Question

15.| Basic Computation: Coefficient of Variation, Chebyshev Interval Consider population data with μ 20 and σ 2. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean.

Answer 1

15. a) Coefficient of Variation = (Standard Deviation / Mean) * 100.
i.e.

$CV = \frac{ \sigma}{\mu }\times 100$

we have  
μ=20
and $\sigma = 2$

Coefficient of Variation =   $\frac{2}{20}\times 100 = 10$

b)  Chebyshev’s rule.  For any data set, the proportion (or percentage) of values that fall within  k  standard deviations from mean i.e. , in the interval $(\mu -k\sigma , \mu +k\sigma )$ is at least   () , where  k > 1.

1k

For k = 3, 1- 1/3² =0.889 = 88.9%

i.e. at least 88.9% data fall within 3 standard deviations from mean.

So 88.9% Chebyshev interval around mean is given by :

(20 - 3*2 , 20 +3*2)

88.9% Chebyshev interval around mean is (14 , 26)