Interquartile range

Definition

The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). It measures the spread of the middle 50% of the data and, unlike the range, isn't affected by outliers.

Worked example

For 3; 5; 7; 8; 9; 11; 13; 15, Q1 = 6 and Q3 = 12, so IQR = 6.

Outliers are often defined as values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.

Where it appears in the exam

Interquartile range is part of the statistics section of CAPS Grade 10 Mathematics and is examined in Paper 2 of the November exam.

Step-by-step method

1. Sort the data.
2. Find the median, which splits the data into two halves.
3. Find Q1 (median of the lower half) and Q3 (median of the upper half).
4. Subtract: IQR = Q3 − Q1.

Common mistake

Finding the quartiles from unsorted data.

Related statistics terms

• Standard deviation
• Least squares regression line
• Correlation coefficient
• Outlier
• Five-number summary
• Ogive

Frequently asked questions

What does interquartile range mean in Grade 10 Maths?

The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). It measures the spread of the middle 50% of the data and, unlike the range, isn't affected by outliers.

Which paper tests interquartile range in Grade 10?

Interquartile range belongs to the Statistics section of CAPS Grade 10 Mathematics, which is examined in Paper 2 of the November exam.

How do I practise questions involving interquartile range?

Snap a question that uses interquartile range into Snap&Learn with your grade set to Grade 10, or work through the Grade 10 topic guide and practice papers.