This deep dive covers Advanced Applications 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 7 of 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Advanced Applications
Detecting Outliers
Values are considered outliers if they are:
- Less than Q1 - 1.5 × IQR
- Greater than Q3 + 1.5 × IQR
Example: Outlier Detection
Using our previous data where Q1 = 16.5, Q3 = 32.5, IQR = 16:
Lower boundary = 16.5 - 1.5 × 16 = 16.5 - 24 = -7.5
Upper boundary = 32.5 + 1.5 × 16 = 32.5 + 24 = 56.5
All values (12 to 38) are within these boundaries, so no outliers.
Comparing Datasets
When comparing two datasets:
- Similar means, different IQRs: One group is more consistent
- Similar IQRs, different means: Groups have similar spread but different centers
- Use both measures to get a complete picture
Real-World Applications
- Quality control: Smaller IQR indicates more consistent production
- Sports performance: Compare consistency between players
- Weather data: Compare temperature variation between cities
- Exam results: Assess how much performance varies in a class
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.