If the average of \(p\) numbers is \(q^2\) and that of \(q\) numbers is \(p^2\), then the average of \((p+q)\) numbers is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(pq\)
The averages of two groups cannot be added, but their sums can. The sum of a group of numbers is their average times how many there are, so both sums are found, added, and divided by the total count \(p+q\).
Sum of the \(p\) numbers \(=p\times q^2=pq^2\)
Sum of the \(q\) numbers \(=q\times p^2=p^2q\)
Sum of all \(p+q\) numbers \(=pq^2+p^2q=pq(p+q)\)
Their average \(\displaystyle =\frac{pq(p+q)}{p+q}=pq\)