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. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. 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.
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
Practice questions for Frequency Tables
The table below shows the number of books read by students in a month: | Books read | Frequency | |---|---| | 0 | 4 | | 1 | 7 | | 2 | 11 | | 3 | 6 | | 4 | 2 | What is the mode?
Explain why the mean calculated from a grouped frequency table is described as an 'estimate' rather than an exact value.