Statistics · SS 2
Range and interquartile range
Measure how spread out the data is.
- Range = highest − lowest
- Interquartile range = Q3 − Q1
- Semi-interquartile range = Q3 − Q12
What the letters mean
- Q1
- the lower quartile (¼ of the way through the ordered data)
- Q3
- the upper quartile (¾ of the way through)
Worked example
From an ogive, Q1 = 12 marks and Q3 = 30 marks. Find the interquartile range.
Step 1: Subtract
30 − 12 = 18 marks
Final answer: 18 marks
See it
Play with this picture from the Cumulative Frequency lesson.
Cumulative freq.20
About 20 of the 40 scored 30.5 or less.
Median
≈ 30.5
at n/2 = 20
Q₁
≈ 19.2
at n/4 = 10
Q₃
≈ 38.7
at 3n/4 = 30
IQR
≈ 19.4
Q₃ − Q₁
| Marks | f | Upper bound. | Cum. freq. |
|---|---|---|---|
| 1–10 | 4 | 10.5 | 4 |
| 11–20 | 7 | 20.5 | 4 + 7 = 11 |
| 21–30 | 9 | 30.5 | 11 + 9 = 20 |
| 31–40 | 12 | 40.5 | 20 + 12 = 32 |
| 41–50 | 8 | 50.5 | 32 + 8 = 40 |