CHAPTER 5
Skewness and Kurtosis
This lesson will focus on the skewness and kurtosis of the
distribution. Skewness refers to the degree of the distribution deviates
from symmetrical or normal. Asymmetrical distribution happens when
most of the scores clustered in either ends of the distribution. Kurtosis,
on the other hand, refers to the “tailedness” and “peakedness” of the
distribution. More about skewness and kurtosis will be discussed in this
chapter.
At the end of this lesson, you should be able to compute and
interpret skewness and kurtosis.
Skewness
Skewness literally means “lack of symmetry”. Thus, it is defined
as the degree of symmetry or departure from symmetry of a set of data.
In a symmetrical distribution, mean, mode and median are equal to
each other. However, in asymmetrical distribution, the tail could be in the
either end of the distribution. Positively skewed distribution extends its
tail in the right and the bump is on the left. This means that most of the
scores clustered on the left of the distribution. The relationship of mean,
median and mode is Mode Median Mean . A negatively
skewed distribution extends its tail in the left side and the bump is on
the right side. In this distribution, most of the scores clustered on the
right side. The relationship of mean, median and mode is
Mean Median Mode .
Positively Skewed Distribution
69
, Negatively Skewed Distribution
Normal Distribution
There are several formulas in finding the coefficient of skewness.
For the sake of this lesson, we will be using the formula used by several
statistical programs. In that way, we can check the skewness of the data
through computer. The formula for skewness Sk is
3
n x − x
Sk =
(n − 1)(n − 2)
i s
and its standard error SE S k is
6n(n − 1)
SE Sk =
(n − 2)(n + 1)(n + 3)
The coefficient of skewness will be converted to its standard
score (z-score). If the alpha level ( level) is set to .05 then the
calculated z-score must fall within – 1.96 and + 1.96 so that the data
approximates the normal distribution. If the z-score goes beyond these
values, it means that the data has an unacceptable skewness at = .05.
The z-score of the skewness is
Sk − 0
z Sk =
SE Sk
70
Skewness and Kurtosis
This lesson will focus on the skewness and kurtosis of the
distribution. Skewness refers to the degree of the distribution deviates
from symmetrical or normal. Asymmetrical distribution happens when
most of the scores clustered in either ends of the distribution. Kurtosis,
on the other hand, refers to the “tailedness” and “peakedness” of the
distribution. More about skewness and kurtosis will be discussed in this
chapter.
At the end of this lesson, you should be able to compute and
interpret skewness and kurtosis.
Skewness
Skewness literally means “lack of symmetry”. Thus, it is defined
as the degree of symmetry or departure from symmetry of a set of data.
In a symmetrical distribution, mean, mode and median are equal to
each other. However, in asymmetrical distribution, the tail could be in the
either end of the distribution. Positively skewed distribution extends its
tail in the right and the bump is on the left. This means that most of the
scores clustered on the left of the distribution. The relationship of mean,
median and mode is Mode Median Mean . A negatively
skewed distribution extends its tail in the left side and the bump is on
the right side. In this distribution, most of the scores clustered on the
right side. The relationship of mean, median and mode is
Mean Median Mode .
Positively Skewed Distribution
69
, Negatively Skewed Distribution
Normal Distribution
There are several formulas in finding the coefficient of skewness.
For the sake of this lesson, we will be using the formula used by several
statistical programs. In that way, we can check the skewness of the data
through computer. The formula for skewness Sk is
3
n x − x
Sk =
(n − 1)(n − 2)
i s
and its standard error SE S k is
6n(n − 1)
SE Sk =
(n − 2)(n + 1)(n + 3)
The coefficient of skewness will be converted to its standard
score (z-score). If the alpha level ( level) is set to .05 then the
calculated z-score must fall within – 1.96 and + 1.96 so that the data
approximates the normal distribution. If the z-score goes beyond these
values, it means that the data has an unacceptable skewness at = .05.
The z-score of the skewness is
Sk − 0
z Sk =
SE Sk
70
