Question

Mean of 15 observations is 23. If each observation is multiplied by 2,find new mean.

Answer 1

Sum of observations: 15*23
=345
If each observation is multiplied by 2 then the sum is also multiplied by 2.
:.New Sum: 345*2=690
:.New mean= 690/15=46

Answer 2

Answer:

The new mean is 46.

Step-by-step explanation:

The number of observations is 15 and their mean is 23.

Let the observations are

$x_1,x_2,...,x_{15}$

The mean of these observations is

$mean=\frac{\sum{x_1+x_2+...+x_{15}}}{15}$

$23=\frac{\sum{x_1+x_2+...+x_{15}}}{15}$            ... (1)

If each number is multiplied by 2, then the observations are

$2x_1,2x_2,...,2x_{15}$

The mean of these observations is

$Mean=\frac{\sum{2x_1+2x_2+...+2x_{15}}}{15}$

$Mean=2\frac{\sum{x_1+x_2+...+x_{15}}}{15}$

Using equation (1), we get

$Mean=2\times 23=46$

Therefore the new mean is 46.