Find the mean and variance for the first n natural numbers

Asked by Abhisek | 11 months ago |  69

1 Answer

Solution :-

We know that Mean = 

\( \dfrac{Sum\; of\; all \;observations}{Number\; of \;observations}\)

Mean, x̅ = \( \dfrac{ ((n(n + 1))2)}{n}\)

\( \dfrac{ (n + 1)}{2}\) 

and also Variance,

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 21

By substitute that value of x̅ we get,

We know that,

\( (a-b)^2=a^2-2ab+b^2\)

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 23

(a + b)(a – b) = a2 – b2

σ2 = \( \dfrac{(n^2 – 1)}{12}\)

Mean = \( \dfrac{ (n + 1)}{2}\) and Variance 

\( \dfrac{(n^2 – 1)}{12}\)

Answered by Pragya Singh | 11 months ago

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