Question
Explain skewness and coefficient of skewness.
✓
Answer
- Skewness:
- Measures of central tendency and dispersion are useful for comparing two or more data.
- But they cannot give information about whether the observations of the data are symmetrically distributed or not.
- This information can be obtained from the frequency curve of the frequency distribution.
- If frequency curve is symmetric on both sides from its peak point. it is said that observations of the data are distributed symmetrically. But, if it is not so, we call it skewness in frequency distribution.
- Thus, skewness gives an idea about nature of the data with respect to shape of frequency curve.
- In short, skewness implies the lack of symmetry in frequency distribution of the data.
- The skewness of a frequency distribution may be positive or negative which can be determined by the shape of frequency curve.
- The measure of skewness can be obtained by using the measures of average - mean, median, mode and the measures of positional average - quartiles ( $Q_1, Q_3$ ). median (M). Symbolically, it is denoted by $S_k$.
- Absolute measure of skewness is $S_k=\bar{x}-M_0$ or $S_k=3(\bar{x}-M) O R S_k=Q_3+Q_1-2 M$.
- Absolute measure of skewness, cannot be used for comparing skewness of two or more frequency distributions.
- Coefficient of skewness :
- It is a relative measure of skewness which is free from unit of measurement. It is denoted by symbol j .
- Coefficient of skewness can be used for comparing the skewness of two or more frequency distributions.
- It is obtained by dividing the absolute measure of skewness by an appropriate measure of dispersion, i.e., $j=$ $\frac{S_k}{s}$ or $j=\frac{S_{ k }}{Q_{ s }-Q_1}$
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