Question

The mean of n observation is x , if the first term is increased by 1 second by 2 and so on . What will be the new mean

Answer 1

Answer: x+n+1

Step-by-step explanation:

Given that the mean of n observations is x,

sum of x observations S(x) / number of observations (n) = x

S(x) / n = x

S(x) = nx

sum of new observations = S(x) + 1 + 2 + 3 + ....... + n

= nx + n/2 (2a + (n-1)d)

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

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

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

New mean = sum of new observations/ number of observations

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

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