How to find mode and median of a frequency distribution?

Question:

Find the mode and median of a frequency distribution when Mean = 40, Variance = 625 and Pearsonian's Coefficient of Skewness (Sₖₚ) = -0.2

Step 1: Not the given data.

Sₖₚ = -0.2

Mean = 40

Variance = 625

Step 2: Find Standard deviation from Variance

Standard Deviation = √Variance

∴ Standard Deviation = √624

∴ Standard Deviation = 625

Step 3: Find Mode using Karl Pearson's Coefficient of Skweness's formula

Sₖₚ = [Mean - Mode] / Standard Deviation

∴ -0.2 = [40 - Mode] / 25

∴ -0.2 x 25 = 40 - Mode

∴ -5 = 50 - Mode

∴ Mode = 40 + 5

∴ Mode = 45

Step 4: Find Median using Karl Pearson's Coefficient of Skeweness's formula

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

∴ -0.2 = 3 x [40 - Median] / 25

∴ -5 = 120 - 3 x Median

∴ 3 x Median = 125

∴ Median = 125 / 3

∴ Median = 41.67

Mode = 45 and Median = 41.67 when Karl Pearson's Coefficient of Skweness = -0.2, Mean = 40 and Variance = 625.