Bar graphs and axis scales

A bar’s height represents its value

Three clubs record how many pupils attended. In this bar graph the vertical axis counts pupils, with five pupils between labelled marks.

Pupils attending clubs

Data table

Club	Pupils
Art	5
Music	10
Drama	15

Do not count three labelled intervals above zero and report three pupils for Drama. Three intervals of five mean 15 pupils.

Compare in units of the quantity

Drama has ten more pupils than Art: 15-5 = 10. Music and Art together have 10 + 5 = 15 pupils. The bar widths separate the categories; they do not add extra pupils.

A different graph may count by twos, tens or hundreds. Divide the difference between two labels by the number of equal gaps between them to find the value of one gap.

Check your understanding 1 Read a changed scale

On another attendance graph, adjacent marked lines are 20, 30 and 40 pupils. A bar reaches the line halfway between 30 and 40. How many pupils does it show?

Attendance with a different scale

Data table

Club	Pupils
Art	15
Music	30
Drama	35

Pupils represented by one labelled axis gap

Number of pupils

Check answer

Show answer

One labelled gap represents 30-20 = 10 pupils. Drama’s bar is halfway from 30 to 40, so it represents 30 + 5 = 35 pupils. The new graph uses ten pupils per labelled gap; the first graph used five. Counting drawn gaps without reading their values would give the wrong quantities.

Check your understanding 2 Judge what can be compared

One graph uses one gap for five books. Another uses one gap for ten books. Each has a bar three gaps high from zero. Are the totals equal?

Your answer or drawing on paper

Show answer

No. The first bar represents 15 books and the second 30 books. Equal drawn heights on different scales do not imply equal quantities.

Question the conclusion

The first graph says how many pupils attended each club. It does not say how many pupils liked each club best. Use the graph’s labels to keep your conclusion about the quantity actually recorded.