Coefficient of Variation

Chapter 13 Class 11 Statistics
Serial order wise

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### Transcript

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.) = π/π Μ Γ 100 where π = Standard Deviation π 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 (π_π) So, the formulas used here will be: Mean (π Μ) = (ββπ₯π)/π where n = number of terms Variance (π)2 = 1/π^2 [πββγπ₯πγ^2 β(ββπ₯π)^2 ] For X Mean (π Μ) = (ββπ₯π)/π = 510/10 = 51 Variance = 1/π^2 [πββγπ₯πγ^2 β(ββπ₯π)^2 ] = 1/γ(10)γ^2 [10 Γ 26360 β γ(510)γ^2] = 1/100 [263600 β 260100] = 3500/100 = 35 Standard Deviation = βππππππππ = β35 = 5.91 For Y Mean (π) = (ββπ¦π)/π = 1050/10 = 105 Variance = 1/π^2 [πββγπ¦πγ^2 β(ββπ¦π)^2 ] = 1/(10)^2 [10 Γ 110290 β γ(1050)γ^2] = 1/100 [1102900 β 1102500] = 400/100 = 4 Standard Deviation = βππππππππ = β4 = 2 Covariance = π/π₯ Μ Γ100 = 5.91/51 Γ100 = 11.58 Covariance = π/π¦ Μ Γ100 = 2/105 Γ100 = 1.904 β΄ Covariance of X > Covariance of Y So, X is more variable than Y β΄ Y is more stable than X.