Interquartile range in geography
How spread out is the middle half of your data?
The interquartile range (IQR) is the upper quartile minus the lower quartile.
What are quartiles?
Put the values in order. Quartiles divide the data into four parts. Q1 is the lower quartile. Q3 is the upper quartile. The IQR measures the spread of the middle 50% of values.
Why use it?
One very large pebble can change the range a lot. It may have little effect on the IQR. Use both measures to describe how varied your sample is.
Worked example
| Pebble length (mm) |
|---|
| 4 · 6 · 8 · 10 · 12 · 14 · 16 · 30 |
- These eight lengths are already in order. Split them into two halves: 4, 6, 8, 10 and 12, 14, 16, 30.
- Q1 = (6 + 8) ÷ 2 = 7 mm. Q3 = (14 + 16) ÷ 2 = 15 mm.
- IQR = 15 − 7 = 8 mm. The middle half spans 8 mm. The full range is 30 − 4 = 26 mm.
This example uses the median of each half. With an odd number of values, leave out the overall median before finding the two halves. Quartile conventions differ; use the method stated in your question.
Check you’ve got it
The largest pebble changes from 30 mm to 60 mm. Does the IQR change?
Check your answer
No, using this method. Q1 stays 7 mm and Q3 stays 15 mm. The range increases to 56 mm.
Try it yourself
Use this new resource. Check your answers, then try another set.
Interquartile range
Use medians of the lower and upper halves: Q1 is the median of the first four sorted values and Q3 the median of the last four. This convention is stated because quartile methods differ.
| Observation | Pebble length (mm) |
|---|---|
| 1 | 9 |
| 2 | 11 |
| 3 | 12 |
| 4 | 14 |
| 5 | 17 |
| 6 | 18 |
| 7 | 21 |
| 8 | 25 |
Resource description
Fictional pebble measurements