Question

The mean of 45 numbers is 25 if each number is multiplied by 3 find the new mean

Answer 1

Answer:

75

Step-by-step explanation:

It is given that the mean of 45 numbers is 25.

Therefore, let the 45 numbers be $x_1,x_2,x_3,.....,x_{45}$.

The mean of those 45 numbers will be calculated as follows:

$\frac{x_1+x_2+x_3+.....+x_{45}}{45}=25\\x_1+x_2+x_3+.....+x_{45}=25*45=1125$.

If each number is multiplied by 3:

$3*x_1+3*x_2+3*x_3+....+3*x_{45}=3(x_1+x_2+x_3+....+x_{45})=3*1125=3375$

$\frac{3*x_1+3*x_2+3*x_3+....+3*x_{45}}{45}=\frac{3375}{45}=75$

Therefore, the new mean is 75.

Answer 2

Answer= New mean 75

Solution:
This problem is solved with the help of theorems on mean.

Theorem 3: If mean of some observations are x and each observation is multiply by n,than new mean will be = nx

The mean of 45 numbers is 25 if each number is multiplied by 3,than the new mean

= old mean × 3

= 25×3

= 75

Hope it helps you