1. Asian School of Business PG Programme in Management (2005-06) Course: Quantitative Methods in Management I Instructor: Chandan Mukherjee Session 4: Summarising a Distribution (contd.) Changing the Shape of a Distribution: Power Transformation

2. Log Transformation to Symmetry

3. COUNTRY India South Korea New Zealand Denmark An Interpretation of Log Transformation: Try to place the following four countries on the scale of Per Capita Gross National Income

4. An Interpretation of Log Transformation (contd.)

7. Compare Wages of Permanent & Casual Workers: (Sample from Industries in Coimbatore)

8. Outliers Indentified by Sex of the Worker

9. Log Transformation to Symmetry: Weekly Earnings Data

10. After Log Transformation: Finding Out What Lies Below the Pattern of Skewness

11. Who Are The Outliers? Women Always Loose Out to Men!

12. Log Transformation to Symmetry: It doesn’t work always

13. Y p if p > 0 reduces negative skewness Log(Y) if p = 0 reduces positive -Y p if p < 0 skewness Ladder of Power p = 3Y 3 reduces negative p = 2Y 2 skewness p = 1Y no effect p = 0.5Y 0.5 reduces p = 0Log(Y)positive p = -0.5-Y -0.5 skewness Changing the Shape of a Distribution: Ladder of Transformation

14. Power Transformation