StatisticsTopic Summary

Knowledge Organiser: Cumulative Frequency

Part of Cumulative Frequency · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Cumulative Frequency within Cumulative Frequency for GCSE Mathematics. Revise Cumulative Frequency in Statistics for GCSE Mathematics with 14 exam-style questions and 20 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 11 of 11 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 11 of 11

Practice

14 questions

Recall

20 flashcards

Knowledge Organiser: Cumulative Frequency

Key Terms

Cumulative frequency: Running total of all frequencies up to each upper boundary
Upper boundary: The highest value in a class — used as the x-coordinate when plotting
Median: Middle value — found at position n ÷ 2 on the curve
Q1 (Lower Quartile): Found at position n ÷ 4 on the curve
Q3 (Upper Quartile): Found at position 3n ÷ 4 on the curve
IQR: Q3 − Q1, both values read from the cumulative frequency curve

Must-Know Facts

Plot cumulative frequency against the upper boundary of each class interval
The curve always rises from bottom-left to top-right — never decreases
The final cumulative frequency equals the total number of data items
Draw a smooth curve through the points — not straight line segments
To read a value: go horizontally from the y-axis to the curve, then vertically down to the x-axis
Always draw construction lines clearly on the graph — they earn marks
A steep section of the curve means many data values are clustered in that interval

Key Formulas

Median position = n ÷ 2
Q1 position = n ÷ 4
Q3 position = 3n ÷ 4
IQR = Q3 − Q1
Percentile position = (p ÷ 100) × n

Common Mistakes

Plotting at class boundaries, not midpoints: Cumulative frequency is plotted at the UPPER boundary of each class
Reading off the wrong axis: To find a value at a given frequency, read across then down — not down then across
Median position = n not n÷2: Median is at n÷2 on a cumulative frequency graph (not (n+1)÷2)
IQR = Q3 only: IQR = Q3 − Q1 — must subtract Q1, not just read off Q3

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Keep building this topic

Read this section alongside the surrounding pages in Cumulative Frequency. That gives you the full topic sequence instead of a single isolated revision point.

Common Mistakes to Avoid Building Up the Picture Key Facts About Cumulative Frequency

Practice Questions for Cumulative Frequency

Cumulative frequency is:

A. The highest frequency in a table
B. The running total of frequencies up to and including each class
C. The mean of all frequencies
D. The difference between the largest and smallest frequencies

1 markfoundation

The graph shows the times for 60 students. The cumulative frequency at 40 seconds reads as 48. Estimate the number of students who took longer than 40 seconds to complete the puzzle.

2 marksstandard

Quick Recall Flashcards

What is cumulative frequency?

Cumulative frequency is the running total of frequencies up to and including each class. It shows how many data values fall below the upper boundary of each class.

How do you calculate cumulative frequency?

Start with the first frequency. For each subsequent class, add the current frequency to the previous cumulative frequency: CF₂ = CF₁ + f₂ CF₃ = CF₂ + f₃, and so on.

14 questions on Cumulative Frequency — practise free

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Common Mistakes to Avoid

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Cumulative Frequency