Question

the mean of a set of numbers is X if each no. Is multiplied by K then the mean of new set will be? ​

Answer 1

Mean of new set is $X \times K$.

Step-by-step explanation:

We are given that the mean of a set of numbers is X.

We have to find the new mean if each no. is multiplied by K.

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 no. by 3, the mean is also multiplied by 3 as $4\times 3=12$ .

Therefore, it is clear that in our question when each no. is multiplied by K, then the mean will be = $X \times K$ .