Question

the mean of n term is x bar if the first term is increased by 1 and second term by 2 and so on then find the new mean​

Answer 1

Mean of n observations is x.

Sum of n observations is nx.

Each of the observations is increased by 2, 4, 6, 8,........, 2n respectively.

Sum of the increased numbers = ∑2n

= 2[n(n+1) / 2]

= n(n+1)

Sum of all the observations = nx + n(n+1)

= n[x + (n+1)]

New mean of observations = n[x + (n+1)] / n

= x + (n+1)