Interquartile Range
Grade 6Quartiles and IQR
The lower quartile (LQ) is the value one quarter of the way through the data. The upper quartile (UQ) is three quarters of the way. The interquartile range is the difference between them.
IQR = upper quartile − lower quartile
The IQR covers the middle 50% of the data — ignoring the top and bottom quarters entirely. That makes it a much more reliable measure of spread than the range.
Reading quartiles from a cumulative frequency curve
EXAMPLE
A cumulative frequency curve has n = 80 values. Read off the LQ, UQ and IQR. The curve gives: cf = 20 → 35 marks; cf = 60 → 58 marks.
LQ position: n ÷ 4 = 80 ÷ 4 = 20. Go across from cf = 20 → LQ = 35 marks.
UQ position: 3n ÷ 4 = 60. Go across from cf = 60 → UQ = 58 marks.
IQR = 58 − 35 = 23 marks.
Using IQR to compare distributions
A smaller IQR means the middle half of the data is packed more tightly — the distribution is more consistent. A larger IQR means more spread in the middle 50%.
When comparing two data sets using cumulative frequency curves, comment on both the median (who scored higher on average) and the IQR (who was more consistent). A complete comparison needs both points.
