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

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  1. Chapter 15 Class 11 Statistics
  2. Serial order wise
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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.) = ๐œŽ/๐’™ ฬ… ร— 100 where ๐œŽ = 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…) = (โˆ‘โ–’๐‘ฅ๐‘–)/๐‘› where n = number of terms Variance (๐œŽ)2 = 1/๐‘›^2 [๐‘โˆ‘โ–’ใ€–๐‘ฅ๐‘–ใ€—^2 โˆ’(โˆ‘โ–’๐‘ฅ๐‘–)^2 ] For X Mean (๐’™ ฬ…) = (โˆ‘โ–’๐‘ฅ๐‘–)/๐‘› = 510/10 = 51 Variance = 1/๐‘›^2 [๐‘โˆ‘โ–’ใ€–๐‘ฅ๐‘–ใ€—^2 โˆ’(โˆ‘โ–’๐‘ฅ๐‘–)^2 ] = 1/ใ€–(10)ใ€—^2 [10 ร— 26360 โˆ’ ใ€–(510)ใ€—^2] = 1/100 [263600 โˆ’ 260100] = 3500/100 = 35 Standard Deviation = โˆš๐‘‰๐‘Ž๐‘Ÿ๐‘–๐‘Ž๐‘›๐‘๐‘’ = โˆš35 = 5.91 For Y Mean (๐’š) = (โˆ‘โ–’๐‘ฆ๐‘–)/๐‘› = 1050/10 = 105 Variance = 1/๐‘›^2 [๐‘โˆ‘โ–’ใ€–๐‘ฆ๐‘–ใ€—^2 โˆ’(โˆ‘โ–’๐‘ฆ๐‘–)^2 ] = 1/(10)^2 [10 ร— 110290 โˆ’ ใ€–(1050)ใ€—^2] = 1/100 [1102900 โˆ’ 1102500] = 400/100 = 4 Standard Deviation = โˆš๐‘‰๐‘Ž๐‘Ÿ๐‘–๐‘Ž๐‘›๐‘๐‘’ = โˆš4 = 2 Covariance = ๐œŽ/๐‘ฅ ฬ… ร—100 = 5.91/51 ร—100 = 11.58 Covariance = ๐œŽ/๐‘ฆ ฬ… ร—100 = 2/105 ร—100 = 1.904 โˆด Covariance of X > Covariance of Y So, X is more variable than Y โˆด Y is more stable than X.

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