Ex 15.3, 2 - Chapter 15 Class 11 Statistics (Term 1)
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
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.) = ๐/๐ ฬ ร 100 where ๐ = Standard Deviation ๐ ฬ = 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 (๐_๐) So, the formulas used here will be: Mean (๐ ฬ ) = (โโ๐ฅ๐)/๐ where n = number of terms Variance (๐)2 = 1/๐^2 [๐โโใ๐ฅ๐ใ^2 โ(โโ๐ฅ๐)^2 ] For X Mean (๐ ฬ ) = (โโ๐ฅ๐)/๐ = 510/10 = 51 Variance = 1/๐^2 [๐โโใ๐ฅ๐ใ^2 โ(โโ๐ฅ๐)^2 ] = 1/ใ(10)ใ^2 [10 ร 26360 โ ใ(510)ใ^2] = 1/100 [263600 โ 260100] = 3500/100 = 35 Standard Deviation = โ๐๐๐๐๐๐๐๐ = โ35 = 5.91 For Y Mean (๐) = (โโ๐ฆ๐)/๐ = 1050/10 = 105 Variance = 1/๐^2 [๐โโใ๐ฆ๐ใ^2 โ(โโ๐ฆ๐)^2 ] = 1/(10)^2 [10 ร 110290 โ ใ(1050)ใ^2] = 1/100 [1102900 โ 1102500] = 400/100 = 4 Standard Deviation = โ๐๐๐๐๐๐๐๐ = โ4 = 2 Covariance = ๐/๐ฅ ฬ ร100 = 5.91/51 ร100 = 11.58 Covariance = ๐/๐ฆ ฬ ร100 = 2/105 ร100 = 1.904 โด Covariance of X > Covariance of Y So, X is more variable than Y โด Y is more stable than X.
Ex 15.3
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