GCSE Maths (AQA)

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Analysing Cumulative Frequency Graphs

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Statistics Statistics

Analysing Cumulative Frequency Graphs

6:23 Quartiles
Spec S3 S4
Previous Interquartile Range Next Line of Best Fit
  • Cumulative frequency graphs can be used to estimate the median and quartiles of a set of data
  • The x coordinates of the points on the graph represent the end values of the data groups, while the y coordinates represent the frequency up to that point
  • The cumulative frequency at the median is equal to the total cumulative frequency divided by 2
  • The cumulative frequency at the lower quartile is equal to the total cumulative frequency divided by 4
  • The cumulative frequency at the upper quartile is equal to three quarters of the total cumulative frequency
  • To estimate the median, find the position on the y axis and draw a horizontal line to the graph, then draw a vertical line down to get the x coordinate
  • To estimate the quartiles, follow the same process as for the median, but use the appropriate cumulative frequency (1/4 for lower quartile, 3/4 for upper quartile)
  • The reverse process can also be used to estimate the cumulative frequency for a certain data value
  • To estimate the cumulative frequency for a certain value, draw a vertical line from the value on the x axis and a horizontal line from where it meets the graph, then read the answer from the y axis

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