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Finding the Median from Cumulative Frequency

Part of Cumulative Frequency — GCSE Mathematics

This deep dive covers Finding the Median from 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 6 of 10 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 10

Practice

14 questions

Recall

20 flashcards

Finding the Median from Cumulative Frequency

Method

  1. Find the median position: n ÷ 2 (where n = total frequency)
  2. Draw horizontal line: From the median position on y-axis to the curve
  3. Draw vertical line: From where the horizontal line meets the curve down to x-axis
  4. Read the median: Value where the vertical line meets the x-axis

Example

Total frequency (n) = 43
Median position = 43 ÷ 2 = 21.5
Draw horizontal line from 21.5 on y-axis to curve, then vertical line to x-axis.
Median ≈ 175 cm

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.

Cumulative Frequency CurveFinding QuartilesBuilding Up the PictureKey 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

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.
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.

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Cumulative Frequency Curve

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Finding Quartiles