How to Read a Five-Number Summary

Five numbers can describe a whole data set at a glance, so which five are they? A five-number summary is the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Together these five values show you where the data starts, where the middle sits, how spread out it is, and where it ends. Draw them as a box plot and you can read center, spread, and skew in one quick look, without staring at a long list of raw values.

The Five Numbers

A five-number summary always lists the same five values, in order from smallest to largest. Each one marks a landmark position in your sorted data.

• Minimum: the smallest value in the data set.
• First quartile (Q1): the value that 25 percent of the data falls at or below.
• Median: the middle value, splitting the data into a lower and upper half.
• Third quartile (Q3): the value that 75 percent of the data falls at or below.
• Maximum: the largest value in the data set.

Notice the pattern: the three quartiles cut the sorted data into four equal groups. To review how Q1 and Q3 are computed, see our guide on percentiles and quartiles explained.

What Each Number Tells You

Each of the five values answers a different question about your data. Read together, they paint a full picture without listing every point.

The minimum and maximum mark the two ends of your data. The distance between them is the range, a rough measure of total spread. The median marks the center, the point where half the values sit below and half sit above. It is a stable center that outliers do not pull around much.

Q1 and Q3 mark the edges of the middle half of the data. The gap between them, called the interquartile range (IQR), tells you how tightly the central values cluster. A small IQR means the middle bunches close together, while a large IQR means it spreads wide.

Because it leans on the median and quartiles, the five-number summary resists the pull of extreme values. One huge or tiny point can drag the mean far off, but it barely moves these landmarks. That makes the summary a sturdy way to describe messy real-world data.

How the Box Plot Is Built

A box plot, also called a box-and-whisker plot, turns the five numbers into a simple picture. It is built the same way every time.

First, draw a box from Q1 to Q3. This box holds the middle 50 percent of the data, and its width is the IQR. Next, draw a line inside the box at the median. That line shows where the center falls within the middle half.

Finally, draw two whiskers: one line from the left side of the box out to the minimum, and one from the right side out to the maximum. The whiskers show how far the data reaches beyond the middle half. That is the whole plot: a box for the center and two whiskers for the tails.

Reading Spread and Skew From a Box Plot

Once the plot is drawn, its shape tells a story. You can read spread and skew straight from the box and whiskers.

• Overall spread: a wider plot from minimum to maximum means more spread; a narrow one means the values sit close together.
• Middle spread: a wide box means a large IQR and a loose middle half; a thin box means a tight middle.
• Median position: a median near the box’s center suggests a fairly balanced middle.
• Right skew: the right whisker or right side of the box is longer, so higher values stretch out further.
• Left skew: the left whisker or left side of the box is longer, so lower values stretch out further.

In our example, the right whisker runs from 11 to 15, a length of 4. The left whisker runs from 2 to 4.5, a length of 2.5. The longer right whisker points to a slight right skew.

Outliers and the 1.5 x IQR Rule

Sometimes a value sits far from the rest of the data. A common way to flag these outliers uses the IQR.

First, find the IQR, then multiply it by 1.5. Subtract that amount from Q1 to get the lower fence, and add it to Q3 to get the upper fence. Any value beyond a fence is a possible outlier.

For our data, IQR = 6.5, so 1.5 x 6.5 = 9.75. The lower fence is 4.5 – 9.75 = -5.25, and the upper fence is 11 + 9.75 = 20.75. Every value from 2 to 15 falls inside these fences, so this data set has no outliers. On a plot, outliers are often drawn as separate dots beyond the whiskers.

Comparing Symmetric and Skewed Shapes

Comparing two box plots side by side makes skew easy to spot. The clue is where the median sits and how the whiskers balance.

In a symmetric shape, the median sits near the center of the box, and both whiskers are close to the same length. In a right-skewed shape, the median leans toward the left side of the box, and the right whisker stretches longer. A left-skewed shape mirrors this, with a longer left whisker.

Skew matters because it hints at what pulls the data. Income and house prices often skew right, since a few very high values stretch the top tail. Spotting that shape on a plot warns you the mean may sit higher than the median.

A Quick Worked Example

Let us build a full five-number summary from scratch. Take this small data set, already sorted: 2, 4, 5, 7, 8, 10, 12, 15. There are eight values.

The minimum is 2 and the maximum is 15. With eight values, the median is the average of the 4th and 5th values: (7 + 8) / 2 = 7.5. The lower half is 2, 4, 5, 7, so Q1 is (4 + 5) / 2 = 4.5. The upper half is 8, 10, 12, 15, so Q3 is (10 + 12) / 2 = 11.

So the summary is: min 2, Q1 4.5, median 7.5, Q3 11, max 15. The IQR is 11 – 4.5 = 6.5. Need a refresher on finding the middle value? See how to find the median. Note that software may compute quartiles slightly differently, so your Q1 or Q3 can vary by method.

Frequently Asked Questions About the Five-Number Summary

Sources

This article is for general education only, not professional statistical advice. Methods and notation can vary by field, course, or software, so follow your textbook or instructor for exact conventions. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 11, 2026.