Concept of Skewness: Bowley's method
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The document discusses Bowley's method for measuring skewness in a distribution. It defines skewness as a lack of symmetry and describes two types: positive and negative. Bowley's method calculates skewness as (Q3 + Q1 - 2Md) / (Q3 - Q1), where a value of 0 means the distribution is symmetric and positive or negative values indicate the direction of skewness. An example calculation demonstrates how to apply Bowley's method to determine the skewness of a sample frequency distribution is symmetric. The conclusion restates that Bowley's method determines if a distribution is symmetric or skewed, and if skewed, in which direction.
![CONTINUED…..
Department Of Master of Business Administration
SkB = Q3 + Q1 – 2 Med. /Q3 – Q1
Q1 = Size of [(N +1)/4]th item = [(95 + 1)/4] = 24th item,
hence Q1 = 2
Q3 = 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
SkB = [4 + 2 – 2 (3)]/(4 – 2) = 0/2 = 0.
Skewness = 0 means that the curve is symmetrical](https://image.slidesharecdn.com/bowleysmethod-180518045459/85/Concept-of-Skewness-Bowley-s-method-12-320.jpg)
Concept of Skewness: Bowley's method
- 1. Presentation On Concept of Skewness: Bowley’s Method Presented by: Ashutosh Sahu MBA 1st 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 FIGURE 1a. Example of a Symmetric Distribution 0 5 10 15 20 25 1 2 3 4 5 6 7 8 9 mean = median = mode No.ofProvinces
- 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 FIGURE 1b. Example of a Skewed to the Right Distribution 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 Mode < Median < Mean NumberofProvinces
- 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 FIGURE 1c. Example of a Skewed to the Left Distribution 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 mean < median < mode NumberofProvinces
- 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 – 2Md)/ (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< SkB <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 SkB = Q3 + Q1 – 2 Med. /Q3 – Q1 Q1 = Size of [(N +1)/4]th item = [(95 + 1)/4] = 24th item, hence Q1 = 2 Q3 = 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 SkB = [4 + 2 – 2 (3)]/(4 – 2) = 0/2 = 0. Skewness = 0 means that the curve is symmetrical
- 13. VERIFICATION Department Of Mechanical Engineering 0 5 10 15 20 25 30 Number Of children per family X 0 1 2 3 4 5 6 Numberoffamilies
- 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< SkB <1 Department Of Master of Business Administration