Coefficient of Skewness Calculator

The Coefficient of Skewness (SK) is a statistical measure that indicates the asymmetry of the distribution of values in a data set relative to its mean. Skewness can help determine if a distribution leans towards higher or lower values, providing insights into the data's nature.

Historical Background

The concept of skewness and measures to quantify it have been part of statistics for over a century. Karl Pearson, a pioneer in statistical theory, was among the first to introduce measures of skewness to assess the asymmetry of a probability distribution.

Calculation Formula

The formula to calculate the coefficient of skewness for a data set is given by:

\[ SK = 3 \times \frac{(M - MD)}{s} \]

where:

• \(SK\) is the coefficient of skewness,
• \(M\) is the mean of the data set,
• \(MD\) is the median of the data set,
• \(s\) is the standard deviation of the data set (not sample size as previously misstated).

Example Calculation

For a data set with a mean (\(M\)) of 10, a median (\(MD\)) of 8, and a standard deviation (\(s\)) of 4, the skewness coefficient is calculated as follows:

\[ SK = 3 \times \frac{(10 - 8)}{4} = 1.5 \]

Importance and Usage Scenarios

The coefficient of skewness is vital in statistics for understanding the distribution characteristics of a data set. It is particularly useful in finance, quality control, and research, where the asymmetry of data affects decision-making and analysis.

Common FAQs

1. What does a positive skewness coefficient indicate?

   • A positive skewness indicates that the tail on the right side of the distribution is longer or fatter than the left side, meaning the data are skewed to the right.

2. What does a negative skewness coefficient mean?

   • A negative skewness means the tail on the left side of the distribution is longer or fatter than the right side, indicating the data are skewed to the left.

3. Is skewness coefficient sensitive to outliers?

   • Yes, skewness is sensitive to outliers. Extreme values in the data set can significantly affect the skewness coefficient.

This calculator facilitates the computation of the skewness coefficient, aiding in the analysis and interpretation of data sets across various fields.