# Cumulative Frequency – The Answers Revealed!

Last week’s question on plotting a Cumulative Frequency Diagram was one of the worst answered questions across the whole of the free daily GCSE Revision Streamto date, with less than 40% of students answering it correctly. This proportion was true across our own Year 11s, despite the fact that we must have covered cumulative frequency diagrams approximately 54 million times over the last few years.

Let’s have a reminder of the question, and a look at how the students answered it: The majority of incorrect responses by students were split across B and C. We can delve into students’ explanations to discover why.

There were two groups of students here – those who had not read the question, and those who have two key misconceptions:

The cost across the x-axis has cumulative values and so median of these values is appropriate to use for the scale. The median of the inequality value 20<£≤40 is 30. The point on the graph must have 30 as it’s x-coordinate. We are told directly that it’s y value is 12 as that is it’s frequency and the label for the y-axis is frequency. The coordinates of the point that would correctly that would represent the highlighted row to draw a cumulative frequency are (30, 12) and the only point with that coordinate is C.”

Because the coordinates are 30 across, because the placement needs to be between 20 and 40, and up 12, which of course is the frequency

because you plot the midpoint and the frequency and on the graph we can see that 12 (frequency) has been plotted and so has 30 which is the mid point.”

With the GCSE Maths exams getting closer, now is the perfect time to sign your Year 11s students up to the free daily GCSE Revision Stream. Over 20,000 students around the country cannot be wrong 