Data from a statistical question is easier to understand in a picture. Two common pictures are the dot plot and the histogram.
Key idea
A dot plot puts one dot above a number line for each value. A histogram groups the values into equal intervals and draws a bar for each interval; the bar's height is how many values fall in it, and the bars touch.
Why it works
A dot plot keeps every single value, which is perfect for a small set of whole numbers. With many values spread over a wide range, a dot plot gets crowded, so a histogram counts how many values land in each interval instead. The intervals must be the same width so that taller really means "more values", and they meet with no gaps so every value has exactly one place to go. That is why the bars touch.
Worked example: Read a dot plot
In the dot plot of pets, how many students have more than 2 pets?
- Count the dots to the right of 2: above 3, 4 and 6.
- $2 + 1 + 1 = 4$.
Answer: 4 students
Worked example: Build a histogram
Sort these travel times into intervals 0–9, 10–19, 20–29 and 30–39: 5, 12, 25, 8, 31, 14, 19, 22, 3, 15.
- 0–9: 5, 8, 3, so 3 values.
- 10–19: 12, 14, 19, 15, so 4 values.
- 20–29: 25, 22, so 2 values. 30–39: 31, so 1 value.
- Check: $3 + 4 + 2 + 1 = 10$ values in all.
Answer: Bar heights 3, 4, 2 and 1.
Common mistake
Leaving gaps between histogram bars, or using intervals of different widths. A gap suggests some values are missing; a wide interval collects more values just because it is wide, so its bar looks important when it is not. Quick check: every interval should hold the same span of numbers, and each interval should start where the last one ended.