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Problems for skewness

Chapter 3 Problems

1. Below is a frequency distribution of earnings of 50 contractors in a country. Regarding this distribution, which statement is correct? [pic]

i) Compute the mean, variance, the standard deviation and the Coefficient of variation (CV) of the earnings of these contractors.

ii) Compute the skewness of the distribution of earnings of these 50 contractors.

iii) Is the distribution positively or negatively skewed?

Solutions:

|Class Interval|x= Midpoints |Frequency |xf |f(x-[pic])2 |[pic] |
|0-10 |5 |2 |10 |1523.5 |-17.74 |
|10-20 |15 |7 |105 |2168.3 |-16.1 |
|20-30 |25 |12 |300 |693.12 |-2.222 |
|30-40 |35 |15 |525 |86.4 |.08747 |
|40-50 |45 |8 |360 |1230.1 |6.4339 |
|50-60 |55 |6 |330 |3010.6 |28.446 |
| | |n = ∑f = 50 |∑xf = 1630 |8712 |-1.08928 |

[pic] [pic]= [pic] = 177.7959

s= Standard deviation = 13.334

Skewness = [pic] = 0.0212585 (-1.08928) = -.0231. If frequencies are all one, then f=1 in the equation, that is Skewness = [pic]

2. The following frequency distribution shows the amount earned yesterday by employees of a large Las Vegas casino. Estimate the mean

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