Question

Listed below are the commissions earned ($000) last year by a sample of 15 sales representatives at Furniture Patch Inc. $ 4.2 $ 6.0 $ 8.0 $ 11.3 $ 12.5 $ 13.6 $ 14.6 $ 16.4 $ 17.1 $ 17.4 $ 18.2 $ 22.3 $ 36.8 $ 43.2 $ 78.8

Determine the mean, median, and the standard deviation. (Round your answers to 2 decimal places.)

Determine the coefficient of skewness using Pearson’s method. (Round your answer to 3 decimal places.)

Determine the coefficient of skewness using the software method. (Round your answer to 3 decimal places.)

Answer 1

Solution-:

Given data:

(a) We find  the mean, median, and the standard deviation by using R-software as follows;

> x=c(4.2,6.0,8.0,11.3,12.5,13.6,14.6,16.4,17.1,17.4,18.2,22.3,36.8,43.2,78.8);x
[1] 4.2 6.0 8.0 11.3 12.5 13.6 14.6 16.4 17.1 17.4 18.2 22.3 36.8 43.2 78.8
> n=length(x);n
[1] 15
> #for mean
> Mean=mean(x);Mean
[1] 21.36
> #for median
> med=median(x);med
[1] 16.4
> #for Standard Deviation
> v=var(x);v
[1] 362.7526
> var=((n-1)/n)*v;var
[1] 338.5691
> sd=sqrt(var);sd # Standard Deviation
[1] 18.40025
> round(sd,2)
[1] 18.4
(b) From above output we get, mean=21.36, median=16.40, dstandard deviation=18.40

The coefficient of skewness using Pearson’s method :

(c) The coefficient of skewness using the software method:

By using R -software:

> skp=(3*(Mean-med))/sd;skp
[1] 0.8086848
> round(skp,3)
[1] 0.809