Box Plot

What is a Box Plot?

With a box plot you can graphically display a lot of information about your data. Among other things, the median, the interquartile range (IQR) and the outliers can be read off from a box plot.

The data used are mostly metric scaled, such as a person's age, annual electricity consumption, or temperature. Often a box plot is created to compare and contrast two or more groups. For example, the age of different groups.

Interpretation of a Box Plot

The box itself indicates the range in which the middle 50% of all values lie. Thus, the lower end of the box is the 1st quartile and the upper end is the 3rd quartile.

Roughly 25% of the data lie at or below Q1, roughly 25% lie at or above Q3, and the middle 50% lie between Q1 and Q3. Exact percentages can differ slightly because of tied values or the method used to calculate quartiles.

Let's say we look at the age of individuals in a box plot, and Q1 is 31 years. This means that roughly 25% of the participants are 31 years old or younger. If Q3 is 63 years, then roughly 75% of the participants are 63 years old or younger. The middle 50% are therefore approximately between 31 and 63 years old. The difference between Q1 and Q3 is the interquartile range.

In the box plot, the solid line indicates the median and the dashed line indicates the mean.

For example, if the median is 42, about half of the observations are at or below 42 and about half are at or above 42. The median thus divides the ordered observations into two halves.

The whiskers extend to the most extreme observed values that are still within the lower and upper fences. These fences are Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Observations beyond the fences are shown separately as potential outliers. If there are no such observations, the whiskers extend to the minimum and maximum.

The upper whisker therefore ends at the largest observed value that is no greater than the upper fence. The lower whisker ends at the smallest observed value that is no less than the lower fence.

Points beyond the fences are considered potential outliers. If no point lies beyond either fence, the T-shaped whiskers indicate the maximum and minimum values.

Box Plot Example

Studying Patient Recovery Times for Different Treatments

In a medical study, researchers may be examining recovery times for patients undergoing different types of treatment for the same condition.

By using box plots for each treatment type, researchers can visualize the distribution of recovery times. They can see the median recovery time for each treatment, the range of times, and any outliers (e.g., unusually long or short recovery times).

This helps in determining which treatment may be most effective, or whether some treatments have more variable outcomes than others.

Create Box Plot online

With numiqo you can easily create a box plot online. To do this, click on the statistics calculator, copy your own data into the table, select the tab "Descriptive" or "Charts" and click on the variables for which you want to create a box plot.

In the upper box plot created with numiqo online, each box represents age for one location of fall (aisle, bathroom, recreation room and hospital).