Bar charts and pie charts — Mathematics, 11–13
Turn a table of frequencies into bars or a pie chart with an honest scale, a title, a source and a legend, and compare two groups side by side.
The table becomes a picture
In a bar chart each category gets a bar and its height shows the frequency; the bars have the same width and the scale starts at 0. In a pie chart the whole circle is 100% and each sector is a part of it in proportion to the relative frequency: 50% is half the circle, 25% a quarter. Juxtaposed bars put two bars side by side for each category to compare two groups, for example girls and boys. Every chart needs a title, a source and a legend.
Choose the chart that tells the story
A chart lets you see at a glance what a table makes you read line by line. A pie chart is good for a few categories when you want to show parts of a whole: with eight or more, the sectors are hard to tell apart. Bars are better to compare categories, and juxtaposed bars to compare two groups. You can draw them by hand, but online forms and spreadsheets make pie charts and bars from the table in seconds.
From the table to a bar chart
Take the break table: football 40%, cards 20%, reading 16%, talking 20%, other 4%. Step 1: choose the scale: the highest value is 40%, so use 0% to 40% and let 1 cm stand for 10%. Step 2: bar heights: 40 ÷ 10 = 4 cm; 20 ÷ 10 = 2 cm; 16 ÷ 10 = 1.6 cm; 4 ÷ 10 = 0.4 cm. Step 3: draw bars of equal width and label the axes. Step 4: add the title “What our class does at break”, the source “class questionnaire” and a legend saying the bars are percentages of the 25 answers.
Comparing groups by counts, not by proportion
Class A has 25 students and 10 chose football. Class B has 40 students and 12 chose football. Juxtaposed bars of the counts show 12 above 10, and it looks as if class B likes football more. But the groups have different sizes. In relative frequencies, 10/25 = 40% and 12/40 = 30%. Football is more popular in class A. To compare groups of different sizes, use relative frequencies.
In the news and in your pocket
Newspapers, school reports, sports pages and the screen-time summary on a phone use bars and pie charts all the time. An online class survey often gives you a pie chart at once. Now you know what to look for: a title, a source, a legend and a scale that starts at 0, and whether percentages or counts are being compared.
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