Data and probability · Ages 14–15
Cumulative frequency worksheet
Part of: Cumulative frequency & charts
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Cumulative frequency worksheet
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.
Part A: Working out and filling in (2 marks each)
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 '?'?
Answer:
2.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 70–79?
Answer:
3.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:
4.The frequency table shows the ages (in years) of a basketball squad (classes on the left, numbers of players on the right). How many are younger than 39.5?
Answer:
5.The five classes of a frequency table have frequencies 2, 10, 15, 10, 8 in order. Their cumulative frequencies are , , , , .
Fill in each blank
Answer:
6.The frequency table shows the ages (in years) of a basketball squad (classes on the left, numbers of players on the right). How many are younger than 44.5?
Answer:
7.The five classes of a frequency table have frequencies 5, 1, 3, 11, 7 in order. Their cumulative frequencies are , , , , .
Fill in each blank
Answer:
8.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 100 hours or more?
Answer:
9.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:
10.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 65 hours or more?
Answer:
Part B: Choose, or true or false (2 marks each)
11.The table is the cumulative frequency table of a badminton club's members' ages (classes on the left, cumulative frequencies on the right). 26 members are younger than 109.5.
True or false?
Answer:
12.The table is the cumulative frequency table of a badminton club's members' ages (classes on the left, cumulative frequencies on the right). 7 members are younger than 34.5.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.The table is the cumulative frequency table of the ages of a water park's visitors one day (classes on the left, cumulative frequencies on the right). The park says, 'More than half our visitors are younger than 89.5.' That is right.
True or false?
Working:
Answer:
14.The table is the cumulative frequency table of how many people ran in a park each day for a month (classes on the left, cumulative frequencies on the right). The class 35–39 has days and the class 40–44 days.
Fill in each blank
Working:
Answer:
15.The table is the cumulative frequency table of what customers spent ($) in a mall one day (classes on the left, cumulative frequencies on the right). The mall gives a gift to everyone who spent at least $65. How many gifts does it need?
Working:
Answer:
16.The table shows how many egg tarts a bakery sold each day for a month (classes on the left, days on the right). As a cumulative frequency table: the third class's cumulative frequency is and the last class's ; on days it sold fewer than 49.5.
Fill in each blank
Working:
Answer:
17.The table is the cumulative frequency table of what customers spent ($) in a mall one day (classes on the left, cumulative frequencies on the right). The mall gives a gift to everyone who spent at least $40. How many gifts does it need?
Working:
Answer:
18.The table is the cumulative frequency table of the ages of a water park's visitors one day (classes on the left, cumulative frequencies on the right). The park says, 'More than half our visitors are younger than 49.5.' That is right.
True or false?
Working:
Answer:
Show the answers and working
Cumulative frequency worksheet: Answers and working
Part A: Working out and filling in
1. 18
A cumulative frequency adds the frequencies from the first class on: the row above's cumulative frequency plus this row's frequency is 18.
2. 13 days
Subtract neighbouring cumulative frequencies to get the class's frequency: 13 days.
3. 3 days
Subtract neighbouring cumulative frequencies to get the class's frequency: 3 days.
4. 13 players
39.5 is a class's upper boundary: those below it are that class and the ones before, its cumulative frequency, 13.
5. 2, 12, 27, 37, 45
Add as you go: 2, 2 + 10 = 12, 12 + 15 = 27, 27 + 10 = 37, 37 + 8 = 45, the last the total.
6. 30 players
44.5 is a class's upper boundary: those below it are that class and the ones before, its cumulative frequency, 30.
7. 5, 6, 9, 20, 27
Add as you go: 5, 5 + 1 = 6, 6 + 3 = 9, 9 + 11 = 20, 20 + 7 = 27, the last the total.
8. 5 players
33 are below 99.5 out of 38 in all, so 38 − 33 = 5 spent 100 or more.
9. 4
This row's cumulative frequency minus the row above's is this row's frequency: 4.
10. 27 players
13 are below 64.5 out of 40 in all, so 40 − 13 = 27 spent 65 or more.
Part B: Choose, or true or false
11. False
109.5 is the upper boundary of the class ending there, so the number below it is that class's cumulative frequency: 35.
12. False
34.5 is the upper boundary of the class ending there, so the number below it is that class's cumulative frequency: 11.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. True
26 are younger than 89.5 out of 35: compare 26 with half the total.
14. 6, 14
Subtract neighbouring cumulative frequencies: 6 and 14.
15. 20 gifts
5 spent less than $65 (the class before's cumulative frequency) out of 25: 25 − 5 = 20 gifts.
16. 25, 31, 20
Add as you go: 12, 20, 25, 27, 31. Fewer than 49.5 (the second class's upper boundary) is the second class's cumulative frequency, 20.
17. 13 gifts
42 spent less than $40 (the class before's cumulative frequency) out of 55: 55 − 42 = 13 gifts.
18. False
15 are younger than 49.5 out of 41: compare 15 with half the total.
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