Measures of Dispersion for Ungrouped Data
Interquartile range
The spread of the middle half of the data, from the first to the third quartile.
| English | Interquartile range |
|---|---|
| Bahasa Melayu | Julat antara kuartil |
| 中文 | 四分位距 |
How it is used
For 3, 5, 7, 9, 11, 13, 15 the median is 9. The lower half 3, 5, 7 gives Q1 = 5 and the upper half 11, 13, 15 gives Q3 = 13, so the interquartile range is 13 − 5 = 8.
Where it shows up in SPM
In Measures of Dispersion for ungrouped data. Paper 1 may ask for Q1, Q3 or their difference from an ordered list; Paper 2 links it to a box plot or asks you to compare the spread of two groups using the middle half.
Don't confuse it with
Open the chapter: Measures of Dispersion for Ungrouped Data →
Frequently asked questions
How do I find the quartiles when there is an odd number of values?
Order the data, take the median as the middle value, then exclude it. The lower half gives Q1 as its median and the upper half gives Q3.
For 3, 5, 7, 9, 11, 13, 15 you drop the 9, so Q1 = 5 and Q3 = 13.
When is the interquartile range better than the range?
When the data contains outliers. Because it looks only at the middle 50 percent, a single very large or very small value does not change it, so it gives a fairer picture of the typical spread than the range does.