Question 1Warm-upFoundation
The table shows the goals scored in 20 matches. Find the mean number of goals.
| Goals | Frequency |
|---|---|
| 0 | 4 |
| 1 | 6 |
| 2 | 7 |
| 3 | 3 |
Work out goals × frequency for each row.
Worked solution
- goals
Answer:
GCSE & IGCSE maths practice
Mean from a frequency table questions and answers
In a frequency table, multiply each value by its frequency, add these up, and divide by the total frequency. For grouped data you don't know the exact values, so use the midpoint of each class: that's why the answer is an estimate. The median is the middle value counting through the frequencies.
8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where mean from a frequency table comes up
| GCSE (AQA, Edexcel, OCR) | Foundation and Higher: measures of central tendency (median, mean, mode and modal class) from discrete, continuous and grouped data. |
|---|---|
| Cambridge IGCSE (0580) | Core: mean, median, mode and range from a frequency table (not grouped). Extended: estimate the mean of grouped data and identify the modal class. |
The method
- Add an fx column: value (or midpoint) × frequency.
- Mean = total of fx ÷ total frequency.
- Median: find the (n + 1) ÷ 2th value with a running total.
- Mode: the value (or class) with the highest frequency.
Mean from a frequency table questions
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Warm-up
Question 2Warm-upFoundation
Using the same table, what is the mode?
| Goals | Frequency |
|---|---|
| 0 | 4 |
| 1 | 6 |
| 2 | 7 |
| 3 | 3 |
The value with the highest frequency.
Worked solution
- 2 goals has the highest frequency (7).
Answer: goals
Exam-style
Question 3Exam-styleFoundation
Using the same table, find the median number of goals.
| Goals | Frequency |
|---|---|
| 0 | 4 |
| 1 | 6 |
| 2 | 7 |
| 3 | 3 |
20 values: the median is between the 10th and 11th.
Worked solution
- Running totals: 4, 10, 17, 20
- 10th value is 1; 11th is 2
- Median
Answer:
Question 4Exam-styleFoundation
20 students were asked how many pets they have. Find the mean.
| Pets | Frequency |
|---|---|
| 0 | 5 |
| 1 | 8 |
| 2 | 4 |
| 3 | 2 |
| 4 | 1 |
Total pets ÷ 20.
Worked solution
Answer:
Question 5Exam-styleFoundation
The table shows the times 20 students took to finish a puzzle. Estimate the mean time.
| Time, t (minutes) | Frequency |
|---|---|
| 0 < t ≤ 10 | 5 |
| 10 < t ≤ 20 | 8 |
| 20 < t ≤ 30 | 7 |
Use the midpoints 5, 15 and 25.
Worked solution
- minutes
Answer: minutes
Question 6Exam-styleFoundation
Using the same table, which is the modal class?
| Time, t (minutes) | Frequency |
|---|---|
| 0 < t ≤ 10 | 5 |
| 10 < t ≤ 20 | 8 |
| 20 < t ≤ 30 | 7 |
The class with the highest frequency.
Worked solution
- Frequency 8 is the highest.
Answer:
Challenge
Question 7ChallengeFoundation
Why is the mean from a grouped frequency table only an estimate?
What don't you know about grouped data?
Worked solution
- The exact values in each class are unknown, so each is replaced by the class midpoint.
Answer: We use the midpoints, not the actual values
Question 8ChallengeFoundation
The heights of 20 plants are shown. Estimate the mean height.
| Height, h (cm) | Frequency |
|---|---|
| 150 < h ≤ 160 | 4 |
| 160 < h ≤ 170 | 10 |
| 170 < h ≤ 180 | 5 |
| 180 < h ≤ 190 | 1 |
Midpoints 155, 165, 175, 185.
Worked solution
- cm
Answer: cm
Common mistakes
- Dividing by the number of rows instead of the total frequency.
- Giving the highest frequency as the mode instead of its value.
- Using class end points instead of midpoints.
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Sources
The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:
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