Cumulative Frequency
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Build a cumulative table
Create a running total column - Draw the curve
Plot cumulative frequency graphs - Read median & quartiles
Find median, LQ, UQ from the graph - Interquartile range
Calculate and interpret IQR
Before This Topic
Your child should be comfortable with:
- Charts & Data (Year 4)
- Probability (Year 7)
Common Mistakes
- Plotting cumulative frequency at the middle of each class interval instead of at the upper boundary
Cumulative frequency values must be plotted at the UPPER boundary of each class interval, not the middle. For the class 10-20, plot the cumulative frequency at 20 (not at 15). This is because the running total shows how many values are up to that point. - Reading the median as the middle value of the frequency column instead of using the graph
The median is NOT found from the frequency column directly. Find n/2 on the cumulative frequency axis (where n is the total frequency), draw a horizontal line to the curve, then drop down to the x-axis to read the median value.
Tips for Parents
- Explain cumulative frequency as a "running total" — each row adds the previous frequencies together. It always goes up or stays the same, never down.
- Practise drawing the S-shaped curve: plot points at upper class boundaries, join with a smooth curve (not straight lines). The shape should look like a stretched S.
- To find the median from the graph, find half the total frequency on the y-axis, go across to the curve, then down to the x-axis. For quartiles, use a quarter and three quarters of the total.
- Discuss what the interquartile range tells us: "The IQR shows the spread of the middle 50% of the data. A small IQR means most values are close together; a large IQR means they are spread out."
Key Words
- Cumulative frequency — A running total of frequencies — each value is the sum of all frequencies up to that point.
- Upper class boundary — The highest value in a class interval — for the class 10-20, the upper boundary is 20.
- Median — The middle value of all the data — found at the n/2 position on a cumulative frequency graph.
- Lower quartile (LQ) — The value one quarter of the way through the data — found at n/4 on the cumulative frequency graph.
- Upper quartile (UQ) — The value three quarters of the way through the data — found at 3n/4 on the cumulative frequency graph.
- Interquartile range (IQR) — The difference between the upper and lower quartiles (UQ - LQ) — it measures the spread of the middle half of the data.
Where This Fits
Before this topic: Children should be able to read and interpret frequency tables, understand grouped data, and know how to find the mean and median from a list.
After this topic: Cumulative frequency leads to box plots, histograms with unequal class widths, comparing distributions, and statistical analysis at GCSE and A-level.
How MathCraft Teaches This
In MathCraft, Cumulative Frequency is taught through the Money, Data & Measure adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Cumulative Frequency with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
Try MathCraft Free No credit card required