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Chapter 13 Class 11 Statistics

Serial order wise

Last updated at May 29, 2023 by Teachoo

Ex 13.2, 2 Find the mean and variance for the first n natural numbers First n natural numbers = 1, 2, 3, 4, β¦β¦ n Mean = (1 + 2 + 3 + 4 + β¦β¦. + n)/n = (n(n + 1)/2)/π = (π§ + π)/π Variance (Ο2) = (ββ(π₯_π β π₯ Μ )^2 )/n As the data is very large hence, "(xi β " π₯ Μ ")" 2 calculation is difficult. Hence, we can use the formula : β΄ Variance (Ο)2 = (π(n + 1)(2n + 1))/6πβ (n + 1)2/4 = ((n + 1)(2n + 1))/6β (n + 1)2/4 = ((π + 1))/2 ((2n + 1)/3 " β " (π + 1)/2) = ((π + 1))/2 ((4n + 2 β 3π β 3)/6) = (π + 1)/2 Γ (π β 1)/6 = (π§^π β π)/ππ