How to find Bowley's Coefficient of Skewness?

Question:

Find Bowley's Coefficient of Skewness when Q₃ - Q₂ = 100 and Q₂ - Q₁ = 120.


Solution Method 1:

Step 1: Find Q₃

Q₃ - Q₂ = 100

∴ Q₃ = 100 + Q₂


Step 2: Find Q₁

Q₂ - Q₁ = 120

∴ Q₁ = Q₂ - 120


Step 3: Find Bowley's Coefficient of Skewness using the formula.

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

∴ Bowley's Coefficient of Skewness = [100 + Q₂ + Q₂ - 120 - 2Q₂] / [100 + Q₂ - (Q₂ - 120)]

∴ Bowley's Coefficient of Skewness = [100 - 120] / [100 + 120]

∴ Bowley's Coefficient of Skewness = -20 / 220

∴ Bowley's Coefficient of Skewness = -2 / 22

∴ Bowley's Coefficient of Skewness = -1 / 11

∴ Bowley's Coefficient of Skewness = -0.09


Answer:

Bowley's Coefficient of Skewness is -0.09 when Q₃ - Q₂ = 100 and Q₂ - Q₁ = 120.


Solution Method 2:

Step 1: Use Bowley's Coefficient of Skewness formula directly.

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

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

∴ Bowley's Coefficient of Skewness = [(Q₃ - Q₂) - (Q₂ - Q₁)] / [(Q₃ - Q₂) + (Q₂ - Q₁)]

∴ Bowley's Coefficient of Skewness = [100 - 120] / [100 + 120]

∴ Bowley's Coefficient of Skewness = -20 / 220

∴ Bowley's Coefficient of Skewness = -2 / 22

∴ Bowley's Coefficient of Skewness = -1 / 11

∴ Bowley's Coefficient of Skewness = -0.09


Answer:

Bowley's Coefficient of Skewness is -0.09 when Q₃ - Q₂ = 100 and Q₂ - Q₁ = 120.


Video Solution:



How to find Bowley's Coefficient of Skewness using solved example from Skewness and Kurtosis