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Example 2
Example 3 Important
Example 4
Example 5 Important
Example 6 (Normal Method)
Example 6 (Shortcut Method) Important
Example 7 Important
Example 8 You are here
Example 9 Important
Example 10 Important
Example 11
Example 12 Important
Example 13 Deleted for CBSE Board 2022 Exams
Example 14 Important
Example 15 Important Deleted for CBSE Board 2022 Exams
Example 16
Example 17 Important
Example 18
Example 19 Important
Examples
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