Median, quartiles and the box plot
Always put the data in order first. The median is the middle value. If there is an odd number of values, it is the one in the middle. If there is an even number, it is the mean of the two middle values. The median splits the data into a lower half and an upper half. The lower quartile Q1 is the median of the lower half and the upper quartile Q3 is the median of the upper half. When the number of values is odd, we leave the median itself out of both halves. Together with the minimum and the maximum we have five numbers, the five-number summary. A box plot draws them: a box from Q1 to Q3, a line inside it at the median, and two whiskers that go to the minimum and the maximum. The box holds about the middle half of the data.
| Minimum | Q1 | Median | Q3 | Maximum |
|---|---|---|---|---|
| 2 | 4 | 8 | 11.5 | 14 |
Human box plot. Seven family members line up from the youngest to the oldest (or from the shortest to the tallest). Find the middle person: that is the median. Find the middle person of each half without the median: those are Q1 and Q3. Write down their ages and draw the box plot.