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 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
12 questions
Recall
20 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