Check sibling questions

Example 8 - Find variance of 6, 8, 10, 12, 14, 16, 18, 20 - Standard deviation and variance - Ungrouped data

Example 8 - Chapter 15 Class 11 Statistics - Part 2
Example 8 - Chapter 15 Class 11 Statistics - Part 3


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 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.