Box Plot Explained: Interpretation, Examples, & Comparison

Why are box plots useful?

Quick summary of key statistics

By displaying the median, interquartile range, and outliers at a glance, boxplots provide a concise snapshot of a dataset’s center and spread.

Box plots divide the data into sections containing approximately 25% of the data in that set.

Box plots are useful as they provide a visual summary of the data enabling researchers to quickly identify mean values, the dispersion of the data set, and signs of skewness.

Note that the image above represents data that has a perfect normal distribution, and most box plots will not conform to this symmetry (where each quartile is the same length).

Average score of a data set

The median is the average value from a set of data and is shown by the line that divides the box into two parts. Half the scores are greater than or equal to this value, and half are less.

Skewness of a data set

The box plot shape will show if a statistical data set is normally distributed or skewed.

When the median is in the middle of the box, and the whiskers are about the same on both sides of the box, then the distribution is symmetric.

When the median is closer to the bottom of the box, and if the whisker is shorter on the lower end of the box, then the distribution is positively skewed (skewed right).

When the median is closer to the top of the box, and if the whisker is shorter on the upper end of the box, then the distribution is negatively skewed (skewed left).

Dispersion of a data set

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

The smallest and largest values are found at the end of the ‘whiskers’ and are useful for providing a visual indicator regarding the spread of scores (e.g., the range).

The interquartile range (IQR) is the box plot showing the middle 50% of scores and can be calculated by subtracting the lower quartile from the upper quartile (e.g., Q3−Q1).