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Question 74
The average of a certain set of 'b' numbers is 'a', and the average of a certain set of 'a' numbers is 'b'. What is the average of all the numbers taken together?
Solution
The average of a certain set of 'b' numbers is 'a'.
total = $$a \times b$$ = ab
the average of a certain set of 'a' numbers is 'b'.
total = $$b \times a$$ = ba = ab
Average of all the numbers taken together =Â $$\frac{sum\ of\ data}{number\ of\ data}$$
=Â $$\frac{ab+ab}{b+a}$$
= $$\frac{2ab}{a+b}$$
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