Data and probability · Ages 14–15
Cumulative frequency & charts worksheet
Covers: Frequency polygons, Cumulative frequency, Cumulative frequency polygons, Interpreting frequency polygons and curves, Choosing a statistical chart, Misleading statistical charts
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Cumulative frequency & charts worksheet
Data and probability · Ages 14–15
Numsprite
numsprite.com
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 frequency polygon shows how many minutes a running club's members ran last week. How many members does the club have?
Answer:
2.The histogram and frequency polygon show how many minutes a swimming squad's members trained in a week. How many are in the classes with class mark 52 or more?
Answer:
3.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:
4.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 40 hours or more?
Answer:
5.The cumulative frequency polygon shows how many minutes 40 passengers waited at a station. What percentage of them waited less than 79.5 minutes?
Answer:
6.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 49.5 m³. How many flats used less than 49.5 m³?
Answer:
7.Ming's poster shows savings as a picture of a money bag. This year's savings are 3 times last year's, and the bag is drawn 3 times as long and 3 times as wide. How many times as large is this year's bag's area?
Answer:
8.A drinks shop's poster compares two drinks' sales in a day (cups) on a bar chart whose vertical axis starts at 40. Drink A sold 42 cups, and bar B looks 2.5 times as tall as bar A. How many cups did drink B really sell?
Answer:
Part B: Choose, or true or false (2 marks each)
9.The cumulative frequency polygon shows the heights (cm) of a dance group. 24 of them are between 69.5 cm and 89.5 cm tall.
True or false?
Answer:
10.The cumulative frequency polygon shows a group of hawkers' takings in a day (in hundreds of dollars). Which class has the most hawkers?
- A. 40–49
- B. 20–29
- C. 30–39
- D. 50–59
Choose the right answer
Answer:
11.An online poll asked 200 people which of football, basketball, swimming and badminton they like best, to compare how many chose each. Which chart suits it best?
- A. A histogram
- B. A bar chart
- C. A line graph
- D. A cumulative frequency polygon
Choose the right answer
Answer:
12.In a survey, each person chose one of four answers, chosen by 12%, 11%, 11% and 71% of people. These figures can be drawn as a pie chart.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.The table shows how many phones a phone shop sold each day for a month (classes on the left, days on the right). The manager draws it as a frequency polygon: the class 80–84 is the point (, ).
Fill in each blank
Working:
Answer:
14.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 $55. How many gifts does it need?
Working:
Answer:
15.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:
16.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:
17.A chain wants to compare how 2 branches' monthly takings rose and fell over the past year. Which chart suits it best?
- A. A pie chart for each branch
- B. A line graph with each branch's line on it
- C. A stem-and-leaf diagram
- D. A histogram
Choose the right answer
Working:
Answer:
18.A telecoms firm advertises with the bar chart below: this year's customers (B, in ten thousands) far outnumber last year's (A), its vertical axis starting at 100. Last year was , this year ; bar B looks times as tall as bar A.
Fill in each blank
Working:
Answer:
Show the answers and working
Cumulative frequency & charts worksheet: Answers and working
Part A: Working out and filling in
1. 36 members
Add the points' heights (the frequencies), leaving out the 0s at the ends: 36 in all.
2. 23 people
From class mark 52 on, add the frequencies of the points to its right: 23.
3. 50
A cumulative frequency adds the frequencies from the first class on: the row above's cumulative frequency plus this row's frequency is 50.
4. 8 players
39 are below 39.5 out of 47 in all, so 47 − 39 = 8 spent 40 or more.
5. 75%
30 waited less than 79.5: 30 ÷ 40 × 100% = 75%.
6. 18 flats
From a percentage to a number: the total × the percentage = 40 × 45% = 18.
7. 9 times
Length and width both times 3 make the area 3 × 3 = 9 times: it looks 9 times as much, though it is really 3 times.
8. 45 cups
The bars start at 40: bar A is 42 − 40 = 2 high, bar B 2.5 × 2 = 5, so B = 40 + 5 = 45 cups, short of 2.5 times A.
Part B: Choose, or true or false
9. False
The number below 89.5 minus the number below 69.5: 22.
10. B. 20–29
A class's frequency is how far its stretch of line rises: the steepest, rising 12, is 20–29.
11. B. A bar chart
Comparing amounts in categories is a bar chart's job: a bar each, compared at a glance.
12. False
A pie chart's parts must make the whole, 100%: 12 + 11 + 11 + 71 = 105.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 82, 11
Across, the class mark (80 + 84) ÷ 2 = 82; up, the frequency 11.
14. 26 gifts
33 spent less than $55 (the class before's cumulative frequency) out of 59: 59 − 33 = 26 gifts.
15. 9 members
The class 80–89 has boundaries 80 − 0.5 and 89 + 0.5; subtract the cumulative frequencies there: 9.
16. 5 laptops
27 last less than 69.5 out of 32: 32 − 27 = 5.
17. B. A line graph with each branch's line on it
Change over time is a line graph's job; several lines on one chart compare the rises and falls.
18. 106, 118, 3
Against the scale, 106 and 118; the bars start at 100, so 118 − 100 is 3 times 106 − 100, though 118 is far from 3 times 106.
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