Knowledge Organiser: Grouped Data
Part of Grouped Data · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Grouped Data within Grouped Data for GCSE Mathematics. Revise Grouped Data in Statistics for GCSE Mathematics with 14 exam-style questions and 20 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 8
Practice
14 questions
Recall
20 flashcards
Knowledge Organiser: Grouped Data
Key Terms
- Class interval: A range grouping similar values (e.g. 160 ≤ h < 170)
- Class width: The size of a class interval (upper − lower boundary)
- Midpoint: The middle of a class interval = (lower + upper) ÷ 2
- Modal class: The class interval with the highest frequency
- Estimated mean: An approximation using class midpoints
- Cumulative frequency: Running total of frequencies up to each upper boundary
Must-Know Facts
- You can only find an estimated mean and modal class from grouped data — not exact values
- "150 ≤ h < 160" means 150 is included but 160 is not
- Class widths should be consistent for fair comparison
- Midpoint = (lower boundary + upper boundary) ÷ 2
- Always state that mean and median are estimates when working with grouped data
- Median position = (n + 1) ÷ 2 for discrete; n ÷ 2 for continuous grouped data
- Always show all steps in estimated mean calculations for full marks
Key Formulas
- Estimated mean = Σ(midpoint × frequency) ÷ Σfrequency
- Midpoint = (lower boundary + upper boundary) ÷ 2
- Class width = upper boundary − lower boundary
- Median position ≈ n ÷ 2 (use cumulative frequency to locate)
Common Mistakes
- Using class boundaries instead of midpoints: For estimated mean, always use the midpoint (lower + upper) ÷ 2 for each class
- Dividing by number of classes: Mean = Σ(f × midpoint) ÷ Σf — total frequency is the denominator, not the count of classes
- Modal class vs mode: State the class interval (e.g. 20 ≤ x < 30), not a single value
- Mean is only an estimate: With grouped data you cannot find the exact mean — always say "estimated mean"
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Practice Questions for Grouped Data
A frequency table uses the class intervals shown below. | Speed, s (mph) | Frequency | |---|---| | 0 < s ≤ 20 | 4 | | 20 < s ≤ 40 | 11 | | 40 < s ≤ 60 | 9 | | 60 < s ≤ 80 | 2 | A car travels at exactly 40 mph. Which class interval does this value belong to?
A teacher groups 30 students' test scores into four class intervals and calculates the estimated mean and estimated median. Explain why both the estimated mean and the estimated median from grouped data are only approximations of the true values. In your answer, refer to the assumptions made.
Quick Recall Flashcards
14 questions on Grouped Data — practise free
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