rakesh kumar

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# how to Measures of skewness in descriptive statistics

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.