Cumulative frequency & charts · Ages 14–15
Cumulative frequency polygons
Points at upper boundaries; for 'at least', take from the total.
How to do it
Method
Points at upper boundaries; for 'at least', take from the total
40 in all, 30 below 59.5: 40 − 30 = 10 are at least 59.5
Another way
Make it a table
Boundaries 49.5, 59.5, 69.5 → cumulative 12, 30, 40
In full
A cumulative frequency polygon plots each class's cumulative frequency at its upper class boundary and joins the points with straight lines; the first point is the first class's lower boundary, at cumulative frequency 0. So the curve only rises or stays level. To read it: going up from the boundary 59.5 to 30 means 30 data are less than 59.5. For how many are at least a value, take the number less than it from the total: with 40 in all and 30 below 59.5, 40 − 30 = 10 are 59.5 or more. For one class's frequency, subtract the cumulative frequencies at its two boundaries. Or first write the points down as a cumulative frequency table and work from the table: the same answers.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The cumulative frequency polygon shows the ages (in years) of a choir's singers. How many are younger than 49.5?
Show the answer and working
Answer: 23 singers
Go up from 49.5 on the axis and read the cumulative frequency: 23 are younger than 49.5.
Example 2
The cumulative frequency polygon shows how much water (m³) each household in an estate used in a month. How many households does it show?
Show the answer and working
Answer: 37 households
The last point of a cumulative frequency polygon is the total frequency: 37.
Example 3
The cumulative frequency polygon shows the heights (cm) of a dance group. 5 of them are between 24.5 cm and 29.5 cm tall.
True or false?
Show the answer and working
Answer: True
The number below 29.5 minus the number below 24.5: 5.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The cumulative frequency polygon shows how much water (m³) each household in an estate used in a month. How many households does it show?
Answer:
2.The cumulative frequency polygon shows the ages (in years) of a choir's singers. How many are younger than 44.5?
Answer:
3.The cumulative frequency polygon shows how many goals each player in a football league scored in a season. How many are in the class 70–79?
Answer:
4.The cumulative frequency polygon shows a group of hawkers' takings in a day (in hundreds of dollars). Which class has the most hawkers?
- A. 70–79
- B. 90–99
- C. 60–69
- D. 100–109
Choose the right answer
Answer:
5.The cumulative frequency polygon shows the heights (cm) of a dance group. 5 of them are between 39.5 cm and 49.5 cm tall.
True or false?
Answer:
All the answers
- 1. 40 households
- 2. 9 singers
- 3. 7 players
- 4. B. 90–99
- 5. True
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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