Find the Median?

Question:

Find the median when Bowley's Coefficient of Skewness = -0.8; Q₁ = 44.1 and Q₃ = 56.6

Step 1: Note the given data.

Bowley's Coefficient of Skewness = -0.8

Q₁ = 44.1

Q₃ = 56.6

Step 2: Find Median using formula for Bowley's Coefficient of Skewness

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

∴ -0.8 = [56.6 + 44.1 - 2Q₂] / [56.6 - 44.1]

∴ -0.8 = [100.7 - 2Q₂] / [12.5]

∴ -0.8 x 12.5 = 100.7 - 2Q₂

∴ -10 = 100.7 - 2Q₂

∴ 2Q₂ = 100.7 + 10

∴ 2Q₂ = 110.7

∴ Q₂ = 110.7 / 2

∴ Q₂ = 55.35

Median is 55.35 when Bowley's Coefficient of Skewness = -0.8; Q₁ = 44.1 and Q₃ = 56.60.