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Last updated at May 29, 2018 by Teachoo
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Ex 15.2, 2 Find the mean and variance for the first n natural numbers First n natural numbers = 1, 2, 3, 4, โฆโฆ n Mean = (1 + 2 + 3 + 4 + โฆโฆ. + n)/n = (n(n + 1)/2)/๐ = (๐ง + ๐)/๐ Variance (ฯ2) = (โโ(๐ฅ_๐ โ ๐ฅ ฬ )^2 )/n As the data is very large hence, "(xi โ " ๐ฅ ฬ ")" 2 calculation is difficult. Hence, we can use the formula : โด Variance (ฯ)2 = (๐(n + 1)(2n + 1))/6๐โ (n + 1)2/4 = ((n + 1)(2n + 1))/6โ (n + 1)2/4 = ((๐ + 1))/2 ((2n + 1)/3 " โ " (๐ + 1)/2) = ((๐ + 1))/2 ((4n + 2 โ 3๐ โ 3)/6) = (๐ + 1)/2 ร (๐ โ 1)/6 = (๐ง^๐ โ ๐)/๐๐
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