How to find the Coefficient of Skewness?

Question:

Find the Coefficient of Skewness when sum of upper and lower quartiles is 200, difference of upper and lower quartiles is 20 and median is 100.

Solution:

Step 1: Note the given data.

Q₃ + Q₁ = 200

Q₃ - Q₁ = 20

Q₂ = 100

Step 2: Find Bowley's Coefficient of Skewness.

Bowley's Coefficient of Skewness = [Q₃ + Q₁ - 2Q₂] / [Q₃ - Q₁]

∴ [200 - 2(100)] / 20

∴ [200 - 200)] / 20

∴ 0 / 20

∴ 0 / 20

Answer:

Coefficient of Skewness is 0 when sum of upper and lower quartiles is 200, difference of upper and lower quartiles is 20 and median is 100. Since the coefficient of skewness is 0, it indicates that the distribution is symmetric.

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