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.
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