Listed below are the commissions earned ($000) last year by a sample of 15 sales representatives at furniture patch inc. $4.2 $6.3 $7.5 $11.2 $13.0 $13.6 $15.2 $15.8 $16.7 $17.4 $18.6 $22.3 $37.6 $43.2 $83.6
a. determine the mean, median, and the standard deviation. (round your answers to 2 decimal places.) mean $ median $ standard deviation $
b. determine the coefficient of skewness using pearson's method. (round your answer to 3 decimal places.) coefficient of skewness
c. determine the coefficient of skewness using the software method. (round your answer to 2 decimal places.)

a)Mean= 21.75, median 15.8 and standard deviation is 19.45

b)0.918

c)0.92

Step-by-step explanation:

a)Given this data in $, the mean is sum of data divided by number of samples

4.2 6.3 7.5 11.2 13.0 13.6 15.2 15.8 16.7 17.4 18.6 22.3 37.6 43.2 83.6

sum will be

Number of samples=15

Mean=326.2/15=21.75

Median is center value in the data set

4.2 6.3 7.5 11.2 13.0 13.6 15.2 15.8 16.7 17.4 18.6 22.3 37.6 43.2 83.6

Median=15.8

Standard deviation

4.2-21.75= -17.55 , -17.55² =308.00

6.3-21.75= -15.45, -15.45²= 238.70

7.5-21.75= -14.25, -14.25² = 203.06

11.2-21.75= -10.55, -10.55² = 111.30

13-21.75= -8.75, -8.75²= 76.56

13.6-21.75= -8.15, -8.15²= 66.42

15.2-21.75= -6.55, -6.55²= 42.90

15.8-21.75= -5.95, -5.95²= 35.40

16.7-21.75= -5.05, -5.05²= 25.50

17.4-21.75= -4.35, -4.35²= 18.92

18.6-21.75= -3.15, -3.15²= 9.92

22.3-21.75= 0.55, 0.55²=0.30

37.6-21.75=15.85. 15.85²=251.22

43.2-21.75=21.45, 21.45²=460.10

83.6-21.75=61.85, 61.85²=3825.42

mean of squared differences

308+238.70+203.06+111.30+76.56+66.42+42.90+35.40+25.50+18.92+9.92+0.30+251.22+460.10+3825.42=5673.72

Mean of squared differences=5673.72/15 =378.25------variance

Standard deviation is square-root of variance= √378.25=19.45

b) The formula for finding the coefficient of skewness using Person's method is;

Multiply the difference between mean and median by three then dividing the answer by the standard deviation

Sk₂=3(x-Md)/s

where  Sk₂=skewness, x=mean, Md =median and s is standard deviation

Sk₂=3(21.75-15.8)/19.45 =0.918

c) using software method, use Excel

Answer=0.92

Step-by-step explanation: