Ex 13.2, 10 - Chapter 13 Class 11 Statistics

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Ex 13.2, 10 The diameters of circles (in mm) drawn in a design are given below: h = class size = 36.5 βˆ’ 32.5 = 4 Mean(π‘₯ Μ…) = A + (βˆ‘β–’π‘“π‘–π‘¦π‘–)/(βˆ‘β–’π‘“π‘–) Γ—β„Ž = 42.5 + 25/100 Γ—4 = 42.5 + 1/4 Γ—4 = 43.5 Variance (𝜎)2 = β„Ž2/N2 [π‘βˆ‘β–’π‘“π‘–π‘¦π‘–2 βˆ’ (βˆ‘β–’π‘“π‘–π‘¦π‘–)^2 ] = 42/1002 [100 Γ— (199) – (25)2] = 16/10000 [19900 βˆ’625] = 16/10000 Γ— 19275 = 30.84 ∴ Standard deviation (𝜎) = √Variance 𝜎 = √30.84 = 5.55

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