This deep dive covers Advanced Techniques within Averages for GCSE Mathematics. Revise Averages in Statistics for GCSE Mathematics with 14 exam-style questions and 20 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 7 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Advanced Techniques
Finding Missing Values Using Averages
If you know the mean and some values, you can find missing values.
Example: Five numbers have a mean of 12. Four of the numbers are 8, 11, 15, and 9. Find the fifth number.
Solution:
Mean = 12, so total of five numbers = 12 × 5 = 60
Sum of known numbers = 8 + 11 + 15 + 9 = 43
Fifth number = 60 - 43 = 17
Comparing Averages
When comparing datasets, consider:
- Which average is most appropriate for the context
- Whether the data contains outliers
- The shape of the data distribution
Real-World Applications
- Mean: Average temperature, average salary (when no extreme outliers)
- Median: House prices, income (when outliers exist)
- Mode: Most popular shoe size, most common grade
Practice questions for Averages
What is the mode of this dataset? 3, 5, 5, 7, 9, 3, 5, 11
Class A has test scores: 55, 62, 58, 60, 61, 63, 57. Class B has test scores: 20, 60, 62, 63, 61, 58, 64. A teacher says 'Class A has a higher mean score, so Class A performed better overall.' Give a mathematical reason why this conclusion may be misleading.