Skill: Create histograms

A histogram shows how numerical data are spread across equal-width intervals.

Example

The numbers of minutes 12 students spent reading are:

$$2,\ 4,\ 5,\ 7,\ 8,\ 10,\ 11,\ 11,\ 13,\ 14,\ 16,\ 18$$

1. Choose equal-width intervals

Use intervals that are each 5 minutes wide:

• $0$–$4$
• $5$–$9$
• $10$–$14$
• $15$–$19$

These intervals are next to one another and do not overlap. In boundary notation, they mean:

• $0 \leq x < 5$
• $5 \leq x < 10$
• $10 \leq x < 15$
• $15 \leq x < 20$

So, a value exactly equal to $5$ goes in the $5$–$9$ interval.

2. Count the values in each interval

Reading time	Values in the interval	Frequency
$0$–$4$	$2,4$	$2$
$5$–$9$	$5,7,8$	$3$
$10$–$14$	$10,11,11,13,14$	$5$
$15$–$19$	$16,18$	$2$

The frequency is the number of data values in each interval.

3. Draw and label the histogram

• Label the horizontal axis Reading time (minutes).
• Label the vertical axis Frequency.
• Mark the frequency scale from $0$ to $5$.
• Draw one bar for each interval.
• Make the bar heights $2,3,5,$ and $2$.
• Make the bars touch because the intervals represent continuous numerical ranges.

The finished histogram has bars over $0$–$4$, $5$–$9$, $10$–$14$, and $15$–$19$, with heights matching their frequencies. Unlike a bar graph, a histogram’s bars touch.