Examples

Chapter 13 Class 11 Statistics
Serial order wise

Transcript

Example 8 - Chapter 15 Class 11 Statistics - NCERT Find the Variance of the following data: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 xi di = (xi - 14)/2 xi – x ̅ ("xi – " x ̅)2 6 8 10 12 14 16 18 20 22 24 (6 − 14)/2 = − 4 (8 −14)/2 = − 3 (10 − 14)/2 = − 2 (12 −14)/2 = − 1 (14 − 14)/2 = 0 (16 − 14)/2 = 1 (18 − 14)/2 = 2 (20 − 14)/2 = 3 (22 − 14)/2 = 4 (24 − 14)/2 = 5 ∑_1^10▒"di" = 5 6 – 15 = -9 8 – 15 = -7 10 – 15 = -5 12 – 15 = -3 14 – 15 = -1 16 – 15 = 1 18 – 15 = 3 20 – 15 = 5 22 – 15 = 7 24 – 15 = 9 (-9)2 = 81 (-7)2 = 49 (-5)2 = 25 (-3)2 = 9 (-1)2 = 1 (1)2 = 1 (3)2 = 9 (5)2 = 25 (7)2 = 49 (9)2 = 81 ∑_1^10▒〖("xi – " 𝑥 ̅ )^2 〗 = 330 Mean 𝑥 ̅ = assumed mean + (∑_1^10▒𝑑_𝑖 )/𝑛 × h Where a = assumed mean = 14 𝑑_𝑖 = (𝑥_𝑖 − 𝑎)/ℎ h = Class width = 8 − 6 = 2 n = number of observations = 10 Mean (𝑥 ̅) = 14 + 5/10 × 2 = 15 Variance (σ2) = 1/n ∑▒〖"(xi – " 𝑥 ̅")" 2〗 = 1/10 × 330 = 33 Standard deviation (σ) = √Variance = √33 = 5.74

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.