Probability and Statistics > Descriptive Statistics > How to read a box plot

## What is a Boxplot?

A boxplot, or box and whisker diagram, is a way to show the spread and centers of a data set. Measures of spread include the interquartile range and the mean of the data set. Measures of center include the mean or average and median (the middle of a data set). When you look at a boxplot, it’s much easier to see how your data is centered.

## How to read a box plot

A boxplot is a way to show a five number summary in a chart. The main part of the chart (the “box”) shows where the middle portion of the data is: the interquartile range. The ends of the box show the first quartile (the 25% mark) and the third quartile (the 75% mark). The far left of the chart (at the end of the left “whisker”) is the minimum and the far right is the maximum. The median is represented by a vertical bar in the center of the box. Box plots aren’t used that much in statistics. However, they can be a useful tool for getting a quick summary of data.

## How to read a box plot: Steps

**Step 1:** *Find the minimum.*

The minimum is the far left hand side of the graph, at the tip of the left whisker. For this graph, the left whisker end is at approximately 0.75.

**Step 2:***Find Q1, the first quartile.*

Q1 is represented by the far left hand side of the box. In this case, about 2.5.

**Step 3:** *Find the median*.

The median is represented by the vertical bar. In this boxplot, it can be found at about 6.5.

**Step 4:** *Find Q3, the third quartile*.

Q3 is the far right hand edge of the box, at about 12 in this graph.

**Step 5:** *Find the maximum*.

The maximum is the end of the “whiskers”: in this graph, at approximately 16.

*All done. That’s how to read a box plot!*

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step solutions, just like this one!

**Note on Outliers:**

Data sets can sometimes contain **outliers** that are suspected to be anomalies (perhaps because of data collection errors or just plain old flukes). If outliers are present, the whisker on the appropriate side is drawn to 1.5*IQR rather than the data minimum or the data maximum. Small circles or unfilled dots are drawn on the chart to indicate where suspected outliers lie. Filled circles are used for known outliers.

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I didn’t know if this would help other people remember 5 number sequence on a box plot. They way I think of it is as a dog…the median is the middle of the dog’s nose, Q1 is the left nostril, Q3 is the right nostril,and minimum is the left wiskers and maximum is the right wiskers. Hope this helps!

Sounds like you are a visual learner :)

My biggest challenge is the heighth of the boxplot. In this example I understand how the minimum, Q1, median, Q3 and the maximum were plotted on the boxplot; however, I don’t understand how we are to determine the heighth of the boxplot OR does that matter as long as the min, Q1, median, Q3 and max are plotted correctly?

Thanks

I think Cathy’s response to the boxplot is a good example to remember. The article is also easy to understand because the example and diagram tells you straight forward where to find the minimun, maximum, median, Q1, and Q3.

Evelyn,

Sometimes the height can give information about the sample size. However, in elementary statistics, that topic isn’t covered (in other words, for this class, height does not matter).

Stephanie

Very helpful, I like the way that it showed the two different boxes and examples.and I liked that it was labeled and that it explained everything.

The lengths of the tails are very easy to calculate. You find your IQR and multiply it by 1.5. Then you add to your Q3 and subtract from your Q1. This gives your fences. Your legs, extend from the ends off the boxes to all the data values within your fences. Every number outside your fences are outliers.

Q3 + 1.5*IQR = Upper fence

Q1 – 1.5*IQR = Lower fence

Its sounds like a visual learning.

It should probably be mentioned that if there is an outlier, your minimum/maximum is not contained within a “whisker” but is the outlier. Just to avoid confusion.

Joshua,

Very true! I did mention more on outliers here: http://www.statisticshowto.com/articles/what-is-a-boxplot/

Thanks for dropping by,

Stephanie

I find that the box and whisker plot is not my best work but it defiantly is improving.

Hi may I know in what condition, the minimum value will be greater than Q1 when the data is with some outlier.

The minimum is defined as Q0 ≡ Quartile 0. It’s not possible for it to be greater than Q1.

Helping my granddaughter with math. Her assignment had me befuddled. Thanks for helping me learn so I can help her!

There are box plot with the 25th percentile or first querter or 0.25 proportion is same as the median. What do you think about these plot. They are in medical literature. Especially on assessment of pain scores reports.