Skewness

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Problems based on Skewness and concepts

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Skewness

  1. 1. Presented byGet placed<br />PGDM@IAMEE www.iamee.in<br />MEASURES OF SKEWNESS AND INTERPRETATION<br />On<br />01/03/2011<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  2. 2. OVERVIEW<br />What is meant by Skewness.<br />What are the different types of Skewness Distributions.<br />Skewness Distributions in graphical representation.<br />Calculation of Skewness Coefficient in different (two types) methods.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  3. 3. Measures of Skewness<br /><ul><li>The statistical technique to indicate the direction and extent of skewness in the distribution of numerical values in the data set.
  4. 4. A frequency distribution of the set of values that is not Symmetrical(normal) is called asymmetrical or skewed.</li></ul>PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  5. 5. Skewed distributions<br />There are three types:<br /><ul><li>Symmetrical distribution</li></ul> A.M = Median = Mode<br /><ul><li>Positively skewed distribution</li></ul> A.M > Median > Mode<br /><ul><li>Negatively skewed distribution.</li></ul> A.M < Median < Mode<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  6. 6. Skewed distribution Curves<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  7. 7. Measures of Skewness <br />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, <br />Absolute, Sk = Mean – Mode<br /> = Q3 + Q1 – 2 Median.<br />For Skewed distribution, if Mean>Mode, the Skewness becomes +ive. Otherwise –ive.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  8. 8. PGDM@IAMEE www.iamee.in<br />Variation tells us about the amount of the variation where as Skewness tells about the direction of variation.<br />In business and economic series, measures of variation have greater practical application than measures of skewness.<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  9. 9. Relative measures of Skewness<br />PGDM@IAMEE www.iamee.in<br /><ul><li>Karl Pearson’s Co-efficient of Skewness,
  10. 10. The value of SKp various b/w ±3.
  11. 11. For moderately skewed distribution,</li></ul>But moderately skewed distribution, the value of SKp lies between ±1.<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  12. 12. Relative measures of Skewness<br /><ul><li>Bowley’s Coefficient of Skewness,
  13. 13. Kelly’s coefficient of Skewness,</li></ul>PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  14. 14. Calculation of SKp<br />Data of rejected items during a production process is as follows:<br />Calculate the mean, standard deviation, and coefficient of skewness and comment on the results.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  15. 15. Solution:<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  16. 16. Assume mean, A=38, then<br />By inspection, mode lies in the class 36-40. <br />PGDM@IAMEE www.iamee.in<br /> =<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  17. 17. Answers:<br />X = 36.96 rejects / operator.<br />𝜎 = 6.736 rejects / operator.<br />Mode = 37.70<br />Coefficient of Skewness = -0.109<br />Interpretation :<br />Distribution is Negatively Skewed and hence the concentration of the rejects/operator is more on the left side.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  18. 18. Calculation of Bowley's coefficient<br />2) The data on the profits(in Rs lakhs) earned by 60 companies is as follows:<br />Obtain the limits of profits of the central 50 percent companies. And also calculate Bowley’s coefficient of skewness.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  19. 19. Solution:<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  20. 20. Q1 = size of (N/4)th observation. And Q3 = size of (3N/4)th observation. Therefore Q1 = 15th observation, Q3 = 45th observation.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  21. 21. Hence, the profit of central 50 percent companies lies b/w Rs.35 lakhs and 18.33 lakhs.<br />Therefore, Coefficient of quartile deviation, <br />Q.D = (Q3 – Q1) / (Q3 + Q1) =____________<br />Median=size of (N/2)th observation =(60/2)th observation. Thus, median lies in the class interval 20-30, and<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  22. 22. Median,<br />Coefficient of Skewness, SKb = 0.02.<br />The positive value of SKb indicates that the distribution in positively skewed.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  23. 23. Answers:<br />Q1 = 18.33 lakhs<br />Q3 = 35 lakhs.<br />Q.D = 0.313<br />Median (Me) = 26.5<br />Coefficient of Skewness = 0.02.<br />Interpretation:<br />The distribution is positively skewed and therefore, concentration of larger value on the right side of the distribution.<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  24. 24. THE END<br />MEASURNESS OF SKEWNESS AND INTERPRETATION<br />PGDM@IAMEE www.iamee.in<br />THANK YOU<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  25. 25. go & read<br /> to today <br />O otherwise<br />PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  26. 26. PGDM@IAMEE www.iamee.in<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />
  27. 27. Try it…<br />The following table gives the distribution of weekly wages of 500 workers in a factory:<br />Obtain the limits of income of the central 50% of the observed workers.<br />Calculate Bowley's coefficient of skewness.<br />ANS:Negatively Skewed.(SKb = -0.102).<br />PGDM@IAMEE www.iamee.in<br />Keeping your work organized will help a lot!!<br />Institute of Advanced Management Education and Entrepreneurship, Hyderabad © 2010. IAMEE<br />

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