Module 8

Ratio, proportion & statistics

Quick-reference revision notes for parents.

8.1 Ratio and proportion

Simplifying a ratio: divide all parts by their highest common factor.

12 : 18 = 2 : 3 (divide both by 6)

Worked example — share £60 in the ratio 2 : 3

Total parts: 2 + 3 = 5
One part: 60 ÷ 5 = £12
Shares: 2 × 12 = £24 and 3 × 12 = £36

Find the value of one unit, then scale up.

Worked example

5 pens cost £3.50. How much do 8 pens cost?

1 pen: 3.50 ÷ 5 = £0.70
8 pens: 8 × 0.70 = £5.60

A straight line through the origin showing one unit converted to another (e.g. £ to $, miles to km). Read across and down to convert.

Quick check

The graph passes through (0, 0) — zero of one unit equals zero of the other. The gradient is the conversion rate.

Compare unit prices — the price of one item, or the price per gram/ml.

Worked example

Pack A: 500g for £3.20. Pack B: 750g for £4.65. Which is better value?

A: 320 ÷ 500 = 0.64p per gram
B: 465 ÷ 750 = 0.62p per gram
Pack B is better value.

Average	How to find
Mode	Value with the highest frequency
Median	Middle value when listed in order
Mean	Σ(value × frequency) ÷ Σfrequency
Range	Largest − smallest value

Worked example

Mean = 53 ÷ 20 = 2.65
Mode = 3 (highest frequency)
Median = average of 10th and 11th values = 3

Watch out

For the mean, divide by total frequency, not the number of categories.

Each category gets a slice. Slice angle:

angle = (frequency ÷ total) × 360°

Worked example

30 people surveyed; 12 chose tea. Tea slice angle?

(12 ÷ 30) × 360 = 144°