Background reading · Mathematics and Statistics

Graphs that tell the truth, and graphs that trick

How to choose the right graph, read its shape, centre and spread, and catch a graph that has been drawn to mislead.

A graph is a picture of data. A good one lets you see in a few seconds what would take minutes to find in a table. A bad one can fool you in even less time.

Choose the graph that fits

Dot plot: for numbers, like reaction times. Each dot is one person, so you can see every value and any outliers.

Bar graph: for categories, like travel modes or bird species. The bars must start at zero. A clustered or stacked bar graph compares categories across two groups, like birds at two spots.

Time-series graph: for data that changes over time, like daily rainfall. Time goes along the bottom.

Read it like a statistician

Look for three things. Shape: is there one peak or two? Is it symmetrical, or does one tail stretch out further (skewed)? Centre: where is the middle of the data? Spread: how far is it from the smallest value to the largest, and where do most values sit?

How graphs trick

Imagine a bar graph where one shop's price is $10 and another's is $11. If the vertical axis starts at $9, the second bar looks twice as tall, even though the difference is only 10%. Other tricks include missing axis labels, no units, uneven scales, 3D bars that hide the real heights, and leaving out who the data came from.

Your graph checklist

Every honest graph has a title that says what it shows, labelled axes with units, an even scale that (for bar graphs) starts at zero, and a note on who or what the data came from and how many. If a graph in the news is missing any of these, ask why. Sometimes it is a mistake. Sometimes someone is hoping you won't look closely.

Sources and further reading

Written for Kōkiri Learn students in our own words. Check facts against the sources.

Used in: What the Data Shows