11.2 Comparing different quantities

On daily basis, there are times when you are required to compare different quantities, like which price is cheaper, which bands have the most fans or anything that includes comparing. In this post I am going to show you how to compare different quantities :)

You will often need to compare groups that are different sizes.
Suppose that, in one school, 85 students took an exam and 59 passed. 
In another school, 237 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 below shows you how to use percentages to help to answer questions like this.


Worked example 11.2:
In school A, 85 students took a mathematics exam and 59 passed.

In school B, 237 took a 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 A is better by 7 percentage points. Why? Because the percentage of students who passed the exam in school A is more than the percentage of students who passed the exam in school B. The difference between 62% and 69% is given in "percentage points".

Understand? No? Ok then let's try with another example :-)

Question 1:
There were 270 people in a cinema. There were 168 women and 102 men.
There were 152 people in a theater. There are 78 women and 74 men.

a. Work out the percentage of women in each venue
answer: 
cinema   = 168/270 x 100
             = 62% (rounded off to the nearest whole number)
theater  = 78 /152 x 100
             = 51% (rounded off to the nearest whole number)
from that, we know that there are more women in cinema than there are in theaters.
b. Work out the percentage of men in each venue
answer:
cinema   = 102/270 x 100
             = 28% (rounded off to the nearest whole number)
theater  = 74 /152 x 100
             = 49% (rounded off to the nearest whole number)
from that, we know that there are more women in cinema than there are in theaters.

 Question 2:
This table below shows the results of a survey in a factory.

a. What percentage of men are smokers?
answer: 
12 / 76 x 100  
= 16% (rounded off to the nearest whole number)
b. Compare the percentages of men and women who are non-smokers.
answer: 
men (nonsmokers)     = 64 / 76 x 100
                               = 84% (rounded off to the nearest whole number)
women (nonsmokers) = 32 / 41 x 100
                               = 78% (rounded off to the nearest whole number)
From the data we have, we know that more men are nonsmokers compared to women.

To practice more about this subchapter, I suggest this interactive educational game for you.
http://www.mathplayground.com/balloon_invaders_percent.html
 Enjoy xx