# Ex 13.2, 2 - Chapter 13 Class 11 Statistics

Last updated at May 7, 2024 by Teachoo

Chapter 13 Class 11 Statistics

Serial order wise

Last updated at May 7, 2024 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, …… n Mean = (1 + 2 + 3 + 4 + ……. + n)/n = (n(n + 1)/2)/𝑛 = (𝐧 + 𝟏)/𝟐 Variance (σ2) = (∑▒(𝑥_𝑖 − 𝑥 ̅ )^2 )/n As the data is very large hence, "(xi – " 𝑥 ̅")" 2 calculation is difficult. Hence, we can use the formula : ∴ Variance (σ)2 = (𝑛(n + 1)(2n + 1))/6𝑛− (n + 1)2/4 = ((n + 1)(2n + 1))/6− (n + 1)2/4 = ((𝑛 + 1))/2 ((2n + 1)/3 " − " (𝑛 + 1)/2) = ((𝑛 + 1))/2 ((4n + 2 − 3𝑛 − 3)/6) = (𝑛 + 1)/2 × (𝑛 − 1)/6 = (𝐧^𝟐 − 𝟏)/𝟏𝟐