Cumulative Frequency

What is Cumulative Frequency?

Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Cumulative Frequency. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.

Check that you can explain Cumulative Frequency in your own words and give one example from everyday life. If you can do that, you have understood the core idea.

Understanding Cumulative Frequency gives you a reliable method you will reuse in later maths units, in science lessons and in data work.

Cumulative Frequency in detail

Cumulative frequency is a running total of frequencies up to the upper boundary of each class. Plotting these totals against the upper class boundaries and joining the points with a smooth curve gives a cumulative frequency graph, or ogive.

From the curve you read the median at half the total, and the lower and upper quartiles at one-quarter and three-quarters, giving the interquartile range. You can also estimate how many values lie below a given number. It is used for exam marks, heights and incomes, and it is the basis for drawing box plots for grouped data.

How the interactive helps you understand Cumulative Frequency

Watch the bar chart in the interactive. Use any sliders or buttons it offers to change the values and see how the bar chart responds.

Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Cumulative Frequency.

Real-life uses and examples

• Explain Cumulative Frequency to a friend with a simple picture, such as a row of tiles or a bag of sweets.
• Spot Cumulative Frequency in exam questions, where it often sits inside a short word problem.
• Check a homework answer about Cumulative Frequency by estimating first, then working it out step by step.

Common mistakes to avoid

• Memorising the steps for Cumulative Frequency without checking why they work.
• Forgetting units, signs or brackets when you apply Cumulative Frequency.
• Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.