EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
📊
Statistics & Probability · Higher

Mean from grouped frequency tables

When data is in grouped classes, you cannot find the exact mean. Instead, you use the midpoint of each class as an estimate. This gives an estimated mean.

Revising mean from grouped frequency tables the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Mean from grouped frequency tables GCSE” on the site for the complete guide.

🔑

Key facts to remember

  • 1Use the midpoint of each class interval as the representative value.
  • 2Midpoint = (lower class boundary + upper class boundary) ÷ 2.
  • 3Estimated mean = Σ(midpoint × frequency) ÷ Σfrequency.
  • 4The modal class is the class with the highest frequency.
  • 5The median class is found using the cumulative frequency — locate the n/2 th value.
  • 6Answers are estimates because the exact data values are unknown.
📐

Formulas

Estimated mean
Mean ≈ Σ(m × f) / Σf

m = midpoint of class, f = frequency

✍️

Worked examples

Example 1

Heights (cm): 150-160 (f=5), 160-170 (f=12), 170-180 (f=8), 180-190 (f=5). Estimate the mean.

Working

  1. Midpoints: 155, 165, 175, 185
  2. Σ(m × f) = 155×5 + 165×12 + 175×8 + 185×5
  3. = 775 + 1980 + 1400 + 925 = 5080
  4. Σf = 5 + 12 + 8 + 5 = 30
  5. Estimated mean = 5080 ÷ 30 ≈ 169.3 cm
Answer≈ 169.3 cm
Example 2

State the modal class from the table above.

Working

  1. The class with the highest frequency is 160-170 (f = 12)
AnswerModal class: 160-170 cm
⚠️

Common mistakes

✗Using the class boundaries instead of the midpoints.
✗Dividing by the number of classes instead of the total frequency.
✗Giving an exact mean rather than an estimate (use "≈" and the word "estimate").
🎯

Exam tips

✓Always add a midpoint column to your table before calculating — it makes the working much clearer.
✓State clearly that your answer is an estimate, not an exact value.

Ready to test yourself on Mean from grouped frequency tables?

Get AI-marked practice questions on exactly this subtopic.

Practice this topic →
← All topicsDashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

▶mean from grouped frequency table GCSE Higher▶estimated mean GCSE maths▶modal class GCSE statistics▶grouped data mean GCSE Higher

Opens YouTube — pick any free GCSE video.