Charts and Graphs | mathismaths.com

What you will learn

Choose the right chart for the question.
Read pie charts, line graphs and scatter graphs.
Spot charts that mislead.

Before you start: you should know how to read bar charts, line graphs and pie charts.

The idea

Raw data is hard to take in. A chart turns a table of numbers into a picture that shows patterns immediately: which category is biggest, how something changed over time, or whether two things are related.

Which chart for which job?

Question	Chart	Data type
How do categories compare?	Bar chart	Categories (e.g. favourite fruit)
What share of the whole is each part?	Pie chart	Parts of a single total
How did it change over time?	Line graph	Continuous time series
How is a measurement distributed?	Histogram	Grouped continuous data (e.g. heights)
Are two variables related?	Scatter graph	Pairs of measurements

A quick guide to the three charts you meet most often and what each one is for.

Bar charts vs histograms

They look similar but answer different questions. Bar charts show separate categories, so the bars have gaps and the order can change. Histograms show continuous ranges, so the bars touch, and it is the area of each bar that represents frequency.

An honest bar chart starts at 0. The two bars are almost the same height, because the rise is only about 6%.

Scatter graphs and correlation

On a scatter graph each point is one individual measured on two variables. If points drift upward from left to right, there is positive correlation; downward means negative correlation; a shapeless cloud means no correlation. A line of best fit summarises the trend and can be used to estimate values.

Worked examples

Example 1: Drawing a pie chart

A survey of $60$ students’ travel to school: walk $24$ , bus $18$ , car $12$ , cycle $6$ . Find the pie-chart angles.

Each student gets $360^\circ \div 60 = 6^\circ$ .
Walk: $24 \times 6 = 144^\circ$ . Bus: $18 \times 6 = 108^\circ$ .
Car: $12 \times 6 = 72^\circ$ . Cycle: $6 \times 6 = 36^\circ$ .
Check: $144 + 108 + 72 + 36 = 360$ . ✓

Answer: $144^\circ$ , $108^\circ$ , $72^\circ$ , $36^\circ$

Example 2: Reading a line of best fit

A line of best fit for hours revised ( $h$ ) against test score ( $s$ ) is $s = 6h + 38$ . Estimate the score for $5$ hours of revision, and comment on using it for $15$ hours.

Substitute $h = 5$ : $s = 6(5) + 38 = 68$ .
For $15$ hours the line predicts $128$ , which is impossible if the test is out of $100$ .

Answer: about $68$ . Predicting far outside the data (extrapolation) is unreliable.

Example 3: Spotting a misleading graph

A bar chart shows sales of $1020$ and $1080$ units, but the vertical axis starts at $1000$ . The second bar looks four times taller than the first.

Actual increase: $1080 - 1020 = 60$ units.
As a percentage: $60 \div 1020 \approx 5.9\%$ .

Answer: a modest $\approx 6\%$ rise made to look dramatic by a truncated axis.

Tip: correlation is not causation. Ice-cream sales and sunburn cases rise together, but ice cream does not cause sunburn. Hot weather drives both.

Why it matters

Charts are how most people meet data: in news reports, company presentations, fitness apps, energy bills and public health briefings. Being able to read them accurately and spot tricks like truncated axes, 3D distortion or cherry-picked time ranges is an essential part of being an informed citizen.