Question

The mean of $7$ numbers is $25$. If one more number is included , the mean of the new set of numbers becomes $27$ . Find the included number.

Answer 1

Step 1 : Finding sum of observation

Given, mean of $7$ numbers $25$

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

So, sum of observation $=25\times 7=175$

Step 2 : Finding sum of observation after including one number

When one number is included , the mean of the remaining number becomes $27$

That is , total number of observation $=7+1=8$

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

So, sum of observation $=27\times 8=216$

Hence, the included number will be $=216-175=41$