Question

The mean of 20observations is 10 and if each observation is multiplied by 3 then the mean will be

Answer 1

Mean will be 30.

Step-by-step explanation:

We are given that the mean of 20 observations is 10.

We have to find the new mean if each observation is multiplied by 3.

For finding this, let us take a simple example;

Suppose there are three data values 2, 4 and 6.

Mean of these three observations is given by;

              Mean, $\bar X$  =  $\frac{\sum X}{n}$

where,  $\sum X$ = Sum of all three observations

                n  = number of observations

So,  Mean, $\bar X$  =  $\frac{2+4+6}{3}$

                        =  $\frac{12}{3}$ = 4

Now, suppose each of three observations is now multiplied by 3 so the new values will be ;  6, 12 and 18

Now, New Mean  =  $\frac{6+12+18}{3}$

                             =  $\frac{36}{3}$ = 12

We see that when we multiplied each of the observations by 3, the mean is also multiplied by 3  as $4\times 3=12$.

Therefore, it is clear that in our question when each observation is multiplied by 3, then the mean will be = $10 \times 3 = 30$ .