Cumulative frequency

Objective. Estimate medians, quartiles and percentiles from curves.

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Learn: the key idea

Cumulative frequency is the running total of frequencies up to the end of each class, plotted against the upper class boundary to form a curve used to estimate medians and quartiles. Plot points at (upper boundary, cumulative total) and join with a smooth curve, then read across from n/2, n/4 and 3n/4 on the vertical axis to estimate the median and quartiles. For example, with 80 data values, the median is read at cumulative frequency 40. The interquartile range is the difference between the upper and lower quartile estimates read from the curve.

Worked example

A cumulative frequency curve shows a total of 60 data values. Use cumulative frequency to estimate the median, given the curve passes through (24, 30).

1 $Median position = n/2 = 60/2 = 30$
2 $Read across from cumulative frequency 30 on the curve$
3 $The curve passes through (24, 30)$
4 $Estimated median = 24$

Answer: 24

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Common mistake. Students sometimes plot cumulative frequency against the midpoint of each class instead of the upper boundary; always use the upper class boundary, since cumulative frequency counts everything up to that point.

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