To combine two cumulative frequency tables, add the two counts at each matching cut-off. The result tells you how many observations across both groups are at or below that value.
Use the same units and the same cut-off rule for both groups. A count of times at or below 10 minutes can be added to another count at or below 10 minutes. Check the labels before combining rows.
- Match the cut-offs by value.
- Add the cumulative counts for those cut-offs.
- Subtract neighbouring totals if asked for a class frequency.
Worked example | Combine two sets of journey times
Group A has cumulative counts of 8, 20 and 30 for journey times of at most 10, 20 and 30 minutes. Group B has counts of 5, 15 and 20 at the same cut-offs. Every journey took at most 30 minutes.
The combined cumulative counts are 8 + 5 = 13, 20 + 15 = 35 and 30 + 20 = 50. If you draw the combined cumulative frequency diagram, the corresponding points are (10, 13), (20, 35) and (30, 50).
Find the number in one interval
For journeys longer than 10 minutes and at most 20 minutes, subtract the 13 journeys at or below 10 from the 35 at or below 20. This gives 22 journeys.
You can check by finding the interval frequency for each group first. Group A contributes 20 − 8 = 12. Group B contributes 15 − 5 = 10. The total is still 22.
Find the percentage above 20 minutes
Use the combined table to find the percentage of journeys lasting more than 20 minutes.
Answer. There are 50 journeys in total and 35 took at most 20 minutes. The remaining 15 journeys account for 15 ÷ 50 × 100% = 30%.
Frequently asked questions
Can I add rows if the cut-offs differ?
Use shared cut-offs where the counts are known for both groups. If one cut-off is missing, you need the original data or a justified estimate before you can combine counts at that value.
Why does the final count equal the total sample size?
Here the final cut-off includes every observation. Each group’s final count is therefore its size, so their sum is the combined size.
Official information
SEAB, 2027 SEC G3 Mathematics syllabus (K310), Data Analysis, cumulative frequency diagrams. Syllabus checked 11 November 2026. The examples are original.