Question

If the average of m numbers is n2and that of n numbers is m2, then average of (m+n) numbers is

Answer 1

Answer:

The average of (m+n) numbers = mn

Step-by-step explanation:

Given that average of m numbers is n²

therefore, average of m numbers = (total sum of m numbers)/m = n²

So, total sum of m numbers = n² × m.....(1)

also given that average of n numbers is m²

therefore, average of n numbers = (total sum of m numbers)/n = m²

So, total sum of n numbers = m² × n.....(2)

Now, average of (m+n) numbers = (total sum of m numbers + total sum of n numbers)/m+n .........(3)

From equations (1), (2) and (3) we get,

Average of (m+n) numbers = [(n² × m ) + (m² × n)]/m+n

= mn (m+n)/ m+n

= mn