Cumulative Frequency Graphs: What is it?

Cumulative frequency is the running total of the frequencies. On a graph, it can be represented by a cumulative frequency polygon, where straight lines join up the points, or a cumulative frequency curve.

Example

Frequency: Cumulative Frequency:
4 4
6 10 (4 + 6)
3 13 (4 + 6 + 3)
2 15 (4 + 6 + 3 + 2)
6 21 (4 + 6 + 3 + 2 + 6)
4 25 (4 + 6 + 3 + 2 + 6 + 4)

This short video shows you how to plotting a cumulative frequency curve from the frequency distribution. How to find the median and inter-quartile range.

The Median Value

The median of a group of numbers is the number in the middle, when the numbers are in order of magnitude. For example, if the set of numbers is 4, 1, 6, 2, 6, 7, 8, the median is 6:
1, 2, 4, 6, 6, 7, 8      (6 is the middle value when the numbers are in order)
If you have n numbers in a group, the median is the (n + 1)/2 th value. For example, there are 7 numbers in the example above, so replace n by 7 and the median is the (7 + 1)/2 th value = 4th value. The 4th value is 6.

When dealing with a cumulative frequency curve, “n” is the cumulative frequency (25 in the above example). Therefore the median would be the 13th value. To find this, on the cumulative frequency curve, find 13 on the y-axis (which should be labelled cumulative frequency). The corresponding ‘x’ value is an estimation of the median.

Read more below-

SS2 Mathematics Third Term: Cumulative Frequency Graph