Question

Mean of n observations is X. If each of these
observations is increased by 1, 2, 3, 4..., respec-
tively, then what will be their new mean? ​

Answer 1

Answer:

nx

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

x¯¯¯=Mean=∑xnx¯=Mean=∑xn

Here, mean = x

Total = ∑x=nx∑x=nx

Now first term is added by 1, second term is added by 2 … the nthnth term is added by n.

The sum of terms added = 1+2+3+…+n = n(n+1)2n(n+1)2

Therefore, new total is nx+n(n+1)2nx+n(n+1)2

=2nx+n(n+1)2=2nx+n(n+1)2

New Mean = 2nx+n(n+1)2n2nx+n(n+1)2n

=n(2x+(n+1)2)n=n(2x+(n+1)2)n

=(2x+(n+1)2)