Question

the mean of 10 observation is 28 if each observation is multiplied by 2 find the new mean

Answer 1

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

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Answer 2

Let the observations be x1, x2 ,x3........................ x10

Given their mean is 28

So:

(x1 + x2 + x3 + ........................x10 ) / 10 =28

So:

==> x1 + x2 + x3 + x4 ............................x10 = 280

If this is multiplied by 2:

==> 2x1 + 2x2 + 2x3 + ...................2x10 = 560

Dividing both sides by 10 :

==> ( 2x1 + 2x2 + 2x3 + ................. 2x10 ) / 10 =56

Thus the mean of 2x1, 2x2 , .......................2x10 is 56

Thus the new mean is 56.

Hope it helps you.

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