Data and probability · Ages 14–15

Cumulative frequency polygons worksheet

Part of: Cumulative frequency & charts

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Data and probability · Ages 14–15

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

1.The cumulative frequency polygon shows the ages (in years) of a choir's singers. How many are younger than 59.5?
Answer:
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?
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 90–99?
Answer:
4.The cumulative frequency polygon shows the serve speeds (km/h) of a group of tennis players. As a table: are below 24.5, below 29.5, below 34.5.
Fill in each blank
Answer:
5.The cumulative frequency polygon shows how many minutes a group of visitors queued at a theme park. How many queued for at least 74.5 minutes?
Answer:
6.The cumulative frequency polygon shows the serve speeds (km/h) of a group of tennis players. As a table: are below 44.5, below 49.5, below 54.5.
Fill in each blank
Answer:
7.The cumulative frequency polygon shows how many goals each player in a football league scored in a season. How many are in the class 50–59?
Answer:
8.The cumulative frequency polygon shows how many minutes a group of visitors queued at a theme park. How many queued for at least 44.5 minutes?
Answer:

9.The cumulative frequency polygon shows a group of hawkers' takings in a day (in hundreds of dollars). Which class has the most hawkers?
- A. 30–34
- B. 45–49
- C. 35–39
- D. 40–44
Choose the right answer
Answer:
10.The cumulative frequency polygon shows the heights (cm) of a dance group. 7 of them are between 44.5 cm and 54.5 cm tall.
True or false?
Answer:
11.The cumulative frequency polygon shows the heights (cm) of a dance group. 14 of them are between 54.5 cm and 59.5 cm tall.
True or false?
Answer:
12.The cumulative frequency polygon shows the heights (cm) of a dance group. 28 of them are between 34.5 cm and 44.5 cm tall.
True or false?
Answer:

13.The cumulative frequency polygon shows how many minutes a firm's staff take to get to work. take less than 24.5 minutes; the firm pays an allowance to those taking at least 39.5 minutes, people.
Fill in each blank
Working:
Answer:
14.The cumulative frequency polygon shows a restaurant's waiting time for a table (minutes) each evening for a month. It says, 'On more than half the evenings the wait is under 69.5 minutes.' That is right.
True or false?
Working:
Answer:
15.The cumulative frequency polygon shows how many seconds a climbing club's members took on a climb. How many took from 70 to 79 seconds?
Working:
Answer:
16.The cumulative frequency polygon shows an online shop's orders each day for a month. Work back to the frequency table: the first class has days, the second , the third .
Fill in each blank
Working:
Answer:
17.The cumulative frequency polygon shows a restaurant's waiting time for a table (minutes) each evening for a month. It says, 'On more than half the evenings the wait is under 49.5 minutes.' That is right.
True or false?
Working:
Answer:
18.The cumulative frequency polygon shows how many seconds a climbing club's members took on a climb. How many took from 80 to 89 seconds?
Working:
Answer:

Show the answers and working

Cumulative frequency polygons worksheet: Answers and working

1. 19 singers
Go up from 59.5 on the axis and read the cumulative frequency: 19 are younger than 59.5.
2. 36 households
The last point of a cumulative frequency polygon is the total frequency: 36.
3. 9 players
Subtract the cumulative frequencies at the class's two boundaries: 9.
4. 10, 15, 27
Read the cumulative frequency above each upper boundary: 10, 15, 27.
5. 21 visitors
28 queued less than 74.5 out of 49: 49 − 28 = 21 queued at least 74.5.
6. 5, 10, 19
Read the cumulative frequency above each upper boundary: 5, 10, 19.
7. 7 players
Subtract the cumulative frequencies at the class's two boundaries: 7.
8. 24 visitors
7 queued less than 44.5 out of 31: 31 − 7 = 24 queued at least 44.5.

9. A. 30–34
A class's frequency is how far its stretch of line rises: the steepest, rising 14, is 30–34.
10. False
The number below 54.5 minus the number below 44.5: 8.
11. True
The number below 59.5 minus the number below 54.5: 14.
12. False
The number below 44.5 minus the number below 34.5: 27.

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

13. 6, 10
Above 24.5 the curve reads 6; at least 39.5 is the total minus those below 39.5: 37 − 27 = 10.
14. False
Above 69.5 the curve reads 15 evenings out of 42: compare 15 with half of 42.
15. 3 members
The class 70–79 has boundaries 70 − 0.5 and 79 + 0.5; subtract the cumulative frequencies there: 3.
16. 10, 13, 8
Each class's frequency is the difference of the cumulative frequencies at its two boundaries: 10, 13, 8.
17. False
Above 49.5 the curve reads 16 evenings out of 52: compare 16 with half of 52.
18. 13 members
The class 80–89 has boundaries 80 − 0.5 and 89 + 0.5; subtract the cumulative frequencies there: 13.

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