The mean of 15 numbers is 44. If 7 is subtracted from each number what will be the new mean?

Given that, mean of 15 numbers = 44

Mean can be given by

Where, ∑x = Sum of all observations

& n = Total number of observations

Here, Mean = 44 and n = 15.

So,

⇒

⇒ ∑x = 44 × 15

⇒ ∑x = 660

We have sum of all observations = 660

If 7 is subtracted from each of the 15 numbers, then the new sum of all observations = 660 – (15 × 7)

⇒ New sum of all observations = 660 – 105 = 555

Now, we have fresh data: ∑x’ = 555, n = 15

⇒ New mean = 37

Thus, new mean of the observation is 37.