Write a short note on Bowley’s method of finding the coefficient of

1.	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 Q₁ and Q₃ are not equidistant from the median M. Measure of skewness: Using the distances of quartiles from median, i.e., (Q₃ – M) and (M – Q₁), the measure of skewness S_k is obtained as follows: S_k = (Q₃ – M) – (M – Q₁) = Q₃ – M – M + Q₁ S_k = Q₃ + Q₁ – 2M Relative measure of skewness : Dividing the absolute measure of skewness by the sum of distances (Q₃ – M) and (M – Q₁), the relative measure of skewness-the coefficient of skewness (j) is obtained, i.e., J = \(\frac{Sk}{(Q_3−M)+(M−Q_1)}\) = \(\frac{Q_3+Q_1−2M}{Q_3−Q_1}\) -» If distances (Q₃ – M) and (M – Q₁) are positive, then their difference may be less than or equal to their sum. Hence, \| j \| ≤ 1, i.e., – 1 ≤ j ≤ 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.

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 Q₁ and Q₃ are not equidistant from the median M.

Measure of skewness: Using the distances of quartiles from median, i.e., (Q₃ – M) and (M – Q₁), the measure of skewness S_k is obtained as follows:
S_k = (Q₃ – M) – (M – Q₁)
= Q₃ – M – M + Q₁
S_k = Q₃ + Q₁ – 2M

Relative measure of skewness : Dividing the absolute measure of skewness by the sum of distances (Q₃ – M) and (M – Q₁), the relative measure of skewness-the coefficient of skewness (j) is obtained, i.e.,
J = \(\frac{Sk}{(Q_3−M)+(M−Q_1)}\)

= \(\frac{Q_3+Q_1−2M}{Q_3−Q_1}\)

-» If distances (Q₃ – M) and (M – Q₁) are positive, then their difference may be less than or equal to their sum. Hence, | j | ≤ 1, i.e., – 1 ≤ j ≤ 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.

Write a short note on Bowley’s method of finding the coefficient of skewness.

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