Problems based on Skewness and concepts

1. Presented byGet placed PGDM@IAMEE www.iamee.in MEASURES OF SKEWNESS AND INTERPRETATION On 01/03/2011 Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

2. OVERVIEW What is meant by Skewness. What are the different types of Skewness Distributions. Skewness Distributions in graphical representation. Calculation of Skewness Coefficient in different (two types) methods. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

4. A frequency distribution of the set of values that is not Symmetrical(normal) is called asymmetrical or skewed.PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

6. Skewed distribution Curves PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

7. Measures of Skewness For an asymmetrical distribution, the distance b/w Mean and Mode may be used to measure the degree of skewness because the Mean is equal to Mode in a symmetrical distribution. Thus, Absolute, Sk = Mean – Mode = Q3 + Q1 – 2 Median. For Skewed distribution, if Mean>Mode, the Skewness becomes +ive. Otherwise –ive. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

8. PGDM@IAMEE www.iamee.in Variation tells us about the amount of the variation where as Skewness tells about the direction of variation. In business and economic series, measures of variation have greater practical application than measures of skewness. Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

10. The value of SKp various b/w ±3.

11. For moderately skewed distribution,But moderately skewed distribution, the value of SKp lies between ±1. Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

13. Kelly’s coefficient of Skewness,PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

14. Calculation of SKp Data of rejected items during a production process is as follows: Calculate the mean, standard deviation, and coefficient of skewness and comment on the results. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

15. Solution: PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

16. Assume mean, A=38, then By inspection, mode lies in the class 36-40. PGDM@IAMEE www.iamee.in = Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

17. Answers: X = 36.96 rejects / operator. 𝜎 = 6.736 rejects / operator. Mode = 37.70 Coefficient of Skewness = -0.109 Interpretation : Distribution is Negatively Skewed and hence the concentration of the rejects/operator is more on the left side. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

18. Calculation of Bowley's coefficient 2) The data on the profits(in Rs lakhs) earned by 60 companies is as follows: Obtain the limits of profits of the central 50 percent companies. And also calculate Bowley’s coefficient of skewness. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

19. Solution: PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

20. Q1 = size of (N/4)th observation. And Q3 = size of (3N/4)th observation. Therefore Q1 = 15th observation, Q3 = 45th observation. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

21. Hence, the profit of central 50 percent companies lies b/w Rs.35 lakhs and 18.33 lakhs. Therefore, Coefficient of quartile deviation, Q.D = (Q3 – Q1) / (Q3 + Q1) =____________ Median=size of (N/2)th observation =(60/2)th observation. Thus, median lies in the class interval 20-30, and PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

22. Median, Coefficient of Skewness, SKb = 0.02. The positive value of SKb indicates that the distribution in positively skewed. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

23. Answers: Q1 = 18.33 lakhs Q3 = 35 lakhs. Q.D = 0.313 Median (Me) = 26.5 Coefficient of Skewness = 0.02. Interpretation: The distribution is positively skewed and therefore, concentration of larger value on the right side of the distribution. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

24. THE END MEASURNESS OF SKEWNESS AND INTERPRETATION PGDM@IAMEE www.iamee.in THANK YOU Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

25. go & read to today O otherwise PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

26. PGDM@IAMEE www.iamee.in Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE

27. Try it… The following table gives the distribution of weekly wages of 500 workers in a factory: Obtain the limits of income of the central 50% of the observed workers. Calculate Bowley's coefficient of skewness. ANS:Negatively Skewed.(SKb = -0.102). PGDM@IAMEE www.iamee.in Keeping your work organized will help a lot!! Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE