Lesson 10.4 · 25 min

Choosing the Right Graph — and Spotting Misleading Ones

Matching each kind of data to the graph that suits it, drawing a pie chart, and recognising the tricks that make graphs mislead.

In this lesson you will learn to…

Choose an appropriate graph for a given set of data
Calculate the angles for a pie chart
Make inferences from a time-series graph
Explain how a graph can be drawn to mislead

Why this matters

Every day you see graphs in adverts, news reports and social media. Choosing the right graph helps you communicate honestly. Recognising a misleading one protects you from being fooled.

Making inferences from a time-series graph

A line graph of average monthly temperatures in Dubai and London shows that both are hottest in July and August and coolest in January — and that Dubai is between 17 and 22 degrees hotter all year round. Reading a trend like this from a table of 24 numbers is much harder. To infer is to reach a sensible conclusion from the evidence, even if it cannot be proved.

The misleading tricks

Trick	Effect
Missing out the baseline (axis starts above 0)	small differences look huge
Stretching the $y$ -axis	real growth looks tiny
3D bars or pictures	sizes are hard to judge; front bars look bigger
Shading or thick borders on one bar	draws your eye to it
Wrong graph type (e.g. a pie chart for yearly profits)	hides the trend

Normal and skewed shapes. Large sets of data such as people’s heights often make a symmetrical, bell-shaped histogram — the normal distribution. If the peak is pushed to one side, the data is skewed.

Key rules and formulas

Which graph?
Bar chart — discrete or categorical data. Pictogram / infographic — the same, with more visual impact. Pie chart — proportions of a whole. Histogram or frequency polygon — grouped continuous data. Line (time-series) graph — trends over time. Scatter graph — a relationship between two variables. Stem-and-leaf — keeps the raw data.
Pie chart angles
$angle = \frac{frequency}{total} \times 36 0^{\circ}$
Spending 30 of 100 dollars on a shirt gives $\frac{30}{100} \times 360 = 10 8^{\circ}$ .
How graphs mislead
Starting the $y$ -axis above zero, stretching or squashing the axis, using 3D or pictures, heavy shading on one bar, or simply choosing the wrong type of graph. The numbers may be correct while the impression is not.

Try it

Misleading axis explorer

y-axis starts at ($ millions)0

y-axis ends at ($ millions)36

Year 3 really is: 1.45 × Year 1
but its bar looks: 1.45 × as tall

Company profits were 22, 26 and 32 million dollars. Drag the axis start up to 20: Year 3 now looks six times Year 1, though it is less than 1.5 times. Then stretch the top to 100 to make growth look tiny.

Worked examples

Worked example 1

Drawing a pie chart

David earned 100 dollars and spent it on: shirt 30, cap 10, cinema 10, music 20, savings 30. Find the angles for a pie chart.

Try it yourself first, then reveal the solution one step at a time.

Worked example 2

Spotting the trick

A bar chart of profits (22, 26 and 32 million dollars) has a

y

-axis starting at 20. Why is it misleading?

Try it yourself first, then reveal the solution one step at a time.

Practice: choosing and misleading graphs

9 questions

Nine questions on picking the right graph and seeing through the wrong ones.

Question 1 of 9Match the pairsFoundation
Match each set of data to the most appropriate graph.
Pick an answer, then choose the row it belongs to. You can also drag it.
- Favourite singers of a class
- How David spent his 100 dollars
- Times taken to travel to school, grouped
- Average temperature each month of the year
- Height and mass of 20 people
Question 2 of 9Complete the table
Hockey results for 30 matches. Find the pie chart angles.
Result Frequency Angle (°)
Win 10 Row 1, Angle (°)
Loss 15 Row 2, Angle (°)
Draw 5 Row 3, Angle (°)
Question 3 of 9Explore and match
Make the profits chart misleading: start the $y$ -axis at 20 so that Year 3 looks 6 times as tall as Year 1.
Move the controls until you match the question, then press Check.
y-axis starts at ($ millions)0
y-axis ends at ($ millions)36
Year 3 really is
1.45 × Year 1
but its bar looks
1.45 × as tall
Question 4 of 9Choose all that apply
A company wants its profits to look like they are growing fast. Which tricks would do that?
Select every correct answer — there may be more than one.
Draw Year 3 with a dark colour and a thick borderStart the $y$ -axis at 20 instead of 0Show the profits as a pie chartUse 3D bars viewed from an angleStretch the $y$ -axis up to 100
Question 5 of 9True or false
A misleading graph must contain incorrect numbers.
Question 6 of 9Type the answer
In a pie chart of 100 dollars of spending, music gets $7 2^{\circ}$ . How many dollars were spent on music?
Your answerdollars
Question 7 of 9Complete the table
A café's pictogram uses one cup for 20 soft drinks. Complete the table.
Day Cups shown Soft drinks sold
Monday 3 Row 1, Soft drinks sold
Tuesday 4 Row 2, Soft drinks sold
Wednesday 2½ Row 3, Soft drinks sold
Saturday 5 Row 4, Soft drinks sold
Question 8 of 9Multiple choice
Monthly highs: Dubai goes from 24 °C in January to 41 °C in July; London from 7 °C to 21 °C. Which is a sensible inference?
Question 9 of 9Multiple choice
A histogram of the heights of 1000 adults is symmetrical with a single peak in the middle. What is this shape called?

Result	Frequency	Angle (°)
Win	10	Row 1, Angle (°)
Loss	15	Row 2, Angle (°)
Draw	5	Row 3, Angle (°)

Day	Cups shown	Soft drinks sold
Monday	3	Row 1, Soft drinks sold
Tuesday	4	Row 2, Soft drinks sold
Wednesday	2½	Row 3, Soft drinks sold
Saturday	5	Row 4, Soft drinks sold