 # Boxplot

What is a boxplot? With a boxplot 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 in a boxplot.

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

## How is a boxplot interpreted?

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. Therefore below Q1 lie 25% of the data and above Q3 lie 25% of the data, in the box itself lie 50% of your data. Let's say we look at the age of individuals in a boxplot, and Q1 is 31 years, then it means that 25% of the participants are younger than 31 years. If Q3 is 63 years, then it means that 25% of the participants are older than 63 years, 50% of the participants are therefore between 31 and 63 years old. Thus, between Q1 and Q3 is the interquartile range.

In the boxplot, the solid line indicates the median and the dashed line indicates the mean. For example, if the median is 42, this means that half of the participants are younger than 42 and the other half are older than 42. The median thus divides the individuals into two equal groups.

The T-shaped whiskers go to the last point, which is still within 1.5 times the interquartile range. What does it mean? The T-shaped whisker is either the maximum value of your data but at most 1.5 times the interquartile range. Any observations that are more than 1.5 interquartile range (IQR) below Q1 or more than 1.5 IQR above Q3 are considered outliers. If there are no outliers, the whisker is the maximum value.

So the upper whisker is either the maximum value or 1.5 times the interquartile range. Depending on which value is smaller. The same is true for the lower whisker, which is either the minimum or 1.5 times the interquartile range. Points that are further away are considered outliers. If no point is further away than 1.5 times the interquartile range, the T-shaped whisker indicates the maximum or minimum value.

## Create boxplot online

On DATAtab you can easily create a boxplot 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 boxplot. In the upper boxplot created with DATAtab online, the location of falls in a hospital was contrasted with the age of the persons who fell.

Cite DATAtab: DATAtab Team (2023). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net