Calculations with the Mean (Cambridge (CIE) IGCSE Maths)
Revision Note
Written by: Mark Curtis
Reviewed by: Dan Finlay
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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.
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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