Question

the mean of 15 number is 23.if each number is multiplied by 2 what will be the new mean?

Answer 1

Let 15 observations are:

x1 , x2 , .......,x15

Given mean of 15 observations = 23

=> (x1 + x2 +.......+ x15 )/15 = 23

=> x1 + x2 +.......+ x15 = 23*15 ...............1

Now, each observation is multiplied by 2.

So, new 15 observations are:

2x1 , 2x2 , .......,2x15

Now, mean = (2x1 + 2x2 +.......+ 2x15 )/15

= 2(x1 + x2 +.......+ x15 )/15

= (2 * 23 * 15)/15 {from eqaution 1}

= 2 * 23

= 46

So, new mean is 46