Statistics » Box plot

When using box plots, you should know about range and quartiles.

A box plot is also known as a box-and-whisker plot or a box-and-whisker diagram. Sometimes box and whisker is written without hyphens.

What is a box plot?

The median and quartiles divide a row of numbers into four groups of equal size.
This data can be shown in a box plot.

Example
For a row of values it is known that Q₁ = 18, Q₃ = 37 and the median is 29.
The lowest value is 2 and the highest value is 48.

The box plot is drawn like this:

The different areas all have 25% of the values.
The range and interquartile range can also be calculated.
These are also drawn above, but not part of the box plot.

How do you draw a box plot?

When you have a row of values, you have to find the lowest and highest value together with Q₁, the median and Q₃.
You draw a number line that will be the horizontal axis.
Note: If your values are, for example, about time in hours this will also be the label of the axis.

Every number mentioned above, will get a vertical line above the axis.
After that you can make the 'box' and draw the lines (whiskers) between Q₁ and the lowest value and between Q₃ and the highest value.

Example
Luke never feels like answering the phone, so he never picks up.
He writes down how many times the phone rings before they hang up.
7, 3, 8, 6, 8, 5, 4, 5, 3, 6, 2, 6, 9, 1, 2, 7, 5, 8, 7, 6.
Draw a box plot for this data.

Answer:
The numbers in ascending order are:
1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9
The median is 6, Q₁ = 3.5 and Q₃ = 7.