A bar for each category
A class votes for its favorite color: 6 children choose red, 9 choose blue and 4 choose green. The answers are categories, and a bar chart shows how many chose each one.
Draw a horizontal axis and write the categories along it. Draw a vertical axis with a scale that starts at 0 and goes up in equal steps. Then draw one bar for each category, all the same width, rising from 0 to that category’s count. Leave a gap between the bars: the categories are separate, and nothing lies between red and blue.
The blue bar reaches 9 on the scale, the red bar 6 and the green bar 4.
Height is the count
Every bar has the same width, so the only thing that differs from one bar to the next is its height. A taller bar means a bigger count, and the eye compares heights at a glance: blue is the most popular color and green the least.
To read the numbers, follow the top of each bar across to the scale. Blue has 9 − 4 = 5 more votes than green, and the class cast 6 + 9 + 4 = 19 votes in all. The order of the bars does not matter, because the categories have no order of their own; they are often arranged from tallest to shortest to make the comparison easier.
A bar chart is for categories. Numerical data such as test scores sit on a number scale, where each value has its own place in order, and they are drawn on charts with a number line along the bottom: dot diagrams, vertical line charts and histograms.
Why the scale starts at zero
A bar stands for its whole count only when it starts at 0. On the chart above, the blue bar is 9 units tall and the green bar is 4, so blue’s bar is 9 ÷ 4 = 2.25 times as tall as green’s, just as 9 votes is 2.25 times 4 votes.
Now suppose the scale started at 3 instead. The blue bar would be drawn from 3 to 9, which is 6 units tall, and the green bar from 3 to 4, which is 1 unit. Blue would look 6 times as popular as green, although the votes have not changed. The bars no longer share a common base, so their heights are no longer in the ratio of the counts.
baseline 0: the bars share their anchor, so their heights are in the ratio of the values, 102 : 98 = 1.04
Raise the baseline to 95 and watch a 4% difference become a gap
Two bars for the values 98 and 102. From a baseline of 0 their heights are in the ratio 102 : 98 = 1.04. Raise the baseline to 95 and they are drawn 7 and 3 units tall, so one bar looks more than twice the other.
Two bars for each category
To compare two sets of the same categories, such as this year’s results and last year’s, a dual bar chart puts two bars side by side for each category, one for each set. A key shows which shading belongs to which set. Compare the two bars within a category to see how that category changed, and compare the categories with each other to see which changed most.
A change can be given as a number or as a percentage. The percentage change divides the increase by the value it started from: a rise from 50 to 60 is an increase of 10, and 10 ÷ 50 = 0.2 = 20%.
Worked example: A Dual Bar Chart of Library Loans in Two Years, Compared as Percentage Changes
Question A dual bar chart shows the loans from a school library in 2023 and in 2024. Fiction went from 500 loans to 560, non-fiction from 200 to 250, and magazines from 100 to 110. (a) Which kind of loan rose by the greatest number, and which rose by the greatest percentage? (b) Find the percentage increase in the total number of loans.
1.Read each pair of bars and subtract. Fiction rose by 560 − 500 = 60 loans, non-fiction by 250 − 200 = 50 loans and magazines by 110 − 100 = 10 loans.
The difference between the two bars of a pair is the increase in number: 60, 50 and 10 loans. 2.Divide each increase by the 2023 value of its own category: fiction 60500 = 12%, non-fiction 50200 = 25%, magazines 10100 = 10%.
Divide each increase by its own 2023 value: 12%, 25% and 10%. 3.(a) Fiction rose by the greatest number, 60 loans. Non-fiction rose by the greatest percentage, 25%, because its increase is measured against a much shorter 2023 bar.
(a) Fiction rose by the greatest number, 60 loans. Non-fiction rose by the greatest percentage, 25%. 4.Add the bars of each year. In 2023 there were 500 + 200 + 100 = 800 loans, and in 2024 there were 560 + 250 + 110 = 920 loans. The increase is 920 − 800 = 120 loans.
Add the bars of each year: 800 loans in 2023 and 920 loans in 2024. 5.(b) 120800 = 15%. The total rose by 15%. Check: 800 × 1.15 = 920.
(b) 120800 = 15%, so the total rose by 15%.
Answer: (a) fiction rose by the greatest number, 60 loans, and non-fiction by the greatest percentage, 25%; (b) the total rose by 15%
Common mistakes
- Finding the change in the total by taking the mean of the three percentages, (12 + 25 + 10) ÷ 3, which is about 15.7%. The three categories are of different sizes, so their percentages do not count equally. The totals, 800 and 920, must be used.
- Choosing fiction for the greatest percentage increase because its two bars differ most in height. The difference in height is the increase in number. A percentage compares that difference with the first bar, and 60 out of 500 is a smaller part than 50 out of 200.