Charts: Bar, Pie and Pictogram

A good chart turns a table of numbers into a picture you can read at a glance. The OCR GCSE Mathematics (J560) Statistics strand asks you to draw and interpret three classic displays: the bar chart, the pictogram and the pie chart. Each suits a different purpose, and each has its own pitfalls — an unlabelled axis, a missing key, or a pie sector with the wrong angle. This lesson shows how to construct each chart accurately, how to read information back out of it, and how to compare two data sets fairly using charts.

This topic blends AO1 (drawing charts correctly with the right scales, keys and angles) with AO2 (interpreting and comparing) and a little AO3 (working from a pie chart back to frequencies). OCR command words here include "Draw", "Work out", "Describe" and "Compare". Accurate drawing and clear interpretation are both examined, so practise the calculations and the written comparisons.

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Key Vocabulary

Term	Meaning
Bar chart	Equal-width bars with gaps; bar height shows frequency
Dual bar chart	Two bars per category, side by side, for comparison
Composite (stacked) bar chart	Bars stacked to show parts of a total
Pictogram	Uses a repeated symbol to show frequency; needs a key
Pie chart	A circle split into sectors; each angle is proportional to frequency
Key	A label explaining what a colour or symbol represents
Frequency	The number of items in a category

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Bar Charts

A bar chart shows the frequency of each category as the height of a bar. The rules for an accurate bar chart are:

• bars are equal width with equal gaps between them,
• the frequency axis is labelled and evenly scaled starting at 0,
• each bar is labelled on the horizontal axis.

The chart below shows the favourite lunch option of 60 students.

Worked Example 1

From the bar chart above, (a) which option was least popular, and (b) how many more students chose pasta than salad?

Solution: (a) The shortest bar is salad (frequency 9). (b) Pasta 20, salad 9, so $20 - 9 = 11$20−9=11 more students chose pasta.

Worked Example 1b

Using the same lunch bar chart (pasta 20, curry 16, salad 9, pizza 15), (a) how many students were surveyed in total, and (b) what fraction chose curry? Give your answer in its simplest form.

Solution: (a) Total $= 20 + 16 + 9 + 15 = 60$=20+16+9+15=60 students. (b) Curry $= \dfrac{16}{60} = \dfrac{4}{15}$=6016​=154​. Reading the totals straight off a bar chart, then converting to a fraction, is a very common opening to a longer question.

Worked Example 2

A dual bar chart compares Year 7 and Year 11 choices of after-school club. The frequencies are: Drama (Y7 14, Y11 6), Sport (Y7 10, Y11 18), Coding (Y7 8, Y11 12). (a) Which club is more popular in Year 11 than Year 7? (b) Describe one change in preference from Year 7 to Year 11.

Solution: (a) Both Sport ($18 > 10$18>10) and Coding ($12 > 8$12>8) are more popular in Year 11. (b) Drama falls sharply with age (14 down to 6) while Sport rises (10 up to 18) — older students prefer Sport over Drama.

Common error: comparing the wrong pair of bars. In a dual bar chart always read the key first so you match each bar to the right group.

Worked Example 3

A composite (stacked) bar chart shows ice-cream sales over three days, split into vanilla and chocolate. On Monday the bar reaches 50 in total, of which the vanilla portion is 30. How many chocolate ice creams were sold on Monday?

Solution: In a stacked bar the total height is the sum of the parts, so chocolate $= 50 - 30 = 20$=50−30=20.

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Pictograms

A pictogram uses a repeated symbol to represent frequency. The crucial feature is the key, which states how many items one symbol stands for. Part-symbols represent fractions of that value.

Worked Example 4

In a pictogram of books read, the key is "one symbol = 4 books". A pupil's row shows 3 full symbols and a half symbol. How many books did the pupil read?

Solution: $3 \tfrac{1}{2}$321​ symbols $\times 4 = 3.5 \times 4 = 14$×4=3.5×4=14 books.

Worked Example 5

A pictogram shows the number of emails received, with key "one symbol = 10 emails". Monday shows 4 symbols, Tuesday shows 2.5 symbols. (a) How many emails on Tuesday? (b) How many symbols are needed for a day with 35 emails?

Solution: (a) $2.5 \times 10 = 25$2.5×10=25 emails. (b) $35 \div 10 = 3.5$35÷10=3.5 symbols (three full symbols and a half symbol).

Common error: ignoring the key and counting symbols as if one symbol equals one item. Always multiply by the key value.

The pictogram below shows how many books four pupils read in a month, with the key "one circle = 4 books". Counting the part-circle for Sam is the crucial skill: a half-circle is worth two books.

Worked Example 5b

Using the pictogram above, (a) how many books did Ben read, and (b) how many books were read altogether by the four pupils?

Solution: (a) Ben shows $2\tfrac{1}{2}$221​ circles, so $2.5 \times 4 = 10$2.5×4=10 books. (b) Ana $3 \times 4 = 12$3×4=12; Ben $10$10; Cara $4 \times 4 = 16$4×4=16; Sam $1.5 \times 4 = 6$1.5×4=6. Total $= 12 + 10 + 16 + 6 = 44$=12+10+16+6=44 books.

Common error: reading a half-circle as one whole book rather than half of the key value (two books).

When to use each chart

Each chart suits a different job. A bar chart is best for comparing the size of separate categories. A pictogram is eye-catching and good for simple data or reports, but is awkward for precise or large values. A pie chart is best for showing how a whole splits into parts — the "share" of each category — but is poor for reading exact frequencies. Choosing the right chart for the question is itself a marked skill in the exam, so think about what you want the reader to see before you draw.

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Pie Charts

A pie chart shows how a total splits into categories, using sector angles proportional to frequency. Since a full circle is $360^{\circ}$360∘:

$\text{angle} = \dfrac{\text{frequency}}{\text{total frequency}} \times 360^{\circ}$angle=total frequencyfrequency​×360∘

Drawing a pie chart

The pie chart below shows how 36 students travel to school: Walk 100°, Bus 80°, Cycle 90°, Car 90°.

Worked Example 6

54 people were asked their favourite season. The results were Spring 9, Summer 21, Autumn 15, Winter 9. Work out the angle for each sector of a pie chart.