# 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 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 of the 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 work out 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

Here, students need to break up the cumulative frequency graph into 4 sections. Each section represents a size and value of 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 currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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