# Interpreting Cumulative Frequency Graphs

In my experience, students have little difficulty drawing cumulative frequency graphs from data presented in a grouped data table. Sometimes they will plot the cumulative frequency against the middle-class value instead of the upper bound, but this is easily corrected. However, while students often do well plotting cumulative frequency graphs marks are often lost when asked to interpret them within the context of the data.

In this video, I demonstrate how to interpret cumulative frequency graphs.

To help students focus on interpreting cumulative frequency graphs within the context of the data, I created five problem-solving questions where interpreting the graph is a small step in solving a much bigger problem. In this blog, I would like to share three questions with you.

## Cumulative Frequency and Percentages

This question challenges students to investigate whether 15% of families browse online for 12 hours of more each week.

Students use the graph to determine the frequency of families who browsed online for 12 or more hours. This is then written as a fraction of the total sample and converted to a percentage.

This question can be completed without a calculator because the sample size is 200.

## Cumulative Frequency and Ratio

In this question, students are challenged to link cumulative frequency with sharing an amount to a ratio.

Of the 120 people who sat a test the ratio of those who failed to those who passed is 3 : 5..

By working out the value of each share, students use the cumulative frequency graph to find the minimum mark needed to pass.

## Cumulative Frequency and Percentage Profit

Students need to break up the cumulative frequency graph into 4 sections. Each section represents the size and value of the onion.

By working out how many onions fall in each price category students calculate the total sale value and compare it to the cost of producing each onion to work out the percentage profit.

## Teach this lesson

My name is Jonathan Robinson, and I am passionate about teaching mathematics. I am Head of Maths in the South East of England and have taught for over 15 years. I am proud to have helped teachers worldwide continue engaging and inspiring their students with my lessons.

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