The mean of 12 numbers is 48. If each numbers is multiplied by 4 what will be the new mean.

Given that, mean of 12 numbers = 48

Mean can be given by

Where, ∑x = Sum of all observations

& n = Total number of observations

Here, Mean = 48 and n = 12.

So,

⇒

⇒ ∑x = 48 × 12

⇒ ∑x = 576

We have sum of all observations = 576

If 4 is multiplied by each of the 12 numbers, then the new sum of all observations = 576 × 4

⇒ New sum of all observations = 2304

Now, we have fresh data: ∑x’ = 2304, n = 12

⇒ New mean = 192

Thus, new mean of the observation is 192.