Question
Write a short note on Bowley’s method of finding the coefficient of skewness.
✓
Answer
- Bowley's method: Base :
- In a skewed frequency distribution. both quartiles $Q_1$ and $Q_3$ are not equidistant from the median $M$.
- Measure of skewness:
- Using the distances of quartiles from median, i.e., $\left(Q_3-M\right)$ and $\left(M-Q_1\right)$, the measure of skewness $S_k$ is obtained as follows :
- $S_k=\left(Q_3-M\right)-\left(M-Q_1\right)$
- $=Q_3-M-M+Q_1$
- $S_k=Q_3+Q_1-2 M$
- Relative measure of skewness :
- Dividing the absolute measure of skewness by the sum of distances $\left(Q_3-M\right)$ and $\left(M-Q_1\right)$. the relative measure of skewness - the coefficient of skewness $(j)$ is obtained, i.e.,
- $j=\frac{s_k}{\left(Q_3-M\right)+\left(M-Q_1\right.}=\frac{Q_8+Q_1-2 M}{Q_3-Q_1}$
- If distances $\left(Q_3-M\right)$ and $\left(M-Q_1\right)$ are positive, then their difference may be less than or equal to their sum. Hence, $|j| \leq 1$, i.e., $-1 \leq j \leq 1$.
- This method is used when we have to compute the skewness by using positional average.
- This is the only method to calculate skewness when the frequency distribution has open-end classes.
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