Question

Approximately, the coefficient of variation for the given data where Pearson's second measure of skewness = 0.42, arithmetic mean = 86 and median = 80, is: 
1. 53
2. 51
3. 50
4. 52

Answer 1

Correct Answer - Option 3 : 50

Given

Pearsaons measure of skewness = 0.42

Mean = x̅ = 86

Median = M_d = 80

Formula

Skewness = Sk_p = 3(Mean – median)/standard deviation

Calculation

0.42 = 3(x̅  - M_d)/σ

⇒ 0.42 = 3(86 – 80)/σ

⇒ σ = 18/0.42

⇒ σ = 300/7

Coefficient of variation = standard deviation/mean = (σ/x̅) × 100

⇒ CV = (300/7/86) × 100

⇒ (300/7 × 86) × 100

∴ Coefficient of variation is 50