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Ex 15.3,  2 - From the prices of shares X, Y, find out stable - Co-efficient of variation

Ex 15.3,  2 - Chapter 15 Class 11 Statistics - Part 2
Ex 15.3,  2 - Chapter 15 Class 11 Statistics - Part 3
Ex 15.3,  2 - Chapter 15 Class 11 Statistics - Part 4

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Ex15.3, 2 From the prices of shares X and Y below, find out which is more stable in value: The group having more Coefficient of Variation will be more variable. Coefficient of Variation (C.V.) = 𝜎/𝒙 Μ… Γ— 100 where 𝜎 = Standard Deviation 𝒙 Μ… = Mean Finding standard deviation & mean of both Group A and Group B. But as the data given is raw data, Hence, there is no values for frequency (𝑓_𝑖) So, the formulas used here will be: Mean (𝒙 Μ…) = (βˆ‘β–’π‘₯𝑖)/𝑛 where n = number of terms Variance (𝜎)2 = 1/𝑛^2 [π‘βˆ‘β–’γ€–π‘₯𝑖〗^2 βˆ’(βˆ‘β–’π‘₯𝑖)^2 ] For X Mean (𝒙 Μ…) = (βˆ‘β–’π‘₯𝑖)/𝑛 = 510/10 = 51 Variance = 1/𝑛^2 [π‘βˆ‘β–’γ€–π‘₯𝑖〗^2 βˆ’(βˆ‘β–’π‘₯𝑖)^2 ] = 1/γ€–(10)γ€—^2 [10 Γ— 26360 βˆ’ γ€–(510)γ€—^2] = 1/100 [263600 βˆ’ 260100] = 3500/100 = 35 Standard Deviation = βˆšπ‘‰π‘Žπ‘Ÿπ‘–π‘Žπ‘›π‘π‘’ = √35 = 5.91 For Y Mean (π’š) = (βˆ‘β–’π‘¦π‘–)/𝑛 = 1050/10 = 105 Variance = 1/𝑛^2 [π‘βˆ‘β–’γ€–π‘¦π‘–γ€—^2 βˆ’(βˆ‘β–’π‘¦π‘–)^2 ] = 1/(10)^2 [10 Γ— 110290 βˆ’ γ€–(1050)γ€—^2] = 1/100 [1102900 βˆ’ 1102500] = 400/100 = 4 Standard Deviation = βˆšπ‘‰π‘Žπ‘Ÿπ‘–π‘Žπ‘›π‘π‘’ = √4 = 2 Covariance = 𝜎/π‘₯ Μ… Γ—100 = 5.91/51 Γ—100 = 11.58 Covariance = 𝜎/𝑦 Μ… Γ—100 = 2/105 Γ—100 = 1.904 ∴ Covariance of X > Covariance of Y So, X is more variable than Y ∴ Y is more stable than X.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.