Question

The mean of $10$ numbers is $32$. If one number is excluded , the mean of the remaining number becomes $30$ . Find the excluded number.

Answer 1

Step 1 : Finding the sum of observation

Given, the mean of $10$ numbers $=32$

Since, $Mean=\frac{Sumofallobservations}{TotalNumberofObservations}.....\left(i\right)$

So, the sum of observation $=32\times 10=320$

Step 2 : Finding the sum of observations after excluding one number

When one number is excluded, the mean of the remaining number becomes $30$

That is, the total number of observation $=10-1=9$

Hence,$Mean=\frac{Sumofallobservations}{TotalNumberofObservations}.....\left(i\right)$

So, the sum of observation $=30\times 9=270$

Hence, the excluded number will be $=320-270=50$.