Calculations with the Mean (Cambridge (CIE) O Level Maths): Revision Note
Exam code: 4024
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Calculations with the mean
How do I solve harder problems involving the mean?
Remember what the mean is
Mean = total of values ÷ number of values
It is a formula involving three quantities
if you know any two, you can find the other one
A question may require you to work backwards from a known mean
It helps to rearrange the formula
Total of values = mean × number of values
Find the total of the values before and after to help with question that involve:
missing values
adding in, or taking out, a value
Examiner Tips and Tricks
It helps to start thinking of the mean as a formula which you can rearrange
Total of values = mean × number of values
Worked Example
A class of 24 students has a mean height of 1.56 metres.
A new student joins the class.
The mean height of the class is now 1.57 metres.
Find the height of the new student.
Answer:
Rearrange the formula for mean to get 'total of heights = mean height × number of students'
Find the total of heights before
Total of heights before = 1.56 × 24 = 37.44
Find the total of heights after
Remember there are now 25 students
Total of heights after = 1.57 × 25 = 39.25
The height of the new student is the difference of the two totals above
39.25 - 37.44 = 1.81
The height of the new student is 1.81 metres
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