Question

The mean of 45 numbers is 25. If each number is multiplied by 3, find the new mean.​

Answer 1

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}x1,x2,x3,.....,x45 .

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

\begin{lgathered}\frac{x_1+x_2+x_3+.....+x_{45}}{45}=25\\x_1+x_2+x_3+.....+x_{45}=25*45=1125\end{lgathered}45x1+x2+x3+.....+x45=25x1+x2+x3+.....+x45=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=33753∗x1+3∗x2+3∗x3+....+3∗x45=3(x1+x2+x3+....+x45)=3∗1125=3375

\frac{3*x_1+3*x_2+3*x_3+....+3*x_{45}}{45}=\frac{3375}{45}=75453∗x1+3∗x2+3∗x3+....+3∗x45=453375=75

Therefore, the new mean is 75.

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Answer 2

Given that mean of 45 numbers(x) = 25

3x = 3 × 25

= 75

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