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Last updated at May 29, 2018 by Teachoo

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Ex 15.3, 5 The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: Which is more varying, the length or weight? The value 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 length(x) and weight(y) For length (๐) : โด Mean ๐ฅ ฬ = (โโ๐ฅ๐)/n where n = number of terms = 50 Mean = 212/50=4.24 Variance = 1/๐^2 [๐โโใ๐๐ใ๐ฅ๐ใ^2 ใโ(โโ๐๐๐ฅ๐)^2 ] = 1/(50)^2 [50 ร902.8 โ(212)^2] = 1/2500[45140 โ44944] = 196/2500 = 0.0784 Standard deviation ("ฯ") = โ๐๐๐๐๐๐๐๐ = โ0.0784 = 0.28 C.VX = ๐/๐ ฬ ร 100 = 1.28/4.24 ร 100 = 6.603 For weight (๐) : โด Mean ๐ฆ ฬ = (โโ๐ฅ๐)/n where n = number of terms = 50 Mean = 261/50 = 5.22 Variance = 1/๐^2 [๐โโใ๐๐ใ๐ฅ๐ใ^2 ใโ(โโ๐๐๐ฅ๐)^2 ] = 1/(50)^2 [50 (1457.6)โ(ใ261)ใ^2] = 1/2500 [72880 โ 68121] = 4759/2500 = 1.9036 Standard deviation = โ๐ฃ๐๐๐๐๐๐๐ = โ1.9036 = 1.37 C.VY = ๐/๐ ฬ ร 100 = 1.37/5.22 ร 100 = 26.24 Since, C.V. of weight (y) > C.V. of length (x) โด Weight is more varying.

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.