Range and IQR

Steps

1. Range = largest − smallest.
2. Order the data. Find the median Q₂.
3. Lower quartile Q₁ = median of the lower half; upper quartile Q₃ = median of the upper half. (This is the usual Hong Kong textbook method; check the student's book.)
4. IQR = Q₃ − Q₁.
5. From a cumulative frequency curve, read Q₁ at ¼ and Q₃ at ¾ of the total.

Want to check an answer? Standard deviation calculator shows every step.

Worked examples

range = 13 − 4 = 9
mean  = 40 ÷ 5 = 8
σ = √[(16 + 1 + 1 + 1 + 25)/5] = √8.8 ≈ 2.97
variance = 8.8

For the whole topic, read Measures of dispersion: key points, common mistakes and how the DSE tests it.

Other methods in this topic