Pie Charts

Grade 3

The idea behind a pie chart

A pie chart shows how a total is split between categories. The whole circle is 360° and represents the whole data set. Each slice's angle is proportional to its share of the total.

The big trap: if the question asks you to draw a pie chart, you must work out angles first — never guess the size of a slice by eye.

The formula you need

Angle = (frequency ÷ total frequency) × 360°
Check your angles add up to 360° before you draw anything. If they don't, one of your calculations has a rounding error.

Worked example — drawing a pie chart

EXAMPLE
40 students chose their favourite subject. Maths: 10, English: 12, Science: 8, History: 10. Work out the angle for each sector.
Total = 40. Maths: (10 ÷ 40) × 360° = 90°. English: (12 ÷ 40) × 360° = 108°. Science: (8 ÷ 40) × 360° = 72°. History: (10 ÷ 40) × 360° = 90°. Check: 90 + 108 + 72 + 90 = 360° ✓

Reading a pie chart — reverse the formula

EXAMPLE
A pie chart shows data for 60 people. The sector for "football" has an angle of 120°. How many people chose football?
Frequency = (angle ÷ 360°) × total = (120 ÷ 360) × 60 = (1/3) × 60 = 20 people.
You can only find an actual number from a pie chart if you know the total. If the question only shows the chart with no total given, you can only give proportions or percentages — not raw counts.
Nova
Try this one

A pictogram shows the number of sandwiches sold at a cafe. The key states that each full symbol represents 8 sandwiches.

DaySymbols
Monday4 full symbols
Tuesday3 full symbols and 1 half symbol
Wednesday2 full symbols and 1 half symbol

(a) Work out the total number of sandwiches sold across all three days. [3]

(b) The cafe owner says: "More than 80 sandwiches were sold in total over these three days." Is the owner correct? Show your working. [1]

Nova's hint:

Interpreting pictograms: convert each row to a number of sandwiches by multiplying full symbols by the key value and adding half the key value for each half symbol.

Ask yourself: 'What is half of 8, and have I accounted for every full and half symbol in each row before adding them all together?'

Try to Solve it with Nova?