Misleading Graphs

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Show your work for each problem.

1.
The vertical axis of a bar graph starts at 90 instead of 0. What is the main danger?
1. a)Differences look smaller than they really are
2. b)The values can no longer be read
3. c)Differences look bigger than they really are
4. d)The bars swap their order
2.
A line graph shows that sales grew from 200 to 230. What is the real percent increase? Write only the number (for 12% write 12).
3.
A pie chart shows four slices labelled 35%, 30%, 25% and 20%. By how many percentage points is the total too big?
4.
A pie chart has four slices. Three are labelled 45%, 25% and 20%; the fourth has no label. What percent should the fourth slice be? Write only the number.
5.
A line graph with a squashed scale shows a price falling from 80 to 60, and the line looks almost flat. What is the real percent change? (A decrease is negative.)
6.
Which of these graphs is drawn fairly?
1. a)A picture graph where twice the amount gets an icon twice as tall and twice as wide
2. b)A bar graph whose axis starts at 95 to show small differences
3. c)A bar graph whose axis starts at 0 with equal steps
4. d)A pie chart whose slices add up to 120%
7.
In a picture graph, one coin icon stands for last year's savings. This year's savings are twice as large, and the artist draws the coin twice as tall and twice as wide. How many times bigger does the new coin look (by area)?
1. a)8 times
2. b)2 times
3. c)3 times
4. d)4 times
8.
A bar graph compares two shops: shop A sold 66 bikes and shop B sold 60 bikes. The vertical axis starts at 57. How many times taller does bar A look, and what is the real percent difference?
9.
A stretched line graph shows a town's electricity use rising from 1200 to 1260 units. The line shoots up steeply. What is the real percent increase?
10.
A 3D graph shows car sales as cubes. The second cube has every edge 2 times as long as the first. How many times bigger is the volume of the second cube?
11.
A line graph puts the years 2000, 2010, 2020, 2021 and 2022 at equal distances on the horizontal axis. What is misleading about it?
1. a)The time gaps are not equal, so the slopes cannot be compared
2. b)The axis should start at year 0
3. c)The values on the vertical axis must be wrong
4. d)Line graphs cannot show years
12.
A graph shows a tree's height: 30 cm in 2000, 50 cm in 2010 and 60 cm in 2015, with the three years at equal distances. The second piece of line looks flatter. Find the growth per year in each period.
13.
A graph of monthly rent uses a vertical axis from 0 to 10000 dollars, so the line looks flat. The rent actually rose from 800 to 1000 dollars. What is the real percent increase? Write only the number.
14.
On a bar graph, bar A looks exactly twice as tall as bar B. Later you notice that the axis starts at 40 and that B = 50. What is the value of A, and how many percent more than B is it?
15.
A share price was 120 in 2019, 60 in 2022 and 75 in 2024. An advert shows only 2022 to 2024. Find the percent change the advert shows, then the percent change over the whole time from 2019 to 2024.
16.
On a bar graph with a truncated axis, a bar for the value 50 is drawn 5 cm tall and a bar for the value 60 is drawn 15 cm tall. At what value does the axis start?
17.
A headline says "Sales doubled!". The bar graph shows 600 for 2023 and 700 for 2024, and its axis starts at 500, so the 2024 bar is drawn twice as tall. What is the real ratio of 2024 sales to 2023 sales?
1. a)2 times
2. b)7/6, about 1.17 times
3. c)1.5 times
4. d)4 times
18.
A country recycled 2 million tons in 2015 and 8 million tons in 2025. An infographic makes the 2025 bottle icon 4 times as tall and 4 times as wide as the 2015 icon. Find how much the picture exaggerates, and the fair scale for each side.