Data and probability · Ages 14–15
Misleading statistical charts worksheet
Part of: Cumulative frequency & charts
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Misleading statistical charts 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 bar chart compares two phones' battery capacities (hundreds of mAh), its vertical axis starting at 50. How many times as tall as bar A does bar B look?
Answer:
2.The bar chart compares two phones' battery capacities (hundreds of mAh), its vertical axis starting at 60. How many times as tall as bar A does bar B look?
Answer:
3.The bar chart shows how many tubs of ice cream two branches sold in a week, its vertical axis starting at 100. Branch A sold tubs and branch B .
Fill in each blank
Answer:
4.The bar chart shows how many tubs of ice cream two branches sold in a week, its vertical axis starting at 80. Branch A sold tubs and branch B .
Fill in each blank
Answer:
5.A drinks shop's poster compares two drinks' sales in a day (cups) on a bar chart whose vertical axis starts at 100. Drink A sold 103 cups, and bar B looks 4 times as tall as bar A. How many cups did drink B really sell?
Answer:
6.Ming's poster shows savings as a picture of a money bag. This year's savings are 2.5 times last year's, and the bag is drawn 2.5 times as long and 2.5 times as wide. How many times as large is this year's bag's area?
Answer:
7.A drinks shop's poster compares two drinks' sales in a day (cups) on a bar chart whose vertical axis starts at 60. Drink A sold 68 cups, and bar B looks 3 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)
8.A bar chart's vertical scale reads 0, 2, 4, 6, 10 from the bottom up, its lines all equally far apart. The scale is even.
True or false?
Answer:
9.A bar chart's vertical scale reads 0, 4, 6, 8, 10 from the bottom up, its lines all equally far apart. The scale is even.
True or false?
Answer:
10.In the bar chart below, the vertical axis starts at 0. Bar B is 2 times as tall as bar A, so B's value is 2 times A's too.
True or false?
Answer:
11.A firm says the bar chart below shows this year's orders (hundreds) are several times last year's: A is last year, B this year. What is misleading about it?
- A. Nothing is misleading
- B. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values
- C. The bars have different widths
- D. It should have been a line graph
Choose the right answer
Answer:
12.In the bar chart below, the vertical axis starts at 50. Bar B is 2 times as tall as bar A, so B's value is 2 times A's too.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.The bar chart compares how much air (m³) two air purifiers clean in an hour, its vertical axis starting at 60. By what percentage is B really more than A, to 1 decimal place?
Working:
Answer:
14.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 80. Last year was , this year ; bar B looks times as tall as bar A.
Fill in each blank
Working:
Answer:
15.A charity's annual report shows two years' donations as squares: $6 million last year, $24 million this year. The designer makes this year's square's side the same multiple of last year's as the donations are. This year's donations are times last year's; drawn like this, this year's square has times the area; for the areas to show the donations fairly, the side should be only times as long.
Fill in each blank
Working:
Answer:
16.Ming's poster compares two years' recycling with two pictures of a bottle: this year's is 4 times last year's, so the bottle is drawn 4 times as tall and 4 times as wide. Comparing the pictures' areas, how many times last year's will this year's look?
- A. 64
- B. 16
- C. 8
- D. 4
Choose the right answer
Working:
Answer:
17.The bar chart compares how much air (m³) two air purifiers clean in an hour, its vertical axis starting at 80. By what percentage is B really more than A, to 1 decimal place?
Working:
Answer:
18.A charity's annual report shows two years' donations as squares: $9 million last year, $81 million this year. The designer makes this year's square's side the same multiple of last year's as the donations are. This year's donations are times last year's; drawn like this, this year's square has times the area; for the areas to show the donations fairly, the side should be only times as long.
Fill in each blank
Working:
Answer:
Show the answers and working
Misleading statistical charts worksheet: Answers and working
Part A: Working out and filling in
1. 2 times
Starting at 50, bar A is 58 − 50 high and bar B 66 − 50: 2 times as tall, though 66 ÷ 58 is far less than 2.
2. 2 times
Starting at 60, bar A is 68 − 60 high and bar B 76 − 60: 2 times as tall, though 76 ÷ 68 is far less than 2.
3. 116, 106
The axis starts at 100, so read each bar against the scale: A is 116, B is 106.
4. 84, 82
The axis starts at 80, so read each bar against the scale: A is 84, B is 82.
5. 112 cups
The bars start at 100: bar A is 103 − 100 = 3 high, bar B 4 × 3 = 12, so B = 100 + 12 = 112 cups, short of 4 times A.
6. 6.25 times
Length and width both times 2.5 make the area 2.5 × 2.5 = 6.25 times: it looks 6.25 times as much, though it is really 2.5 times.
7. 84 cups
The bars start at 60: bar A is 68 − 60 = 8 high, bar B 3 × 8 = 24, so B = 60 + 24 = 84 cups, short of 3 times A.
Part B: Choose, or true or false
8. False
On an even scale neighbouring marks differ by the same amount; here they differ by 2, 2, 2, 4.
9. False
On an even scale neighbouring marks differ by the same amount; here they differ by 4, 2, 2, 2.
10. True
A is 10, B is 20. Only when the axis starts at 0 is the ratio of the heights the ratio of the values.
11. B. The vertical axis doesn't start at 0, so the heights aren't in proportion to the values
Starting at 100, the bars are only 104 − 100 and 118 − 100 high, stretching the gap; really 118 is just 118 − 104 more than 104.
12. False
A is 75, B is 100. Only when the axis starts at 0 is the ratio of the heights the ratio of the values.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 11.8%
A = 68, B = 76: (76 − 68) ÷ 68 × 100% ≈ 11.8%, far less than the bars suggest.
14. 82, 88, 4
Against the scale, 82 and 88; the bars start at 80, so 88 − 80 is 4 times 82 − 80, though 88 is far from 4 times 82.
15. 4, 16, 2
24 ÷ 6 = 4; a side 4 times as long makes the area 4 × 4 = 16 times, an exaggeration; for 4 times the area the side need only be 2 times, as 2 × 2 = 4.
16. B. 16
Height and width both times 4 make the area 4 × 4 = 16 times: it looks 16 times, though it is really 4.
17. 7.3%
A = 82, B = 88: (88 − 82) ÷ 82 × 100% ≈ 7.3%, far less than the bars suggest.
18. 9, 81, 3
81 ÷ 9 = 9; a side 9 times as long makes the area 9 × 9 = 81 times, an exaggeration; for 9 times the area the side need only be 3 times, as 3 × 3 = 9.
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