GCSE Maths / Edexcel

Estimated mean from grouped data

Estimate a mean from grouped data by using class midpoints, and identify the modal class from a grouped frequency table.

Probability and StatisticsFoundation and HigherGrades 4 to 6Focused skill

Curriculum path: GCSE Maths > Edexcel > Probability and Statistics > Estimated mean from grouped data

Pearson Edexcel GCSE Maths Statistics S3 and S4: interpret grouped data and use measures of average and spread.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Grouped data puts values into intervals such as 0 < t <= 10. You usually do not know the exact values inside each group.

Because the exact values are unknown, the mean from grouped data is an estimate.

Use the midpoint of each class interval as a sensible representative value. For 10 < t <= 20, the midpoint is 15.

Multiply each midpoint by its frequency. Add these products and divide by the total frequency.

The modal class is the class interval with the highest frequency. It is a class interval, not a single value.

Always write estimated mean when the data is grouped. This is a common Edexcel wording mark.

Key ruleEstimated mean = total of midpoint x frequency / total frequency.

Diagram guide

Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.

Worked examples

Estimate the mean

A grouped table shows times in minutes: 0 < t <= 10 frequency 4, 10 < t <= 20 frequency 7, 20 < t <= 30 frequency 9. Estimate the mean.

Grouped timesEach interval is replaced by its midpoint for the estimate.

The midpoints are 5, 15 and 25.
Midpoint x frequency: 5 x 4 = 20, 15 x 7 = 105, 25 x 9 = 225.
Estimated total = 20 + 105 + 225 = 350.
Total frequency = 4 + 7 + 9 = 20.
Estimated mean = 350 / 20 = 17.5.

Answer: 17.5 minutes

Find the modal class

For the same table, find the modal class.

Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.

The modal class is the interval with the highest frequency.
The highest frequency is 9.
This belongs to 20 < t <= 30.

Answer: 20 < t <= 30

Explain why it is an estimate

Why is the mean from a grouped frequency table only an estimate?

Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.

The table gives intervals, not the exact data values.
Using midpoints assumes the values are spread evenly inside each interval.
The real values may not all be at the midpoint.

Answer: Because the exact values are unknown, so midpoints are used as estimates.

Common mistakes

Using the class width instead of the midpoint.
Dividing by the number of groups instead of the total frequency.
Writing a single number for the modal class.
Forgetting to say the mean is an estimate.
Using the upper class boundary as the midpoint.

Quick exercise

Try these before moving to the exam-style questions.

Find the midpoint of 20 < x <= 30.
Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.
Classes 0-10, 10-20, 20-30 have frequencies 3, 5, 2. Find the modal class.
Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.
For 0 < x <= 10 with frequency 6, what is midpoint x frequency?
Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.
Midpoint x frequency totals are 40, 90 and 70. Total frequency is 20. Estimate the mean.
Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.
Why should the final answer usually say estimated mean?
Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.

Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundation and HigherCalculator4 marks

The table shows time, t minutes, taken by students to finish a task. 0 < t <= 10: 6 students, 10 < t <= 20: 8 students, 20 < t <= 30: 6 students. Estimate the mean time.

Question tableUse midpoints 5, 15 and 25.

Your answer and working

grouped dataestimated meanmidpoints

Standard exam styleFoundation and HigherCalculator5 marks

Lengths, l cm, are grouped as 0 < l <= 5 frequency 4, 5 < l <= 10 frequency 10, 10 < l <= 15 frequency 6. Estimate the mean length and state the modal class.

Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.

Your answer and working

estimated meanmodal classgrouped frequency

ChallengeHigherCalculator4 marks

A grouped table has equal class widths. A student says, 'The estimated mean must be in the modal class.' Explain why this is not always true.

Grouped frequency tableUse the midpoint of each interval because the exact values inside each group are not known.

Your answer and working

grouped datareasoningcompare averages

Next step in the app

Use the notes with a real answer.

Reading the method helps, but the progress comes from answering, marking, and fixing one question at a time.

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