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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 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.