Ex 13.2, 9 - Chapter 15 Class 11 Statistics (Important Question)

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Ex15.2, 9 Find the mean, variance and standard deviation using short-cut method Mean(π‘₯ Μ…) = A + (βˆ‘β–’π‘“π‘–π‘¦π‘–)/(βˆ‘β–’π‘“π‘–) Γ—β„Ž where A = assumed mean = 92.5 𝑦_𝑖=(π‘₯_𝑖 βˆ’ 𝐴)/β„Ž h = class size = 75 βˆ’ 70 = 5 Variance (𝜎)2 = β„Ž2/N2 [π‘βˆ‘β–’π‘“π‘–π‘¦π‘–2 βˆ’ (βˆ‘β–’π‘“π‘–π‘¦π‘–)^2 ] = 52/602 [N Γ— (254) – (6)2] = 25/3600 [60 Γ—254 βˆ’36] = 25/3600 Γ— 15204 = 105.58 ∴ Standard deviation (𝜎) = √Variance = √105.58 = 10.27

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