Key Terms

Range: Total spread of data (highest − lowest)
Quartile: A value that divides ordered data into four equal parts
Q1 (Lower Quartile): 25% of data lies below this value
Q2 (Median): 50% of data lies below this value
Q3 (Upper Quartile): 75% of data lies below this value
IQR: Interquartile range — spread of the middle 50% of data

Must-Know Facts

Always sort data into ascending order before finding quartiles
Range is affected by outliers; IQR is not
IQR is always less than or equal to the range
A smaller IQR means data is more consistent (less spread)
A larger IQR means data is more variable
Use IQR when comparing consistency between two datasets
IQR and range share the same units as the original data

Key Formulas

Range = highest value − lowest value
IQR = Q3 − Q1
Q1 = median of the lower half of data
Q3 = median of the upper half of data

Common Mistakes

Not ordering data first: Always sort data in ascending order before finding quartiles or range
Including the median in quartile halves: For an odd number of values, exclude the median when finding Q1 and Q3
Range vs IQR: Range uses all values (affected by outliers); IQR uses only the middle 50% (more reliable)
IQR = Q3 − Q1, not Q3 ÷ Q1: Subtract the lower quartile from the upper quartile

This topic summary covers Knowledge Organiser: Range and Interquartile Range (IQR) 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 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Practice questions for Range & IQR

The range of a set of data is calculated by:

A. Adding all the values together
B. Dividing the total by the number of values
C. Subtracting the smallest value from the largest value
D. Finding the middle value when ordered

1 markfoundation

Explain why the interquartile range (IQR) is sometimes preferred over the range as a measure of spread.

2 marksstandard

Quick recall flashcards

What are quartiles?

Quartiles are values that divide an ordered dataset into four equal parts: - Q1 (Lower quartile): 25% below - Q2 (Median): 50% below - Q3 (Upper quartile): 75% below

What is the range?

The range is the difference between the highest value and the lowest value in a dataset. Range = Highest value - Lowest value

Knowledge Organiser: Range and Interquartile Range (IQR)