Skill: Interpret histograms

A histogram shows how many data values fall within each numerical interval, called a bin.

• The horizontal axis shows ranges, such as $10$–$19$.
• The vertical axis shows frequency, or how many values are in each range.
• The bars touch because the intervals are connected numerical ranges.
• A bar does not represent one exact value. For example, the $10$–$19$ bar represents every value from $10$ through $19$.

Worked example

A histogram shows the ages of people at a community event. Its bars have these heights:

Age interval	Frequency
$0$–$9$	$1$
$10$–$19$	$2$
$20$–$29$	$5$
$30$–$39$	$8$
$40$–$49$	$5$
$50$–$59$	$2$
$60$–$69$	$1$

Step 1: Find the most common interval

The tallest bar is for ages $30$–$39$, with a frequency of $8$.

So, the most common age range is approximately $30$–$39$.

Step 2: Estimate the center

The bars are highest near $30$–$39$ and decrease on both sides. Therefore, the center of the data is approximately in the $30$–$39$ age range.

A histogram usually lets us estimate the center, not find an exact value.

Step 3: Describe the spread

The data extend from about age $0$ to age $69$. Thus, the ages have a spread of roughly $70$ years.

The exact smallest and largest ages cannot be determined from the histogram; we only know the intervals containing them.

Step 4: Describe the shape

The bars rise toward the middle and then fall in a similar way on both sides. The distribution is approximately symmetric and mound-shaped.

There is one clear peak, or main high point, at $30$–$39$.

Main idea

To interpret a histogram, look for:

1. The tallest bar: the most common interval.
2. The middle of the bars: the approximate center.
3. The full span of the bars: the spread.
4. The overall pattern: such as a single peak, several clusters, gaps, or a tail extending farther on one side.

Always remember that the bars represent ranges of values, not individual categories or exact data values.