Skill: Construct histograms

A histogram shows how often numerical values fall within equal-width intervals.

Example

The scores on a quiz were:

$$12,\ 18,\ 21,\ 24,\ 27,\ 31,\ 33,\ 35,\ 41,\ 44,\ 46,\ 48$$

1. Choose equal-width intervals

Use intervals of width $10$:

• $10$–$19$
• $20$–$29$
• $30$–$39$
• $40$–$49$

These intervals are numerical ranges, not separate categories.

2. Count the values in each interval

Score interval	Scores in the interval	Frequency
$10$–$19$	$12, 18$	$2$
$20$–$29$	$21, 24, 27$	$3$
$30$–$39$	$31, 33, 35$	$3$
$40$–$49$	$41, 44, 46, 48$	$4$

3. Draw and label the axes

• Label the horizontal axis Quiz score.
• Label the vertical axis Frequency.
• Mark the score intervals $10$–$19$, $20$–$29$, $30$–$39$, and $40$–$49$ on the horizontal axis.
• Use a consistent vertical scale: $0,1,2,3,4$.

4. Draw the bars

Draw one bar for each interval:

• The bar for $10$–$19$ has height $2$.
• The bar for $20$–$29$ has height $3$.
• The bar for $30$–$39$ has height $3$.
• The bar for $40$–$49$ has height $4$.

The bars should touch because the intervals represent ranges of numerical values. A histogram uses touching bars, while a bar graph usually has separated bars for categories such as fruits or colors.