What is the purpose of a cumulative frequency graph?

A cumulative frequency graph shows the running total of frequencies up to each data point.

A cumulative frequency graph, also known as an ogive, is a useful tool in statistics for displaying the cumulative totals of data points in a dataset. It helps you to see how the frequencies accumulate over a range of values, making it easier to analyse the distribution of data. For example, if you have a list of test scores, a cumulative frequency graph can show you how many students scored up to a certain mark.

To create a cumulative frequency graph, you start by organising your data into a frequency table. This table lists the data values and their corresponding frequencies. Next, you calculate the cumulative frequency for each data value, which is the sum of the frequencies for that value and all previous values. You then plot these cumulative frequencies on a graph, typically with the data values on the x-axis and the cumulative frequencies on the y-axis.

One of the main benefits of a cumulative frequency graph is that it allows you to quickly determine the median, quartiles, and percentiles of a dataset. For instance, the median can be found by locating the point where the cumulative frequency reaches half of the total frequency. Similarly, the lower and upper quartiles can be identified by finding the points where the cumulative frequency reaches one-quarter and three-quarters of the total frequency, respectively.

Overall, cumulative frequency graphs are a powerful way to visualise and interpret data, making them an essential tool for GCSE Maths students.