11.2 Comparing Different Quantities

You will often need to compare that are different sizes.
Suppose that, in one school, 85 students took an exam and 56 passed.
In another school, 237 students took an exam and 147 passed.
Which school did better? It is hard to say because each school had a different number of students.

The worked example shows how to use percetages to help to answer question like this:

WORKED EXAMPLE 1:

In school A, 85 students took a mathematics exam and 56 passed.
In School B, 237 stundets took an mathematics exam and 147 passed.
Which school had a better pass rate?

59  out of 85 = 59/85 = 69%
59/85 = 0.694... = 69% to the nearest whole number.

147 out of 237 = 147/237 = 62 %
147/237=0.620... = 62% to the nearest whole number.

The pass rate in school B is better by seven percentages points!
The difference between 62% and 69% is given in 'percentage points'

Exercise 1:

There were 270 people in a cinema. There were 168 women and 102 men.
There were 152 people in the theatre. There were 78 women and 74 men.

a)  Work out the percentage of women in each venue
b)  Work out the percentage of men in each venue

Exercise 2:

This table shows the results of a survey in a factory.

	Smoker	Non-Smokers	Total
Men	12	64	76
women	9	32	41

a) what percentage of men are smoker?

b) Compare the percentages of men and women who are non-smokers?

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