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Coefficient of Variation

Nov 29, 2020

The coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation(σ) to the mean(μ).

It gives the measure of variability

CV = Standard Deviation / Mean

Q) What is the variance and standard deviation of the possibilities associated with rolling a fair die?

Ans:

Possible outcomes = {1,2,3,4,5,6}
mean = (6+5+4+3+2+1)/6 = 3.5
variance = (6.25+2.25+0.25+0.25+2.25+6.25)/6=2.917
std. deviation = (2.917) ^0.5 = 1.71

Q) The following data set has a mean of 14.7 and a variance of 10.01.

Ans:

18, 11, 12, a, 16, 11, 19, 14, b, 13
Compute the values of a and b.
Ans: -From the formula of the mean we have
14.7 = (114+a+b)/10
a+b = 147−114
a=33−b
From the formula of the variance we have
10.01 = (69.12+(a−14.7) ^2+(b−14.7) ^2)/10
Substitute a=33−b and solve: -
b= 13 0r b=20
Since a=33−b
we have a=20 or a=13. 
So, the two unknown values in the data set are 13 and 20
We do not know which of these is a and which is b since the mean and variance tell us nothing about the order of the data.

Covariance, Correlation & Causation >

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Coefficient of Variation

Coefficient of Variation

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