Data and probability · Ages 14–15

Interpreting frequency polygons and curves worksheet

Part of: Cumulative frequency & charts

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Data and probability · Ages 14–15

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The cumulative frequency polygon shows how many minutes 40 passengers waited at a station. What percentage of them waited less than 29.5 minutes?
Answer:
2.The water 40 flats on an estate used in a month is drawn as a cumulative frequency polygon, and from it 20% of the flats used less than 49.5 m³. How many flats used less than 49.5 m³?
Answer:
3.The water 40 flats on an estate used in a month is drawn as a cumulative frequency polygon, and from it 65% of the flats used less than 59.5 m³. How many flats used less than 59.5 m³?
Answer:
4.The cumulative frequency polygon shows how many minutes 50 passengers waited at a station. What percentage of them waited less than 39.5 minutes?
Answer:
5.The cumulative frequency polygon shows the weights (g) of a batch of apples. How many weigh between 59.5 g and 79.5 g?
Answer:
6.The cumulative frequency polygon shows the weights (g) of a batch of apples. How many weigh between 49.5 g and 69.5 g?
Answer:
7.The cumulative frequency polygon shows the battery life (hours) of 40 phones. What percentage last at least 69.5 hours?
Answer:
8.The cumulative frequency polygon shows the battery life (hours) of 40 phones. What percentage last at least 49.5 hours?
Answer:

9.The two frequency polygons show two branches' customers each day (solid: branch A, dashed: branch B). In the classes with class mark 37 or more, branch A has more days than branch B.
True or false?
Answer:
10.The two frequency polygons show two branches' customers each day (solid: branch A, dashed: branch B). In the classes with class mark 72 or more, branch A has more days than branch B.
True or false?
Answer:
11.A cumulative frequency polygon shows 49 data, its first class starting at 40 with class width 5. From the chart alone, which of these can be found?
- A. The sum of the data
- B. The largest value
- C. How many data are below 49.5
- D. The mode
Choose the right answer
Answer:
12.A cumulative frequency polygon shows 51 data, its first class starting at 50 with class width 5. From the chart alone, which of these can be found?
- A. The mode
- B. How many data are below 59.5
- C. The sum of the data
- D. The largest value
Choose the right answer
Answer:

13.The cumulative frequency polygon shows how many minutes 40 runners took for a stage of a race. took at least 79.5 minutes, which is % of them.
Fill in each blank
Working:
Answer:
14.The cumulative frequency polygon shows how many minutes 25 customers waited at a bank. waited less than 69.5 minutes, which is % of them.
Fill in each blank
Working:
Answer:
15.The cumulative frequency polygon shows the battery life (hours) of a batch of laptops. Those lasting at least 69.5 hours are labelled 'long-life'. How many are labelled long-life?
Working:
Answer:
16.The two frequency polygons show two branches' customers each day for a month (solid: branch A, dashed: branch B). Which branch has more days in the classes with class mark 77 or more?
- A. It can't be told
- B. They are the same
- C. Branch A
- D. Branch B
Choose the right answer
Working:
Answer:
17.The two frequency polygons show two branches' customers each day for a month (solid: branch A, dashed: branch B). Which branch has more days in the classes with class mark 52 or more?
- A. It can't be told
- B. Branch A
- C. Branch B
- D. They are the same
Choose the right answer
Working:
Answer:
18.The cumulative frequency polygon shows the battery life (hours) of a batch of laptops. Those lasting at least 49.5 hours are labelled 'long-life'. How many are labelled long-life?
Working:
Answer:

Show the answers and working

Interpreting frequency polygons and curves worksheet: Answers and working

1. 47.5%
19 waited less than 29.5: 19 ÷ 40 × 100% = 47.5%.
2. 8 flats
From a percentage to a number: the total × the percentage = 40 × 20% = 8.
3. 26 flats
From a percentage to a number: the total × the percentage = 40 × 65% = 26.
4. 80%
40 waited less than 39.5: 40 ÷ 50 × 100% = 80%.
5. 10 apples
The number below 79.5 minus the number below 59.5: 10.
6. 21 apples
The number below 69.5 minus the number below 49.5: 21.
7. 52.5%
19 last less than 69.5, so 40 − 19 = 21 last at least 69.5: 21 ÷ 40 × 100% = 52.5%.
8. 42.5%
23 last less than 49.5, so 40 − 23 = 17 last at least 49.5: 17 ÷ 40 × 100% = 42.5%.

9. False
Class mark 37 or more: branch A (solid) 7 days in all, branch B (dashed) 10.
10. True
Class mark 72 or more: branch A (solid) 26 days in all, branch B (dashed) 18.
11. C. How many data are below 49.5
49.5 is an upper boundary, so the cumulative frequency above it can be read; the other three need every exact value.
12. B. How many data are below 59.5
59.5 is an upper boundary, so the cumulative frequency above it can be read; the other three need every exact value.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 16, 40
At least 79.5 is the total minus those below 79.5: 16; 16 ÷ 40 × 100% = 40%.
14. 12, 48
Above 69.5 the curve reads 12; 12 ÷ 25 × 100% = 48%.
15. 11 laptops
30 last less than 69.5 out of 41: 41 − 30 = 11.
16. D. Branch B
Class mark 77 or more: A (solid) 11 days, B (dashed) 18.
17. C. Branch B
Class mark 52 or more: A (solid) 14 days, B (dashed) 27.
18. 33 laptops
18 last less than 49.5 out of 51: 51 − 18 = 33.

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