Answer to Question #199442 in Statistics and Probability for khan ahad

Question

The Gauteng chamber of business conducted a survey amongst 17 furniture retailers to identify the percentage of bad debts in each company’s debtors’ book. The bad debts percentages are as follows:

 

2.2, 4.7, 6.3, 5.8, 5.7, 7.2, 2.6, 2.4, 6.1, 6.8, 2.2, 5.7, 3.4, 6.6, 1.8, 4.4, 5.4

 

Calculate the Pearson Coefficient of skewness coefficient for percentage of bad debts. Is the data skewed?

Answer 1

Pearson Coefficient of skewness coefficient

For a given set of values

2.2, 4.7, 6.3, 5.8, 5.7, 7.2, 2.6, 2.4, 6.1, 6.8, 2.2, 5.7, 3.4, 6.6, 1.8, 4.4, 5.4

Mean = (2.2 + 4.7 + 6.3 + 5.8 + 5.7 + 7.2 + 2.6 + 2.4 + 6.1 + 6.8 + 2.2 + 5.7 + 3.4 + 6.6 + 1.8 + 4.4 + 5.4)/17

=79.3/17

=4.66470588235

Median =5.4

Variance (σ²)

$=(2.2 - 4.66)^2+ (4.7 - 4.66)^2+ (6.3 - 4.66)^2 + (5.8- 4.66)^2+\\(5.7- 4.66)^2+(7.2- 4.66)^2+ (2.6 - 4.66)^2+ (2.4 - 4.66)^2 +\\ ( 6.1- 4.66)^2+ (6.8 - 4.66)^2+ ( 2.2 - 4.66)^2 +(5.7- 4.66)^2+\\ ( 3.4 - 4.66)^2+ (6.6 - 4.66)^2 + ( 1.8- 4.66)^2+ (4.4 - 4.66)^2+ ( 5.4 - 4.66)^2] / 17 \\ =1.79638237$

standard deviation (σ)

$=\sqrt{3.22698961925}\\ =1.79638237$

Pearson's Coefficient of Skewness coefficient

$=\frac{3 (mean- median)}{σ}\\ =\frac{3 (4.66470588235- 5.4)}{1.79638237}\\ =-1.228$

If skewness is negative, the data are negatively skewed or skewed left.