Boxplot (box plot)

A boxplot is suitable for the graphical representation of data. The following values are considered:

• Minimum (the smallest value)
• First / lower quartile
• Median
• Third / upper quartile
• Maximum (the largest value)

A boxplot looks like this:
The minimum is shown on the left and the maximum on the right as an antenna. In between is the box, which consists of the two middle quarters, which are divided by a quartile and the median. The left end of the box is the first and the right end the third quartile. The median is marked by a vertical line in the box.

Example

Ten students were asked how many hours they spend on the computer each week. Present the results in a box plot.
4, 8, 5, 5, 9, 6, 14, 8, 12, 13

1. Sort the data series by size:

   $4, 5, 5, 6, 8, 8, 9, 12, 13, 14$

2. Determine parameters

   $4, 5, \color{blue}{5}, 6, 8, |$ $8, 9, \color{green}{12}, 13, 14$
   
   Mimimum: $4$ (smallest value)
   1st quartile: $\color{blue}{5}$ (median of the first half)
   Median: $8$ (the average of 8 and 8)
   3rd quartile: $\color{green}{12}$ (median of the second half)
   Maximum: $14$ (largest value)

3. Create and evaluate boxplot

   
   
   
   The median is 8 hours a week. There were 4 to 14 hours a week represented. 50% of the students spend 5 to 12 hours on the computer. There is no strong outlier (extreme value).