Cumulative frequency & charts · Ages 14–15
Interpreting frequency polygons and curves
Compare positions; percentage = number ÷ total × 100%.
How to do it
Method
Compare positions; percentage = number ÷ total × 100%
35 of 50 below 59.5: 35 ÷ 50 × 100% = 70%
Another way
From a percentage to a number
50 × 70% = 35
In full
To compare two sets drawn on one chart, look at where each sits: the set whose frequency polygon peaks further right generally has larger values; adding up each set's frequencies above the same value and comparing is surer still. A cumulative frequency polygon gives percentages: the number below a value ÷ the total × 100%. With 35 of 50 below 59.5, that is 35 ÷ 50 × 100% = 70%. Or the other way, from a percentage to a number: the total × the percentage. Careful: a chart shows how many are in each class, not each value exactly, so a question like 'what is the largest value?' can't be settled from it.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The cumulative frequency polygon shows how many minutes 40 passengers waited at a station. What percentage of them waited less than 49.5 minutes?
Show the answer and working
Answer: 2.5%
1 waited less than 49.5: 1 ÷ 40 × 100% = 2.5%.
Example 2
The two frequency polygons show two branches' customers each day (solid: branch A, dashed: branch B). In the classes with class mark 44.5 or more, branch A has more days than branch B.
True or false?
Show the answer and working
Answer: True
Class mark 44.5 or more: branch A (solid) 18 days in all, branch B (dashed) 13.
Example 3
The cumulative frequency polygon shows the battery life (hours) of 40 phones. What percentage last at least 79.5 hours?
Show the answer and working
Answer: 57.5%
17 last less than 79.5, so 40 − 17 = 23 last at least 79.5: 23 ÷ 40 × 100% = 57.5%.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The water 40 flats on an estate used in a month is drawn as a cumulative frequency polygon, and from it 45% of the flats used less than 39.5 m³. How many flats used less than 39.5 m³?
Answer:
2.The cumulative frequency polygon shows how many minutes 50 passengers waited at a station. What percentage of them waited less than 49.5 minutes?
Answer:
3.The cumulative frequency polygon shows the weights (g) of a batch of apples. How many weigh between 34.5 g and 44.5 g?
Answer:
4.A cumulative frequency polygon shows 63 data, its first class starting at 60 with class width 10. From the chart alone, which of these can be found?
- A. How many data are below 79.5
- B. The mode
- C. The sum of the data
- D. The largest value
Choose the right answer
Answer:
5.The cumulative frequency polygon shows the battery life (hours) of 50 phones. What percentage last at least 24.5 hours?
Answer:
All the answers
- 1. 18 flats
- 2. 56%
- 3. 15 apples
- 4. A. How many data are below 79.5
- 5. 78%
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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