Question 2 - Co-efficient of variation - Chapter 13 Class 11 Statistics

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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.) = 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.

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.

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