Check sibling questions

Ex 15.2, 2 - Find mean and variance for first n natural numbers - Standard deviation and variance - Ungrouped data

Ex 15.2,  2 - Chapter 15 Class 11 Statistics - Part 2


Transcript

Ex 15.2, 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

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.