Question

the mean of 5 numbers is 27. If one number is included, then the mean is 25. find the 8. included number​

Answer 1

Answer:

Given the mean of 5 numbers is 27

i.e., no. of numbers=5

Mean=27

We know

Mean=

No. of numbers/

sum of numbers

Sum of 5 numbers = Mean × No. of numbers

=27×5

=135

Here

one more number is included

Then no. of numbers is increased by one obstruction

∴ No. of numbers=6

and their mean=25

∴ Sum of 6 numbers =No. of numbers× mean

=6×25

=150

The included number is

=sum of 6 numbers− sum of 5 numbers

=150−135

=15

∴ Included number is 15.

Answer 2

Answer :-

Let the numbers be $\rm x_1 , x_2 , x_3 , x_4 \: and \: x_5$

Mean of the 5 numbers = 27

So,

➩ $\rm \dfrac{x_1 + x_2 + x_3 + x_4 + x_5}{5} = 27$

➩ $\rm x_1 + x_2 + x_3 + x_4 + x_5 = 27 \times 5$

➩ $\rm x_1 + x_2 + x_3 + x_4 + x_5 = 135$

Now, let the new number be y,

New mean = 25

Total number = 5 + 1 = 6

So,

➩ $\rm \dfrac{x_1 + x_2 + x_3 + x_4 + x_5 + y}{6} = 25$

➩ $\rm 135 + y = 25 \times 6$

➩ $\rm 135 + y = 150$

➩ $\rm y = 150 - 135$

➩ $\boxed{\rm y = 15}$