Calculating Averages from Frequency Tables
Part of Frequency Tables — GCSE Mathematics
This deep dive covers Calculating Averages from Frequency Tables within Frequency Tables for GCSE Mathematics. Revise Frequency Tables in Statistics for GCSE Mathematics with 11 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
11 questions
Recall
20 flashcards
Calculating Averages from Frequency Tables
Mean from Simple Frequency Tables
Formula: Mean = Σ(f × x) ÷ Σf
Where f = frequency, x = value
Example: Pet Ownership
| Number of Pets (x) | Frequency (f) | f × x |
|---|---|---|
| 0 | 8 | 0 |
| 1 | 12 | 12 |
| 2 | 15 | 30 |
| 3 | 5 | 15 |
| Total | Σf = 40 | Σ(f × x) = 57 |
Mean = 57 ÷ 40 = 1.425 pets per family
Estimated Mean from Grouped Data
For grouped data, use the midpoint of each class.
Formula: Estimated Mean = Σ(f × midpoint) ÷ Σf
Finding the Median from Frequency Tables
Method:
- Find total frequency (n)
- Find median position = (n + 1) ÷ 2
- Use cumulative frequency to locate the median
Applications
- Surveys: Organizing responses to questionnaires
- Quality control: Tracking defect frequencies
- Sports statistics: Recording scores, times, distances
- Market research: Analyzing customer preferences