This deep dive covers Understanding Quartiles and Interquartile Range within Range & IQR for GCSE Mathematics. Revise Range & IQR in Statistics for GCSE Mathematics with 12 exam-style questions and 20 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 4 of 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Understanding Quartiles and Interquartile Range
Finding Quartiles
Step 1: Arrange data in ascending order
Step 2: Find the median (Q2)
Step 3: Find Q1 (median of lower half)
Step 4: Find Q3 (median of upper half)
Detailed Example: Finding Quartiles
Data: 12, 15, 18, 22, 24, 28, 30, 35, 38
Step 1: Already in order: 12, 15, 18, 22, 24, 28, 30, 35, 38
Step 2: Q2 (median) = 24 (5th value of 9)
Step 3: Lower half: 12, 15, 18, 22 → Q1 = (15 + 18) ÷ 2 = 16.5
Step 4: Upper half: 28, 30, 35, 38 → Q3 = (30 + 35) ÷ 2 = 32.5
Calculating IQR
IQR = Q3 - Q1 = 32.5 - 16.5 = 16
What IQR Tells Us
The IQR represents the spread of the middle 50% of the data. It's not affected by outliers, making it more reliable than range when extreme values are present.
Practice questions for Range & IQR
The range of a set of data is calculated by:
Explain why the interquartile range (IQR) is sometimes preferred over the range as a measure of spread.