Question

Listed below is the amount of commissions earned last month for the eight members of the sales staff at Best Electronics. Calculate the coefficient of skewness using both methods. Hint: Use of a spreadsheet will expedite the calculations. (Round your intermediate calculations and final answers to 3 decimal places.
980.9 1036.5 1099.5 1153.9 1409.0 1456.4 1718.4 1721.2

a. Pearson coefficient of skewness
b. Coefficient of skewness (using software)

Answer 1

Answer:

0.438

Step-by-step explanation:

Given the data:

980.9, 1036.5, 1099.5, 1153.9, 1409.0, 1456.4, 1718.4, 1721.2

Coefficient of skewness:

3 * (mean - median) / standard deviation

The mean of the dataset :

Σ(X) / N ; N = sample size = 8

980.9+1036.5+1099.5+1153.9+1409.0+1456.4+1718.4+1721.2

= 10575.8 / 8

= 1321.975

Median :

980.9, 1036.5, 1099.5, 1153.9, 1409.0, 1456.4, 1718.4, 1721.2

1/2(n + 1)th term

1/2(9) = 4.5th term

(1153.9+1409.0) / 2

= 1281.45

Standard deviation:

Sqrt[Σ(X - mean)²/ (N - 1)]

Using calculator :

Standard deviation estimate of population = 277.882456

Coefficient of skewness :

3(1321.975 - 1281.45) / 277.882456

121.575 / 277.882456

= 0.4375051

= 0.4375

Using software excel :

Using excel's AVERAGE, MEDIAN and STDEV.P functions, the Coefficient of skewness can be obtained using the formula :

3 * (mean - median) / standard deviation

Coefficient of skewness obtained is 0.438