Mathematics
Reading charts
Bars, pies, lines: which chart fits which job, and which tricks make some of them mislead?
What you need first
Hardly anybody reads numbers in a table. As a picture you grasp them in seconds, and that is exactly where the strength of charts lies, and at the same time their danger. A well made chart shows you at once what the point is. A badly made one shows you something that is not in the data at all. Recognising both is one of the most practical skills maths lessons offer.
Three kinds of chart, three jobs
A bar chart compares quantities side by side, the turnover of several branches for instance. A pie chart shows shares of one whole, for instance how a household's electricity use splits up. A line chart shows a development over time, the temperature across a year for instance. Choosing the wrong kind makes the data harder to read, not easier.
The truncated axis trick
The most common trick is an axis that does not start at zero. Two bars with the values 98 and 102 look almost equally tall on an axis from 0 to 110, which matches the truth. If the axis starts at 96 instead, one bar is twice as tall as the other. The data are unchanged, the impression is entirely different.
For bar charts that is a genuine error, because the height of the bar is supposed to represent the size. For line charts a cut-off zero point sometimes makes sense, for instance with body temperatures between 36 and 40 degrees. What matters is that it is clearly marked and that you notice it while reading.
More traps
In a pie chart all the shares have to add up to 100%. If the total is higher, then either multiple answers were allowed, which needs saying, or something is wrong. In pies drawn in three dimensions the front slice looks bigger than it is, purely through perspective. And with pictures instead of bars, money bags of twice the height for instance, the width doubles too, so the area looks four times as large.
One last point concerns not the drawing but the selection. A chart showing only the years 2019 to 2021 can display a dramatic rise that, seen over 30 years, is a normal fluctuation. So always ask: why exactly this section?
Exercises
0 of 6 solvedTime to try it yourself. You can't break anything, every attempt counts.
A pie chart shows four shares: 40%, 25%, 20% and a remainder. How large is the remainder in percent?
Two bars show 98 and 102. The axis starts at 96. What impression does that create?
Why is it important for a bar chart that the axis starts at zero?
Match each question to the right chart.
A survey shows a pie chart whose shares add up to 140%. What is the most likely explanation?
In a pie chart all the shares have to add up to ….