Bowley skewness 1

Bowley skewness 1

1. PROGRAMME B.COM SUBJECT QUANTITATIVE TECHNIQUE – I SEMESTER III UNIVERSITY VIJAYANAGAR SRI KRISHNADEVARAYA UNIVERSITY, BALLARI SESSION 54

2. RECAP Karl Pearson's Co-efficient of Skewness Under Continuous Series Problems---------02

3. LEARNING OBJECTIVES The aim of the chapter is to make students to understand Measures of Skewness, Karl Pearson Co-efficient of Skewness and Bowley's Co-efficient of skewness

4. LEARNING OUTCOMES After this Unit The Students can be able to apply to Sample Population Data by Differentiating Normal and Abnormal Distributions with regard to Dispersion & Skewness.

5. SESSION - 54 Bowely's Co-efficient of Skewness Under Individual and Discrete Series Problems----------------02

6. Bowley’s Co-efficient of Skewness In Karl Pearson method of measuring skewness the whole of the series is needed. Prof. Bowley has suggested a formula based on position of quartiles. In symmetric distribution quartiles will be equidistance from the median.  Q 2  –  Q 1  =  Q 3  –  Q 2  , but in skewed distributions it may not happen . Hence Q3 + Q1 – 2Median OR Q2 SK = Q3 – Q1

7. CONTD Ex ; 1. Calculate B owley’s skewness under individual series; 10,15,20,25,30,35,40, Calculation of Bowely’s skewness 10,15,20,25,30,35,40, N = 7 Q1= size of (N+1/4) = (7+1/4) = 8/4= 2 nd item, Q1 = 15 Q3 = size of 3(N+1/4) = 3(7+1/4) = 3(8)/4 = 24/4 Q3 = 24/4 , 6 th item Q3 = 35 Median = size of N+1/2 = 7+1/2= 8/2 = 4 th item Median = 25 Q3 + Q1 – 2Median OR Q2 SK = Q3 – Q1 = 35 + 15 – 2x25 35 - 15 SK = 00

8. CONTD Ex; 2.Calculate Bowley’s skewness under discrete series Ans ; Here, quartiles can be calculated: After calculating less than cumulative frequency (L.C.f) Qj class = size of j(N+1/4) th  item ; j = 1, 2, 3

9. CONTD Q3 +Q1 – 2Median SK = Q3 – Q1 OR

10. SUMMARY As we already discussed and learnt today on skewness as below Bowely's Co-efficient of Skewness Under Individual and Discrete Series Problems----------------02

11. MCQs 1 .The distribution in sum of Q3+Q1= 44,Q3–Q1= 16 and median = 21, bowley skewness 0.125 Positive skewed Negative skewed None of these 2.   formula of Bowley’s of skewness Sk = Q3+ Q1 – 2median/ Q3 – Q1 Negatively skewed Symmetrical None of these

12. MCQs 3 . If mean = 36.31 and Mode = 32 and S.D =15.8 then Karl Pearson co efficient of skewness is 0.27 Different Zero None of these 4. If mean = 36.31 and Mode = 32 and Karl Pearson co efficient of skewness is 0 .27, S.D = ? Positive Skewed Negative Skewed 15.8 None of these

13. MCQs 5 . The values of mean, median and mode can be Some time equal Never equal Always equal None of these

14. CONTD ANSWERS 1. A 2. A 3 . A 4. C 5. A

15. REFERENCES S.P . Gupta, Sultan Chand and Sons Publications, 2017 S. C. Gupta, Himalaya Publishing House, Fundamentals of Statistics, 2018 R.S.N Pillai and Bagavathi, S.Chand publications, 2010

16. THANK YOU