## How to read and interpret a box plot

A box plox, or box and whisker plot, is a way to visualize the spread and centers of a data set. The measures of spread include the interquartile range and the mean of the data set. The measures of center include the mean or average and median.

The lines extending from the boxes are known as the "whiskers", and indicate variability outside the upper and lower quartiles.  Outliers are plotted as individual dots in-line with the whiskers.  Box plots can be drawn vertically or horizontally.

### What you can learn from a Box Plot

• What the key values are, such as

• minimum

• first quartile

• median

• third quartile

• maximum

• If there are any outliers and their values

• Is the data symmetrical

• How tightly is the data grouped

• If the data is skewed and the direction

### How to read a Box Plot

The following explanations use the labels shown in the example to explain where to locate data on a box plot: source: Data Visualization Catalog

#### Find the minimum

The minimum (10) is the found at the Lower Extreme

#### Find the first quartile

The first quartile or Q1 (30) is found at the Lower Quartile

#### Find the median

The median (about 55) is marked by the vertical bar

#### Find the third quartile

The third quartile or Q3 (about 78) is found at the Upper Quartile

#### Find the maximum

The maximum (90) can be found at the Upper Extreme

#### Identify outliers

An outlier exists (about 5) outside of the box and its whiskers near the Lower Extreme

### How to interpret a Box Plot

The following statements use an example from [email protected] to describe how box plots can be used to interpret their student survey data and provides an overview of interpreting box plots in general: source: [email protected]

#### General observations about box plots

• The quartiles of the box plot divides the data into quartile groups labeled 1-4 from the bottom for vertical and left for horizontal

• A box plot that is comparatively short (2) suggests a high level of agreement between groups

• A box plot that is comparative tall (1) and (3) suggests very different opinions between groups

• One box plot that is much higher or lower (3) and (4) than another suggests a difference between groups.

• Obvious differences between box plots (1) and (2) suggests areas worthy of further investigation

• If the four sections of the box are uneven in size (1), this shows agreement in certain parts but more variable results in others.

• The same median with different distributions (1), (2), (3) should be interpreted within the patter of the whole distribution.

### References

"Understanding and interpreting box plots"; [email protected]

https://www.wellbeingatschool.org.nz/information-sheet/understanding-and-interpreting-box-plots

"Box and Whisker Plot"; The Data Visualisation Catalogue

https://datavizcatalogue.com/methods/box_plot.html

"Box Plot (Box and Whiskers): How to Read One & How to Make One"; Statistics How To

http://www.statisticshowto.com/probability-and-statistics/descriptive-statistics/box-plot/