cumulative frequency

In statistics, the total frequency of a given value up to and including a certain point in a set of data. It is calculated by adding together the frequencies to give a running total and used to draw the cumulative frequency curve, the ogive.

To plot a cumulative frequency diagram, the cumulative frequency is always plotted along the vertical axis and data are always plotted at the top range of the interval: for example, frequency for weekly salary ranges £100–150 and £151–200 would be plotted at 150 and 200.

Following the collection of raw data, a cumulative frequency diagram can be plotted from a table of results. For example, this table shows the results of a survey among a group of pupils, who were asked how many sets of homework they had to complete each week:

From the data the cumulative frequency diagram can be plotted.

From this graph the median and the upper and lower quartiles can be obtained and hence the interquartile range.

The median is the reading at the halfway point on the vertical axis of the cumulative frequency curve (27), and in this case is approximately 4.2 sets of homework.

The lower quartile is the reading one-quarter of the way up the vertical axis of the cumulative frequency curve (13.5), and in this case is approximately 3.8 sets of homework.

The upper quartile is the reading three-quarters of the way up the vertical axis of the cumulative frequency curve (40.5), and in this case is approximately 5.1 sets of homework.

The interquartile range = upper quartile − lower quartile, and in this case = 5.1 − 3.8 = 1.3 sets of homework.