If the mean of n observations is x.
Of the observation is increased by 2 ,the second by 4,the third by 6 and so on,find the mean of new observations.
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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) + 2 + 4 + 6 + ....... + n
= nx + n/2 (2a + (n-1)d)
= nx + n/2 (4 + (n-1)2)
= nx + n/2 (2 + 2n)
= nx + n(n+1)
= n(x+n+1)
New mean = sum of new observations/ number of observations
= n(x+n+1)/n
= x+n+1
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