📊 Histograms and Dot Plots
SAT Math — Statistics & Data Analysis
Master reading, interpreting, and computing statistics from two of the most common data displays on the SAT.
1. What Is a Histogram?
A histogram is a special bar graph that displays the frequency distribution of numerical (quantitative) data.
- Horizontal axis — shows equal-width intervals (also called bins).
- Vertical axis — shows frequency (count) or relative frequency (percentage).
- No gaps between bars — the data is continuous.
- Each bar tells you how many values fall within that interval.
Sample Histogram — Test Scores
Interactive visualization — available in the full lesson
2. Reading a Histogram
| Task | How To |
|---|---|
| Interval width | Subtract the left endpoint from the right endpoint of any bin. |
| Frequency of an interval | Read the height of that bar. |
| Total data values | $\text{Total} = \sum (\text{all bar heights})$ |
| Relative frequency | $\text{Relative freq} = \dfrac{\text{frequency}}{\text{total}}$ |
| Percentage | $\text{Percentage} = \text{relative frequency} \cdot 100\%$ |
⚠️ SAT Trap: Read the height of the bar, not its width. The width tells you the interval size, not the count.