Sec 1 Maths · Statistics (Sec 1)

Misleading graphs questions with answers

Practice questions on misleading graphs, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

The graph was drawn to show the books sold at a book fair. Which feature makes the graph misleading?

Step 1 of 1

Check the axes, the scale, the bars or pictures, and the key

The vertical axis does not start at 0. The vertical axis starts above 0, so small differences between the bars look much bigger than they are.

Try a question: Misleading graphs

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

Questions

Question 1What makes the graph misleading?
The graph was drawn to show the sales of a shop. Which feature makes the graph misleading?
Show the worked solution
1. Step 1: Check the axes, the scale, the bars or pictures, and the keyThere is no key. Without a key we cannot tell how many each symbol stands for.
Question 2What makes the graph misleading?
The graph was drawn to show the members of a sports club. Which feature makes the graph misleading?
Show the worked solution
1. Step 1: Check the axes, the scale, the bars or pictures, and the keyThe bars are of different widths. Wider bars have more area, so the eye sees them as bigger than their heights say.
Question 3A vertical axis that doesn't start at 0
The bar graph shows the number of cars sold in 2019 and 2023. The 2023 bar is $k$ times as tall as the 2019 bar. By measuring the bars, find the value of $k$ .
Show the worked solution
1. Step 1: Where does the vertical axis start? Measure each bar's drawn height from thereDrawn height of the 2019 bar: $85 - 80 = 5$ Drawn height of the 2023 bar: $95 - 80 = 15$
2. Step 2: Divide $\dfrac{15}{5}$ $= 3$ It looks $3$ times as tall, but the real ratio is only $\dfrac{95}{85}$ .
Question 4A vertical axis that doesn't start at 0
The bar graph shows the number of cars sold in 2019 and 2023. The 2023 bar is $k$ times as tall as the 2019 bar. By measuring the bars, find the value of $k$ .
Show the worked solution
1. Step 1: Where does the vertical axis start? Measure each bar's drawn height from thereDrawn height of the 2019 bar: $95 - 90 = 5$ Drawn height of the 2023 bar: $110 - 90 = 20$
2. Step 2: Divide $\dfrac{20}{5}$ $= 4$ It looks $4$ times as tall, but the real ratio is only $\dfrac{110}{95}$ .
Question 5Pictures enlarged in two dimensions
The number of books sold went up from $300$ in Year 1 to $1200$ in Year 3, which is $4$ times as many. The artist drew the Year 3 picture $4$ times as tall and $4$ times as wide as the Year 1 picture. The area of the Year 3 picture is $k$ times the area of the Year 1 picture. Find the value of $k$ .
Show the worked solution
1. Step 1: Area grows with BOTH the height and the width $4 \times 4$ $= 16$ The picture looks $16$ times as big, though the number is only $4$ times as large.
Question 6Pictures enlarged in two dimensions
The number of cars sold went up from $150$ in 2019 to $450$ in 2023, which is $3$ times as many. The artist drew the 2023 picture $3$ times as tall and $3$ times as wide as the 2019 picture. The area of the 2023 picture is $k$ times the area of the 2019 picture. Find the value of $k$ .
Show the worked solution
1. Step 1: Area grows with BOTH the height and the width $3 \times 3$ $= 9$ The picture looks $9$ times as big, though the number is only $3$ times as large.

More on statistics (sec 1)

Notes: Statistics (Sec 1)Worksheet with answers (PDF)

Endless questions on misleading graphs

A free account gives you new questions every time, step-by-step help, and tracks what you've mastered.

Start free

Worked example

The graph was drawn to show the books sold at a book fair. Which feature makes the graph misleading?

Step 1 of 1

Check the axes, the scale, the bars or pictures, and the key

The vertical axis does not start at 0. The vertical axis starts above 0, so small differences between the bars look much bigger than they are.

Questions

Question 1What makes the graph misleading?

The graph was drawn to show the sales of a shop. Which feature makes the graph misleading?

Show the worked solution

Step 1: Check the axes, the scale, the bars or pictures, and the keyThere is no key. Without a key we cannot tell how many each symbol stands for.

Question 2What makes the graph misleading?

The graph was drawn to show the members of a sports club. Which feature makes the graph misleading?

Show the worked solution

Step 1: Check the axes, the scale, the bars or pictures, and the keyThe bars are of different widths. Wider bars have more area, so the eye sees them as bigger than their heights say.

Question 3A vertical axis that doesn't start at 0

The bar graph shows the number of cars sold in 2019 and 2023. The 2023 bar is $k$ times as tall as the 2019 bar. By measuring the bars, find the value of $k$ .

Show the worked solution

Step 1: Where does the vertical axis start? Measure each bar's drawn height from thereDrawn height of the 2019 bar: $85 - 80 = 5$ Drawn height of the 2023 bar: $95 - 80 = 15$
Step 2: Divide $\dfrac{15}{5}$ $= 3$ It looks $3$ times as tall, but the real ratio is only $\dfrac{95}{85}$ .

Question 4A vertical axis that doesn't start at 0

The bar graph shows the number of cars sold in 2019 and 2023. The 2023 bar is $k$ times as tall as the 2019 bar. By measuring the bars, find the value of $k$ .

Show the worked solution

Step 1: Where does the vertical axis start? Measure each bar's drawn height from thereDrawn height of the 2019 bar: $95 - 90 = 5$ Drawn height of the 2023 bar: $110 - 90 = 20$
Step 2: Divide $\dfrac{20}{5}$ $= 4$ It looks $4$ times as tall, but the real ratio is only $\dfrac{110}{95}$ .

Question 5Pictures enlarged in two dimensions

The number of books sold went up from $300$ in Year 1 to $1200$ in Year 3, which is $4$ times as many. The artist drew the Year 3 picture $4$ times as tall and $4$ times as wide as the Year 1 picture. The area of the Year 3 picture is $k$ times the area of the Year 1 picture. Find the value of $k$ .

Show the worked solution

Step 1: Area grows with BOTH the height and the width $4 \times 4$ $= 16$ The picture looks $16$ times as big, though the number is only $4$ times as large.

Question 6Pictures enlarged in two dimensions

The number of cars sold went up from $150$ in 2019 to $450$ in 2023, which is $3$ times as many. The artist drew the 2023 picture $3$ times as tall and $3$ times as wide as the 2019 picture. The area of the 2023 picture is $k$ times the area of the 2019 picture. Find the value of $k$ .

Show the worked solution

Step 1: Area grows with BOTH the height and the width $3 \times 3$ $= 9$ The picture looks $9$ times as big, though the number is only $3$ times as large.