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Question -

Find the mean and variance for the data 

First n natural numbers



Answer -

We know that Mean =Sum of all observations/Number of observations

Mean, x̅ = ((n(n +1))2)/n

= (n + 1)/2

and also WKT Variance,

By substitute thatvalue of x̅ we get,

WKT, (a + b)(a – b) =a2 – b2

σ2 =(n2 – 1)/12

Mean = (n + 1)/2 andVariance = (n2 – 1)/12

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