KPC and Bowley skewness

KPC and Bowley skewness Numerical

1. PROGRAMME B.COM SUBJECT QUANTITATIVE TECHNIQUE – I SEMESTER III UNIVERSITY VIJAYANAGAR SRI KRISHNADEVARAYA UNIVERSITY, BALLARI SESSION 56

2. RECAP Bowely'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 - 56 Karl Pearson's and Bowely's Co-efficient of Skewness Under Continuous Series Problems--------01

6. KARL PEARSON SKEWNESS Compute Karl Pearson's Co-efficient of Skewness ANS; Calculation of Karl Pearson's Co-efficient of Skewness SK= Mean - Mode/ S.D or SK= - Z /  

7. CONTD

8. CONTD Modal class = size of highest frequency=25 Assumed Mean = 05, N= 70, =117, =341, C=10, f1=25,f2=12,f0=15,L=10 K.P.C SK= - Z /  

9. BOWLEY SKEWNESS Calculate Bowley’s co efficient of skewness, Ex;1 ANS; Q3 + Q1 – 2Median OR Q2 SK = Q3 – Q1 To compute quartiles, Qj class = (Nth/4) item

10. CONTD

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

12. CONTD Bowley's coefficient of skewness : Q3 +Q1 – 2Median SK = Q3 – Q1 OR

13. SUMMARY As we already discussed and learnt today on skewness as below Karl Pearson's and Bowely's Co-efficient of Skewness Under Continuous Series Problems--------01

14. MCQs 1 .The distribution in sum of Q3+Q1= 44,Q3–Q1= 16 and median = 21, B owley 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

15. 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

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

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

18. 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

19. THANK YOU