The mean of 16 numbers is 54. If each number is divided by 9 what will be the new mean.

Given that, mean of 16 numbers = 54

Mean can be given by

Where, ∑x = Sum of all observations

& n = Total number of observations

Here, Mean = 54 and n = 16.

So,

⇒

⇒ ∑x = 54 × 16

⇒ ∑x = 864

We have sum of all observations = 864

If 9 is divided from each of the 16 numbers, then the new sum of all observations = 864 ÷ 9

⇒ New sum of all observations = 96

Now, we have fresh data: ∑x’ = 96, n = 16

⇒ New mean = 6

Thus, new mean of the observation is 6.