Question

Find the coefficient of variation for the following data set and determine which one has a larger variation. Set 1- 6,9,10,15 Set2- 100,104.106.114. Please show all formlulars and workings.

Answer 1

Set1.

Input: 6, 9, 10, 15

Mean(µ) = (6 + 9 + 10 + 15)/4
Mean = 40/4
µ = 10

For standard deviation

= √( (1/4-1) * (6-10)²+(9-10)²+(10-10)²+(15-10)²)
= √( (1/3) * (-4² + -1² + 0² + 5²))
= √( (1/3) * (16 + 1 + 0 + 25))
= √ 13.99957056
σ= 3.7416

Coefficient of Variance = σ/µ
= 3.7416 / 10
Coefficient of Variance = 0.3741

For set2.

Mean(µ) = (100 + 104 + 106 + 114)/4
Mean = 424/4
µ = 106

Standard deviation is calculated as

= √( (1/4-1) * (100-106)²+(104-106)²+(106-106)²+(114-106)²)
= √( (1/3) * (-6² + -2² + 0² + 8²))
= √( (1/3) * (36 + 4 + 0 + 64))
= √ 34.66618884
σ= 5.8878

Coefficient of Variance = σ/µ
= 5.8878 / 106
Coefficient of Variance = 0.0555

Hence it is clear that set 1 has larger variation.