What Is a Box Plot? Quartiles and Spread

A box plot summarizes a batch of numbers without plotting every value. The box marks the middle half of the data. A line inside the box marks the median. Whiskers extend toward the lower and upper ends, and isolated markers flag points that sit far outside that range. The chart is also called a box-and-whisker plot. This page explains how to read that summary. To draw one, use the box and whisker plot maker.

What the five numbers mean

Sort the observations from smallest to largest. Then pick five landmarks:

• Minimum used by the whisker, not always the smallest raw value once outliers are split off.
• First quartile (Q1). One quarter of the values are at or below this point. It is the bottom of the box.
• Median (Q2). Half the values are at or below this line. It splits the box.
• Third quartile (Q3). Three quarters of the values are at or below this point. It is the top of the box.
• Maximum used by the whisker, again after extreme points are set aside.

The distance from Q1 to Q3 is the interquartile range (IQR). It is the height of the box if the plot is vertical. A tall box means the middle half of the data is spread out. A short box means those values sit close together.

Whiskers and outliers

A common rule draws each whisker to the last observation that still falls within 1.5 times the IQR beyond the box. Points outside that fence are plotted as separate markers. Those markers are the outliers.

That rule is a convention, not a law of the data. Always check the caption. Some charts extend whiskers to the actual minimum and maximum and do not mark outliers at all. If you compare two box plots, they need the same rule.

Outliers are not automatically errors. A delivery time of 40 hours can be a real failure in a set that otherwise finishes in under 4. Investigate the row before you drop it.

A worked comparison

Two support queues record resolution time in hours:

Queue	Q1	Median	Q3	Low whisker	High whisker	Outlier
Email	2	4	6	1	11	18
Chat	1	2	3	0.5	6	none

Email's box is taller, so the middle half of email tickets takes longer and varies more. Chat's median is lower and its box is shorter. The email outlier at 18 hours is visible as a separate point; chat has none under the same fence rule.

A bar chart of average resolution time would hide this. Email might average close to chat if you ignore the spread, or look worse only because of the single 18-hour ticket. The box plot shows both the typical case and the extreme.

When to use a box plot

Use one when the question is about distribution, not a single total:

• Test scores for several classes
• Salaries across teams, when you are allowed to show the spread
• Latency for a few services
• Lab measurements repeated on each group

You need enough observations for quartiles to mean something. Five numbers can be computed from a tiny sample, but the box will jump around if you add one row. Dozens of observations per group is a more stable picture. For a handful of raw points, a scatter plot that shows every value is more honest.

Skip a box plot when:

• You are comparing one number per category, such as revenue by region. Use a bar graph maker.
• You need the full shape, including two peaks. A box cannot show that a distribution is bimodal. Use a histogram maker.
• The audience has never seen quartiles and you only have time for one sentence. A sorted bar of medians may be clearer, with the box plot in an appendix.

How to read several boxes

Put groups on one axis and the numeric measure on the other. In a vertical layout, compare:

• Median lines for the typical value.
• Box heights for the spread of the middle half.
• Whisker length for how far the non-extreme values reach.
• Outlier markers for rare extremes.

Do not rank groups by the top whisker alone. A group with a low median and one wild outlier is not "higher" than a group with a high, tight box.

Horizontal boxes help when group names are long. The statistics are the same; only the orientation changes.

Box plot versus a histogram

A histogram counts how many values fall in each bin, so you see peaks and gaps. A box plot compresses that shape into a few landmarks, which makes several groups comparable in one row. Use both when you have one group to explain in detail and several groups to compare: histogram for the shape, boxes for the comparison.

Neither chart shows the sample size by itself. Label n for each group. A tight box on 12 observations is weaker evidence than the same box on 12,000.

Common mistakes

• Reading the box as the full range. The box is only the middle 50 percent.
• Assuming the median cuts the box in half visually. It does not, unless Q2 sits halfway between Q1 and Q3. An off-center median is skew.
• Comparing averages to medians without saying which is which. The box plot's center line is the median.
• Hiding the fence rule. State whether whiskers stop at 1.5 IQR or at the min and max.
• Starting the axis at a value that clips the lower whisker. If length encodes spread, include zero when the measure can be zero, or mark a broken axis explicitly.

Build one in BeCharts

1. Open the box and whisker plot maker or a layout under box plot templates.
2. Enter grouped samples or a five-number summary, depending on the template.
3. Check that every group uses the same whisker rule and that outliers you care about are still visible.
4. Export PNG, SVG, or PDF. No account is required.

For the wider choice among bars, lines, and distributions, use types of charts.

Frequently asked questions

What does the box in a box plot show?

The box is the middle half of the data, from the first quartile to the third quartile. The line inside the box is the median.

What is the difference between a box plot and a histogram?

A box plot summarizes a distribution with quartiles and whiskers. A histogram counts values in each bin so you can see peaks. https://www.becharts.com/histogram-maker

How do I make a box plot in BeCharts?

Open the box and whisker plot maker, enter the groups, and export PNG, SVG, or PDF. https://www.becharts.com/boxplot-maker