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MathidiaMathematics Academy
Statistical investigation
Lesson 63 of 75
Standard practice

Cumulative frequency

Objective. Read medians and quartiles from cumulative totals.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Cumulative frequency is a running total of frequencies up to the end of each class interval, used to read off the median and quartiles from a cumulative frequency graph. To find the median from such a graph, locate half the total frequency on the vertical axis, draw across to the curve, then down to read the corresponding value on the horizontal axis. The lower quartile uses a quarter of the total frequency and the upper quartile uses three-quarters, located the same way. For example, with a total frequency of 80, the median is read at 40, the lower quartile at 20, and the upper quartile at 60 on the cumulative frequency axis.

Worked example

A cumulative frequency graph shows a total frequency of 60 pupils' test scores. At what cumulative frequency value should the median be read from the graph?

60
Coordinate grid with the line 60
  1. 1The median position uses half of the total frequency.
  2. 2Calculate half of 60.
  3. 360 ÷ 2 = 30.
  4. 4Read across from cumulative frequency 30 to the curve, then down to the score axis.

Answer: 30

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Common mistake. Pupils often read the median from half the highest class value rather than half the total cumulative frequency, misunderstanding what the vertical axis of the graph represents. Always use half of the total frequency, not half of a data value, to locate the median.

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