Measures of skewness are used in descriptive statistics to describe the degree of asymmetry or lack of symmetry in a dataset. There are several measures of skewness, but the most commonly used are the Pearson's skewness coefficient and the moment coefficient of skewness.
Pearson's skewness coefficient: Pearson's skewness coefficient measures the degree of skewness by comparing the mean, median, and standard deviation of a dataset. It is calculated as 3 times the difference between the mean and median, divided by the standard deviation. A positive value indicates that the distribution is skewed to the right, while a negative value indicates that the distribution is skewed to the left. For
example, consider the following dataset of
exam scores: 85, 90, 75, 80, 95.
The Pearson's skewness coefficient for
this dataset is calculated as 0.17,
which is close to zero and
indicates that the distribution
is approximately symmetric.
Moment coefficient of skewness: The moment coefficient of skewness is calculated as the third standardized moment of a dataset. It measures the degree of skewness based on the differences between each data point and the mean, cubed. A positive value indicates that the distribution is skewed to the right, while a negative value indicates that the distribution is skewed to the left. For example, using the same dataset of exam scores as before,
the moment coefficient of skewness is calculated as -0.36,
which is negative and indicates
that the distribution is slightly skewed to the left.
In summary, measures of skewness provide information about the degree of asymmetry or lack of symmetry in a dataset. Pearson's skewness coefficient and the moment coefficient of skewness are commonly used measures of skewness, and each one provides different information about the data.
Top comments (0)