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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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.) = 𝜎/𝒙 ̅ × 100 where 𝜎 = Standard Deviation 𝒙 ̅ = 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 ̅) = (∑▒𝑥𝑖)/𝑛 where n = number of terms Variance (𝜎)2 = 1/𝑛^2 [𝑁∑▒〖𝑥𝑖〗^2 −(∑▒𝑥𝑖)^2 ] For X Mean (𝒙 ̅) = (∑▒𝑥𝑖)/𝑛 = 510/10 = 51 Variance = 1/𝑛^2 [𝑁∑▒〖𝑥𝑖〗^2 −(∑▒𝑥𝑖)^2 ] = 1/〖(10)〗^2 [10 × 26360 − 〖(510)〗^2] = 1/100 [263600 − 260100] = 3500/100 = 35 Standard Deviation = √𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = √35 = 5.91 For Y Mean (𝒚) = (∑▒𝑦𝑖)/𝑛 = 1050/10 = 105 Variance = 1/𝑛^2 [𝑁∑▒〖𝑦𝑖〗^2 −(∑▒𝑦𝑖)^2 ] = 1/(10)^2 [10 × 110290 − 〖(1050)〗^2] = 1/100 [1102900 − 1102500] = 400/100 = 4 Standard Deviation = √𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = √4 = 2 Covariance = 𝜎/𝑥 ̅ ×100 = 5.91/51 ×100 = 11.58 Covariance = 𝜎/𝑦 ̅ ×100 = 2/105 ×100 = 1.904 ∴ Covariance of X > Covariance of Y So, X is more variable than Y ∴ Y is more stable than X.

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.