …):
| Score Range | Frequency |
|---|---|
| 40–49 | 2 |
| 50–59 | 5 |
| 60–69 | 8 |
| 70–79 | 9 |
| 80–89 | 4 |
| 90–100 | 2 |
A histogram would show:
- A peak around 70–79
- Fewer very low or very high scores
- A roughly bell‑shaped distribution
Example 2: Heights of 100 People
Heights (in cm) might fall between 150 and 200.
If we use bins of width 5 cm:
- 150–155: 3 people
- 155–160: 7
- 160–165: 15
- 165–170: 22
- 170–175: 25
- 175–180: 18
- 180–185: 8
- 185–190: 2
The histogram would show:
- A strong peak around 170–175
- A symmetric, bell‑shaped pattern
- Very few extremely tall or short individuals
Example 3: Daily Coffee Consumption
Survey 50 adults on how many cups of coffee they drink per day.
| Cups per Day | Frequency |
|---|---|
| 0 | 6 |
| 1 | 12 |
| 2 | 18 |
| 3 | 10 |
| 4 | 3 |
| 5+ | 1 |
A histogram would show:
- A right‑skewed distribution
- Most people drink 1–2 cups
- A long tail of heavy coffee drinkers
⭐ Histogram vs. Bar Chart (Quick Reminder)
| Feature | Histogram | Bar Chart |
|---|---|---|
| Data type | Numerical | Categorical |
| Bars touch? | Yes | No |
| X‑axis | Intervals | Categories |
| Shows | Distribution | Counts per category |