1. SKEWNESS
Skewness is a term for the degree of distortion from symmetry exhibited by a frequency
distribution.
When a distribution is perfectly symmetrical, the values of the mean, median and the mode
coincide.
In an asymmetrical distribution the values of the averages will depart from one another.
Since arithmetic mean is most affected by extreme values, it will move the greatest distance
from the mode. The mode is not affected by the unusual value; therefore the greater the
degree of skewness the greater the distance between the mean and the mode.
The skewness is computed by the formula:
Or by the formula
Where the curve is right skewed, the extremely large values will increase in value of the
mean. This results in increasing the value of the mean over that of the mode. The coefficient
will then be a positive value.
If the distribution is skewed to the left, the extreme cases will reduce the value of the mean.
This makes it smaller than the mode and results in a negative coefficient of skewness.
Left skew Right skew

2. Example:
Class Frequency Xm f  Xm f  Xm Class
Interval boundary
90-98 6 94 564 53 016 89.5-98.5
99-107 22 103 2266 233 398 98.5-107.5
108-116 43 112 4816 539 392 107.5-116.5
117-125 28 121 3388 409 948 116.5-125.5
126-134 9 130 1170 152 100 125.5-134.5
N=108 ∑=12204 ∑=1387854
Mean:
= 113
Mode:
Standard Deviation:
Skewness:
Homework: Find the Mean, Mode, Standard Deviation and Skewness.
Class Interval Frequency
18-25 45
26-33 36
34-41 30
42-49 25
50-57 16
58-65 8
66-73 8
74-81 7