Find Mode and Median?

Question:

Find Mode and Median when Karl Pearson's Coefficient of Skweness = -0.4, Mean = 50

and Variance = 400?

Step 1: Find Standard deviation from Variance

Standard Deviation = √Variance

∴ Standard Deviation = √400

∴ Standard Deviation = 20

Step 2: Find Mode using Karl Pearson's Coefficient of Skweness's formula

Sₖₚ = [Mean - Mode] / Standard Deviation

∴ -0.4 = [50 - Mode] / 20

∴ -0.4 x 20 = 50 - Mode

∴ -8 = 50 - Mode

∴ Mode = 50 + 8

∴ Mode = 58

Step 3: Find Median using Karl Pearson's Coefficient of Skeweness's formula

Sₖₚ = 3 x [Mean - Median] / Standard Deviation

∴ -0.4 = 3 x [50 - Median] / 20

∴ -8 = 150 - 3 x Median

∴ 3 x Median = 158

∴ Median = 158 / 3

∴ Median = 52.67

Mode = 58 and Median = 52.67 when Karl Pearson's Coefficient of Skweness = -0.4, Mean = 50 and Variance = 400.