GCSE-readyGrouped data and estimating the mean
When there is lots of continuous data, such as times or heights, we group it. You lose the exact values, but you can still estimate the mean.
Class intervals
10 ≤ t < 20 includes 10 but not 20. A time of exactly 20 minutes goes in 20 ≤ t < 30.
Times to finish a puzzle, in minutes:
| Time t (minutes) | Frequency |
|---|---|
| 0 ≤ t < 10 | 4 |
| 10 ≤ t < 20 | 9 |
| 20 ≤ t < 30 | 12 |
| 30 ≤ t < 40 | 5 |
Modal class and median class
There are 30 values, so the median lies between the 15th and 16th. Running totals: 4, 13, 25, 30. The 15th and 16th are in 20 ≤ t < 30.
Estimating the mean
Multiply each midpoint by the frequency, add, then divide by the total frequency.
5 × 4 + 15 × 9 + 25 × 12 + 35 × 5 = 20 + 135 + 300 + 175 = 630. 630 ÷ 30 = 21 minutes.
It is an estimate because we do not know the exact values.
Find the midpoint of the class 30 ≤ t < 40.
- Add the ends: 30 + 40 = 70
- Halve: 70 ÷ 2
Answer: 35
Classes use inequalities so they do not overlap. Modal class: highest frequency. Estimated mean: midpoint × frequency, add up, divide by the total frequency.
- Mean
- An average: add up all the values and divide by how many values there are.
- Estimate
- An approximate answer, often found by rounding each number to 1 significant figure first.
- Frequency
- How many times something happens or a value appears in a set of data.
- Time
- 60 seconds = 1 minute, 60 minutes = 1 hour. 0.5 hours = 30 minutes, 0.25 hours = 15 minutes.
- Median
- The middle value when the data is in order. With an even number of values, it is halfway between the middle two.
- Not “10 ≤ t < 20”. Only 13 values are below 20, so the 15th is not in this class.
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2 more questions
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Puzzle times: 0 ≤ t < 10 (6 people), 10 ≤ t < 20 (11), 20 ≤ t < 30 (8), 30 ≤ t < 40 (5). How many people are in the table?
Show the answer
Answer: 30
6 + 11 + 8 + 5 = 30.
Times t (minutes): 0 ≤ t < 10 (5 people), 10 ≤ t < 20 (14 people), 20 ≤ t < 30 (9 people), 30 ≤ t < 40 (2 people). What is the modal class?
- 10 ≤ t < 20
- 20 ≤ t < 30
- 30 ≤ t < 40
- 0 ≤ t < 10
Show the answer
Answer: 10 ≤ t < 20
The modal class has the highest frequency, 14.
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Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.