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F13 Recognising Misleading Graphs

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Which of these is the best reason why a bar chart's vertical (frequency) axis should normally start at zero?

A) It makes the chart look more colourful
B) It means the height of each bar fairly represents its value, so differences between bars are not exaggerated
C) It allows more bars to fit on the same page
D) It means the axis needs fewer numbers written on it

(Total for Question 1 is 1 mark)

For each statement about misleading graphs, write down whether it is True or False.

(i)A graph whose vertical axis does not start at zero can make differences between bars look bigger than they really are.(1)

(ii)Adding a 3D effect to a pie chart never changes how big the slices appear to be.(1)

(iii)If two graphs show the same data using different axis scales, they will always give exactly the same visual impression.(1)

(iv)Choosing to show only a short time period of data, rather than the full data set, can be used to make a trend look more dramatic than it really is.(1)

(Total for Question 2 is 4 marks)

Two branches of a bakery, on Elm Street and on Oak Street, recorded how many loaves of bread they sold last Saturday. The bar chart shows the results.

(a)Write down the number of loaves sold at Elm Street.(1)

(b)Write down the number of loaves sold at Oak Street.(1)

(c)Explain why this bar chart could give a misleading impression of the difference in sales between the two bakeries.(2)

(Total for Question 3 is 4 marks)

Two seaside kiosks sold ice creams last weekend. Graph 1 and Graph 2 show exactly the same sales figures, drawn on two different vertical scales.

(a)Using Graph 1, write down the number of ice creams sold at each kiosk.(1)

(b)Which graph, Graph 1 or Graph 2, gives a fairer impression of how the two kiosks compare? Give a reason for your answer.(2)

(c)Explain how Graph 2 could mislead someone into thinking Kiosk Y sold far more ice creams than Kiosk X.(2)

(Total for Question 4 is 5 marks)

A poster advertises two packs of stickers using scaled pictures. The small pack picture is a rectangle 3 cm by 2 cm and is labelled '5 stickers'. The large pack picture is a rectangle 6 cm by 4 cm and is labelled '10 stickers'.

(a)Write down the ratio of the number of stickers in the small pack to the number in the large pack, in the form 1 : n.(1)

(b)Work out the area of each rectangle used in the picture, and hence write down the ratio of the two areas in the form 1 : n.(2)

(c)Explain why using rectangles scaled like this to represent the number of stickers could give a misleading impression.(2)

(Total for Question 5 is 5 marks)

A local newsletter wants to check whether a bar chart is a fair representation of some data before publishing it.

List three checks that could be used to help decide whether a bar chart might be giving a misleading impression.

(Total for Question 6 is 3 marks)

A school records the number of trips run by two clubs. Poster A shows this using rows of identical icons, where each icon stands for 2 trips. Poster B shows the same data using a single icon per club, but the icon is drawn a different size for each club.

(a)Using Poster A, write down the number of school trips run by each club.(1)

(b)State which poster, A or B, gives a fairer impression of the number of trips run by each club. Give a reason for your answer.(2)

(Total for Question 7 is 3 marks)

A survey of 60 people found their favourite pizza topping: Cheese (30 people), Pepperoni (18 people), Vegetable (12 people). Chart 1 shows this data as a flat (2D) pie chart. Chart 2 shows the same data as a 3D pie chart.

(a)Work out the angle that should be used to represent Cheese in a correctly drawn pie chart.(2)

(b)Chart 2 shows the same data as a 3D pie chart. State one reason why drawing a pie chart in 3D, like Chart 2, can give a misleading impression, even though the underlying percentages have not changed.(2)

(Total for Question 8 is 4 marks)

40 students were asked to name their favourite subject.

Subject	Maths	Science	Art
Frequency	16	14	10

A magazine drew a pie chart of this data, using sector angles of 90 degrees for Maths, 90 degrees for Science and 180 degrees for Art.

(a)Using the frequency table, work out the angle that should be used to represent Maths in a correctly drawn pie chart.(2)

(b)Work out the angle that should be used to represent Art in a correctly drawn pie chart, and use this to explain how the magazine's pie chart is misleading.(2)

(Total for Question 9 is 4 marks)

The diagram shows the vertical axis planned for a chart of 'Number of visitors to a museum each day'. The values 0, 10, 20, 50 and 100 are marked at equal distances apart along the axis.

(a)Write down the four gaps between consecutive numbers marked on the axis (0 to 10, 10 to 20, 20 to 50, and 50 to 100).(2)

(b)Explain why marking these values at equal distances apart, despite their gaps being different sizes, could give a misleading impression of any data plotted against this axis.(2)

(Total for Question 10 is 4 marks)

A school records the number of pupils arriving late in a month. Class 7 had 12 late arrivals and Class 8 had 15. The bar chart shows this, with the vertical axis starting at 10.

(a)Write down the number of late arrivals recorded for Class 7 and for Class 8.(1)

(b)Use one of the checks you listed in Question 6 to explain why this chart could give a misleading impression of the difference between the two classes, and work out the actual percentage increase in late arrivals from Class 7 to Class 8.(3)

(Total for Question 11 is 4 marks)

A shop plots its ice cream sales and sun cream sales on the same graph, over 5 months.

Month	Apr	May	Jun	Jul	Aug
Ice cream sales (£)	200	400	800	1000	900
Sun cream sales (£)	10	20	40	50	45

The graph uses a left-hand vertical axis from 0 to 1000 for ice cream sales, and a separate right-hand vertical axis from 0 to 50 for sun cream sales. Drawn this way, the two lines lie exactly on top of each other.

(a)Using the table, work out how many times greater the ice cream sales are than the sun cream sales in April.(2)

(b)The graph has been drawn so that the two lines lie exactly on top of each other. Explain why this could give a misleading impression to someone reading the graph.(2)

(Total for Question 12 is 4 marks)

A charity records its monthly online donations.

Month	Jan	Feb	Mar	Apr	May	Jun
Donations (£)	1000	1050	980	1020	1010	2000

June's total was unusually high because of a single viral social media campaign. A news article only shows a graph of May and June, under the headline 'Donations have doubled - the charity's strategy is working!'

(a)Work out the percentage increase in donations from May to June.(2)

(b)Work out the percentage increase in donations from January to May (the period the article's graph does not show).(2)

(c)Explain why a graph that only shows May and June's donations, like the one above, could give a misleading impression of the charity's overall fundraising trend.(2)

(Total for Question 13 is 6 marks)

Amir is investigating whether the graphs used in local newspaper articles give readers a fair impression of the data. He plans to look at bar charts printed in newspaper articles over one month.

(a)Plan: Suggest one thing Amir should decide before he starts collecting his sample of newspaper bar charts, and give a reason for your suggestion.(2)

(b)Collect: Amir records, for each of his 10 sampled bar charts, whether the vertical axis starts at zero. His results: Yes - 3 charts, No - 7 charts. Write down the fraction of charts in his sample where the axis did not start at zero.(1)

(c)Process: Work out this fraction as a percentage.(2)

(d)Interpret: Amir concludes 'Most of the newspaper bar charts I sampled could be giving a misleading impression, because their vertical axis doesn't start at zero.' Comment on whether his sample of 10 articles is likely to be enough to draw a reliable general conclusion about ALL newspaper graphs.(2)

(Total for Question 14 is 7 marks)

A fitness app's advert shows average daily steps for its users 'Before' using the app (8000 steps) and 'After' using the app for 8 weeks (8800 steps). The bar chart's vertical axis starts at 7500 and goes up to 9000.

(a)Work out the actual percentage increase in average daily steps from Before to After.(2)

(b)Using the values marked on the vertical axis (starting at 7500), work out the ratio of the height of the 'After' bar to the height of the 'Before' bar as drawn on the chart.(2)

(c)Use your answers to parts (a) and (b) to explain how the advert's chart exaggerates the improvement in users' step counts.(2)

(Total for Question 15 is 6 marks)

A charity poster shows money raised in two years using circles. Year A raised £4,000, shown as a circle of radius 2 cm. Year B raised £8,000 (exactly double), shown as a circle of radius 4 cm (double the radius).

(a)Using π = 3.14, work out the area of the circle used for Year A (radius 2 cm). Give your answer correct to 1 decimal place.(2)

(b)Using π = 3.14, work out the area of the circle used for Year B (radius 4 cm). Give your answer correct to 1 decimal place.(2)

(c)The amount raised in Year B is exactly double the amount raised in Year A. Compare this to the ratio of the two circles' areas, and explain why the poster could give a misleading impression.(2)

(Total for Question 16 is 6 marks)

A council records the number of electric car charge points in a county each year.

Year	2021	2022	2023	2024	2025
Charge points	40	55	75	100	140

A newspaper is choosing between two graphs of this data to publish. Graph P shows all five years with a vertical axis from 0 to 150 and years equally spaced. Graph Q shows the same five years, but its vertical axis starts at 40, and the gap between 2024 and 2025 is drawn much smaller than the gaps between the earlier years.

(a)Which graph, Graph P or Graph Q, should the newspaper publish if it wants to give a fair representation of the data? Give one reason.(2)

(b)Identify two separate features of Graph Q that could mislead a reader, referring to specific axes.(2)

(c)Work out the actual percentage increase in the number of charge points from 2021 to 2025.(2)

(Total for Question 17 is 6 marks)

A soft drinks company always chooses to publish whichever version of a sales graph makes their new product look most successful, and never publishes any version that does not support this message.

(a)Give one example of how the company could exploit the vertical axis to make a small increase in sales look bigger than it really is.(2)

(b)Give one example, different from your answer to part (a), of another way a chart could be drawn to exaggerate the company's success.(2)

(c)Explain why it is important for readers to check a graph's axes and scales carefully before drawing conclusions from it, rather than just looking at the general shape of the graph.(2)

(Total for Question 18 is 6 marks)

Mark scheme · F13 Recognising Misleading Graphs

Question 1

B1 B cao
Answer: B) It means the height of each bar fairly represents its value, so differences between bars are not exaggerated

Question 2

(i) B1 True cao
(i) Answer: True
(ii) B1 False cao
(ii) Answer: False
(iii) B1 False cao
(iii) Answer: False
(iv) B1 True cao
(iv) Answer: True

Question 3

(a) B1 46 cao
(a) Answer: 46
(b) B1 50 cao
(b) Answer: 50
(c) B1 identifies that the vertical axis starts at 40, not 0 (a truncated/non-zero axis)
(c) B1 explains this makes the real difference of 4 loaves look much bigger than it really is, since the Oak Street bar looks much taller even though it is only a small amount more
(c) Answer: The vertical axis starts at 40 instead of 0, so the small true difference of 4 loaves (46 compared with 50) is stretched to fill most of the chart, making Oak Street's sales look far higher than Elm Street's.

Question 4

(a) B1 Kiosk X = 82 and Kiosk Y = 90, both cao
(a) Answer: Kiosk X = 82, Kiosk Y = 90
(b) B1 Graph 1
(b) B1 valid reason: its vertical axis starts at 0, so the bar heights are in proportion to the actual number of ice creams sold
(b) Answer: Graph 1, because its vertical axis starts at 0, so the height of each bar is proportional to the true number of ice creams sold.
(c) B1 identifies that Graph 2's vertical axis starts at 76, not 0 (a truncated axis)
(c) B1 explains this makes the relatively small difference of 8 ice creams look enormous, since Kiosk Y's bar appears far taller even though the true values (82 and 90) are less than 10% apart
(c) Answer: Graph 2's vertical axis starts at 76 instead of 0, so the small 8-ice-cream difference between the kiosks fills almost the whole height of the chart, making it look as though Kiosk Y sold far more than Kiosk X, when really the difference is under 10%.

Question 5

(a) B1 1 : 2 cao
(a) Answer: 1 : 2
(b) M1 3 x 2 (=6) and 6 x 4 (=24), oe
(b) A1 1 : 4 cao
(b) Answer: 1 : 4
(c) B1 identifies that the area ratio (1 : 4) is much bigger than the true sticker ratio (1 : 2)
(c) B1 explains the large pack therefore looks four times as big as the small pack, when it really only has twice as many stickers
(c) Answer: Doubling both the width and height of the rectangle quadruples its area, so the large pack's picture looks four times bigger than the small pack's, even though it only contains twice as many stickers.

Question 6

B1 Does the vertical axis start at zero (rather than a higher value)?
B1 Are the gaps between the values marked on the axis all equal (a consistent scale)?
B1 Is the chart clearly labelled with a title, axis labels and units, so it cannot be misread? (oe - accept any three valid checks, e.g. consistent bar widths, or whether the sample size/source is stated)
Answer: e.g. (1) Does the vertical axis start at zero? (2) Are the axis intervals equally spaced? (3) Is the chart fully labelled with a title and units?

Question 7

(a) B1 Chess Club = 6 and Art Club = 10, both cao
(a) Answer: Chess Club = 6, Art Club = 10
(b) B1 Poster A
(b) B1 valid reason: each icon represents a fixed, equal number of trips, so counting icons directly reflects the true numbers, whereas Poster B changes the size of a single icon, distorting the impression via area
(b) Answer: Poster A, because every icon stands for the same fixed number of trips (2), so the totals can be found fairly by counting icons; Poster B instead changes the size of one icon, which exaggerates the visual difference.

Question 8

(a) M1 30/60 x 360, oe
(a) A1 180 (degrees) cao
(a) Answer: 180 degrees
(b) B1 identifies that the tilt/perspective makes the sector nearest the front of the chart look bigger than its true percentage
(b) B1 explains the added 'depth' or side band gives extra visual size that is not part of the real data, so slices can no longer be fairly compared by eye
(b) Answer: Tilting the pie chart and adding a 3D depth band makes the sector at the front look bigger than sectors further back, even when the true percentages are unchanged, so the chart can no longer be judged fairly by eye.

Question 9

(a) M1 16/40 x 360, oe
(a) A1 144 (degrees) cao
(a) Answer: 144 degrees
(b) M1 10/40 x 360 (=90 degrees), oe
(b) A1 explains the magazine used 180 degrees for Art, double the correct 90 degrees, so Art looks twice as popular as it should - making it look like half of students prefer Art when only a quarter (25%) do
(b) Answer: Art should have a 90 degree sector (10/40 x 360), but the magazine drew it as 180 degrees - double the correct size - making it look like half the students prefer Art when really only a quarter do.

Question 10

(a) M1 at least two of the four gaps identified correctly
(a) A1 10, 10, 30, 50 all correct
(a) Answer: 10, 10, 30, 50
(b) B1 explains that equal spacing normally represents equal value gaps, but here the last two gaps (30 and 50) are much bigger than the first two (10 and 10)
(b) B1 explains a value plotted near the top of the axis is squashed into the same visual space as a much smaller true gap lower down, so differences in that region are understated (or a reader could misjudge where a value in that region truly sits)
(b) Answer: Equal spacing usually means equal-sized gaps, but here the top two gaps (30 and 50) are far bigger than the bottom two (10 and 10); this squashes large differences near the top of the axis into the same visual space as small differences near the bottom, so a reader could badly misjudge how visitor numbers really compare.

Question 11

(a) B1 Class 7 = 12 and Class 8 = 15, both cao
(a) Answer: Class 7 = 12, Class 8 = 15
(b) B1 identifies the check that fails: the vertical axis starts at 10, not 0
(b) M1 (15-12)/12 x 100, oe
(b) A1 25% cao, with a comment that this real increase is much smaller than the chart makes it look
(b) Answer: The axis starts at 10, not 0, which fails the zero-start check; the real increase from 12 to 15 is only 25%, far smaller than the chart's appearance suggests (Class 8's bar looks roughly two and a half times as tall as Class 7's).

Question 12

(a) M1 200 / 10, oe
(a) A1 20 (times) cao
(a) Answer: 20 times
(b) B1 identifies that the two vertical axes use very different scales (0 to 1000 for ice cream, 0 to 50 for sun cream)
(b) B1 explains a reader could think the two amounts are similar in size or strongly linked, without noticing the axes do not match, when ice cream sales are actually always 20 times bigger
(b) Answer: The left axis (0 to 1000) and right axis (0 to 50) use completely different scales, chosen so the two lines coincide; a reader glancing at the graph could think sun cream and ice cream sales are similar in size or perfectly linked, without noticing that ice cream sales are actually always 20 times bigger in pounds.

Question 13

(a) M1 (2000-1010)/1010 x 100, oe
(a) A1 awrt 98%
(a) Answer: 98%
(b) M1 (1010-1000)/1000 x 100, oe
(b) A1 1% cao
(b) Answer: 1%
(c) B1 identifies that the full data (Jan to May) shows donations were almost flat, only increasing by about 1% over four months
(c) B1 explains the article's graph ignores this and only shows the sudden 98% jump in June, making it look like fundraising is steadily/rapidly growing when really June was a one-off spike
(c) Answer: From January to May, donations barely changed (only a 1% rise over four months), so the charity's strategy was not producing steady growth; the article's graph hides this and shows only the 98% jump in June, wrongly suggesting an ongoing, dramatic improvement rather than a single unusual month.

Question 14

(a) B1 valid decision suggested, e.g. which newspapers to include, how many articles to sample, or what counts as a 'bar chart'
(a) B1 valid reason linked to getting a fair/representative sample or a workable, consistent definition
(a) Answer: e.g. Amir should decide in advance exactly how many newspapers and articles he will look at, so that his sample is a manageable, consistent size and is not chosen to fit whatever result he expects to find.
(b) B1 7/10 cao
(b) Answer: 7/10
(c) M1 7/10 x 100, oe
(c) A1 70% cao
(c) Answer: 70%
(d) B1 recognises a sample of only 10 is quite small and may not be representative of all newspapers or all types of chart
(d) B1 explains a bigger and more varied sample (e.g. more newspapers, more chart types, over a longer time) would give a more reliable general conclusion
(d) Answer: A sample of only 10 charts, likely from a small number of newspapers, is unlikely to be reliable evidence about ALL newspaper graphs; Amir would need a much bigger, more varied sample (more newspapers, more articles, over a longer period) before drawing a general conclusion with confidence.

Question 15

(a) M1 (8800-8000)/8000 x 100, oe
(a) A1 10% cao
(a) Answer: 10%
(b) M1 1300 (=8800-7500) and 500 (=8000-7500), oe
(b) A1 2.6 : 1 oe (e.g. 13 : 5)
(b) Answer: 2.6 : 1
(c) B1 identifies the vertical axis starts at 7500, not 0, so relatively small differences are stretched to fill the whole chart
(c) B1 correct comparison: the bars suggest steps have increased by a factor of 2.6 (roughly 160%), when the true increase is only 10%
(c) Answer: Because the axis starts at 7500 instead of 0, the 'After' bar is drawn 2.6 times as tall as the 'Before' bar, making it look as though steps have grown by around 160%, when the true increase in average daily steps is only 10%.

Question 16

(a) M1 3.14 x 2², oe
(a) A1 12.6 cm² (awrt)
(a) Answer: 12.6 cm²
(b) M1 3.14 x 4², oe
(b) A1 50.2 cm² (awrt, allow 50.24)
(b) Answer: 50.2 cm²
(c) B1 identifies the area ratio is 4 : 1 (50.24 / 12.56 = 4), not 2 : 1
(c) B1 explains the Year B circle looks four times as big as the Year A circle, even though only twice as much money was raised, exaggerating the improvement
(c) Answer: Doubling the radius quadruples the area (50.24 is 4 times 12.56), so Year B's circle looks four times bigger than Year A's, even though Year B only raised twice as much money - the poster exaggerates how much fundraising improved.

Question 17

(a) B1 Graph P
(a) B1 valid reason, e.g. its vertical axis starts at zero and its years are equally spaced, so both the heights and the gaps between points are proportional to the real data
(a) Answer: Graph P, because its vertical axis starts at 0 and the years are equally spaced, so the shape of the line fairly represents the true year-on-year changes.
(b) B1 the vertical axis does not start at zero (it starts at 40)
(b) B1 the horizontal (year) axis intervals are not equal - the 2024-2025 gap is compressed compared with the other years, exaggerating the steepness of the final rise
(b) Answer: (1) The vertical axis starts at 40, not 0. (2) The horizontal axis is not evenly spaced - the gap between 2024 and 2025 is drawn much smaller than the gaps between the earlier years, making the final rise look steeper than it really is.
(c) M1 (140-40)/40 x 100, oe
(c) A1 250% cao
(c) Answer: 250%

Question 18

(a) B1 identifies starting the vertical axis at a value above zero (a truncated axis)
(a) B1 explains this stretches a small true difference to fill much more of the chart, making it look bigger than it really is
(a) Answer: The company could start the vertical axis at a value close to the sales figures, rather than at zero, so that a small real increase fills most of the height of the chart and looks much larger than it truly is.
(b) B1 valid distinct technique named, e.g. scaling a pictogram symbol's height and width together, using a 3D pie chart effect, using inconsistent pie sector sizing, showing only a cherry-picked short time window, using uneven axis intervals, or using a dual axis chosen to make two data sets appear to match
(b) B1 brief correct explanation of how the chosen technique exaggerates the impression given
(b) Answer: e.g. Showing only a short, cherry-picked time window (such as the single best week of sales) instead of the full year, so a temporary spike looks like a lasting trend of rising success.
(c) B1 explains the shape/pattern alone can look convincing even when the underlying numbers show a much smaller (or different) effect
(c) B1 explains that checking axes and scales (e.g. zero start, equal intervals, clear labels) lets the reader judge the true size of any difference or trend, rather than being misled by the visual impression alone
(c) Answer: A graph's overall shape can look dramatic even when the real underlying change is small, because that shape depends heavily on choices like where the axis starts and how it is scaled; checking the axes and scales lets a reader work out the true size of a difference or trend, instead of being misled by visual impression alone.

Recognising Misleading Graphs - Worksheets, Questions and Revision