Question

:
The mean of five numbers is 25
.
​
​If one of the numbers is excluded, the mean gets reduced by 3
.
​
​Find the value of the excluded number.

Answer 1

The excluded number is 37.

Step-by-step explanation:

Let the numbers a, b, c, d and e.

Total numbers = 5

Sum of all numbers = a + b + c + d + e

Mean of five numbers = 25

$=> \frac{a + b + c + d + e}{5} = 25\\\\=> a + b + c + d + e = 25 \times 5\\\\=> a + b + c + d + e = 125...........(i)$

If one number is excluded, let the excluded number be 'e'.

The total numbers = 4.

Sum of four numbers = a + b + c + d

Mean gets reduced by 3.

Mean = 25 - 3 = 22

$=> \frac{a+b+c+d}{4} = 22\\\\=> a + b+c+d = 22 \times 4\\\\=> a + b+c+d = 88............(ii)$

From equation(i) and (ii),

(a + b + c + d + e) - (a + b + c + d) = 125 - 88

=> e = 37

Hence, the excluded number is 37.