Cumulative frequency & charts · Ages 14–15
Cumulative frequency
Add as you go; to go back, subtract neighbours.
How to do it
Method
Add as you go; to go back, subtract neighbours
Frequencies 3, 5, 8, 4 → cumulative 3, 8, 16, 20
Another way
Subtract to go back
16 − 8 = 8
In full
A cumulative frequency is how many data there are up to and including a class: add the frequencies class by class from the first. Frequencies 3, 5, 8, 4 give cumulative frequencies 3, 3 + 5 = 8, 8 + 8 = 16, 16 + 4 = 20; the last is always the total. A class's cumulative frequency is the number of data less than its upper class boundary: 60–69 has upper boundary 69.5, so its cumulative frequency of 16 means 16 data are below 69.5. The other way round, to get the frequencies back, subtract neighbouring cumulative frequencies: 16 − 8 = 8 is the third class's. Check: the frequencies you get back add up to the last cumulative frequency.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The table shows how far (km) a cycling club's members rode in a month: classes on the left, frequencies in the middle, cumulative frequencies on the right. What is the '?'?
Show the answer and working
Answer: 27
A cumulative frequency adds the frequencies from the first class on: the row above's cumulative frequency plus this row's frequency is 27.
Example 2
The five classes of a frequency table have frequencies 1, 12, 11, 15, 8 in order. Their cumulative frequencies are , , , , .
Fill in each blank
Show the answer and working
Answer: 1, 13, 24, 39, 47
Add as you go: 1, 1 + 12 = 13, 13 + 11 = 24, 24 + 15 = 39, 39 + 8 = 47, the last the total.
Example 3
The table is the cumulative frequency table of a badminton club's members' ages (classes on the left, cumulative frequencies on the right). 21 members are younger than 44.5.
True or false?
Show the answer and working
Answer: True
44.5 is the upper boundary of the class ending there, so the number below it is that class's cumulative frequency: 21.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The table is the cumulative frequency table of how many books a bookshop sold each day for a month (classes on the left, cumulative frequencies on the right). How many days are in the class 60–64?
Answer:
2.The table shows how far (km) a cycling club's members rode in a month: classes on the left, frequencies in the middle, cumulative frequencies on the right. What is the '?'?
Answer:
3.The table is the cumulative frequency table of a badminton club's members' ages (classes on the left, cumulative frequencies on the right). 10 members are younger than 29.5.
True or false?
Answer:
4.The table shows a restaurant's lunchtime customers each day for a month (classes on the left, frequencies in the middle, cumulative frequencies on the right). What is the '?' in the middle column?
Answer:
5.The table is the cumulative frequency table of how many hours an online game's players spent online in a week (classes on the left, cumulative frequencies on the right). How many players spent 30 hours or more?
Answer:
All the answers
- 1. 5 days
- 2. 24
- 3. False
- 4. 13
- 5. 37 players
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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