Concept of Skewness: Bowley's method

Business Statistics: Concept of Bowley's Method

1. Presentation On Concept of Skewness : Bowley’s Method Presented by: Ashutosh Sahu MBA 1 st Semester

2. OVERVIEW Introduction: Skewness Symmetric Distribution Two types of skewness Measure of Skewness : Bowley’s Method Illustration Verification Conclusion Department Of Master of Business Administration Department Of Master of Business Administration

3. INTRODUCTION: SKEWNESS Measure of  lack  of symmetry Absence of symmetry Extreme values in either side of a distribution If the two sides do not coincide, distribution is said to be asymmetric A distribution that is asymmetric with respect to a vertical axis is said to be skewed. Department Of Master of Business Administration

4. SYMMETRIC DISTRIBUTION Department Of Master of Business Administration A distribution is symmetric if it can be folded along the vertical axis so that the two side coincide If the distribution is symmetric, the mean, the median, and the mode are equal and are located at the same position along the horizontal axis

5. TWO TYPES OF SKEWNESS Positively Skewed or Skewed to the Right Distribution Distribution tapers more to the right than to the left Has a longer tail to the right compared to a much shorter left tail Values are more concentrated below than above the mean Department Of Master of Business Administration

6. CONTINUED.... Department Of Master of Business Administration

7. CONTINUED.... Negatively Skewed or Skewed to the Left Distribution Distribution tapers more to the left than to the right Has longer tail to the left compared to a much shorter right tail Values are more concentrated above than below the mean Department Of Master of Business Administration

8. CONTINUED.... Department Of Master of Business Administration

9. MEASURE OF SKEWNESS: BOWLEY’S METHOD Shows the degree of asymmetry, or departure from symmetry of a distribution Indicates also the direction of the distribution Bowley Skewness = (Q3 +Q1 – 2M d )/ (Q3 – Q1) Skewness = 0 means that the curve is symmetrical. Skewness > 0 means the curve is positively skewed. Skewness < 0 means the curve is negatively skewed. Result range: -1< Sk B <1 Department Of Master of Business Administration

10. ILLUSTRATION Find Bowley’s Coefficient of Skewness for the following frequency distribution: Department Of Master of Business Administration

11. SOLUTION Department Of Master of Business Administration Solution:  Calculation of Bowley’s Coefficient of Skewness

12. CONTINUED….. Department Of Master of Business Administration Sk B  = Q 3  + Q 1  – 2 Med. /Q 3  – Q 1 Q 1   = Size of [( N +1)/4] th   item = [( 95 + 1)/4] = 24th  item, hence  Q1 = 2 Q 3   = Size of  3[(N + 1)/4] th  item =  3 × 96/4 = 72th  item Size of  72th  item is 4, hence  Q3 = 4 Med. = Size of [( N + 1)/2] th  item =  96/2 = 48th  item. Size of  48th  item is 3. Hence median =  3 Sk B  = [4 + 2 – 2 (3)]/(4 – 2) = 0/2 = 0.  Skewness = 0 means that the curve is symmetrical

13. VERIFICATION Department Of Mechanical Engineering Number of families

14. CONCLUSION Skewness : Measure of lack of symmetry The Bowley’s method to measure the skewness is actually a test to check, whether given distribution is in symmetry or not. Conditions are: Skewness = 0 means that the curve is symmetrical. Skewness > 0 means the curve is positively skewed. Skewness < 0 means the curve is negatively skewed. Result range: -1< Sk B <1 Department Of Master of Business Administration