Skewness
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The document contains calculations to determine skewness using grouped data. It includes frequency distributions of grouped data with ranges of values for X, frequencies (f), deviations (d), d-squared (d2), and d-cubed (d3). Formulas are provided to calculate the second (m2) and third (m3) moments about the mean. The computations are presented in a table with columns for X, M, f, fM, d, d2, d3, fd2, and fd3.
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Skewness
- 1. SKEWNESS Ermie Grace Ellorando Prepared by:
- 16. X 6 9 14 16 20 24 31 40 SUM X 20 20 20 20 20 20 20 20 – d d2 d3
- 18. X 6 9 14 16 20 24 31 40 SUM X 20 20 20 20 20 20 20 20 – d -14 -11 -6 -4 0 4 11 20 – d2 d3
- 20. X 6 9 14 16 20 24 31 40 SUM X 20 20 20 20 20 20 20 20 – d -14 -11 -6 -4 0 4 11 20 – d2 196 121 36 16 0 16 121 400 906 d3
- 22. X 6 9 14 16 20 24 31 40 SUM X 20 20 20 20 20 20 20 20 – d -14 -11 -6 -4 0 4 11 20 – d2 196 121 36 16 0 16 121 400 906 d3 -2744 -1331 -216 -64 0 64 1331 8000 5040
- 25. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n
- 26. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n fM = 2585
- 27. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n
- 28. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n
- 29. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n d2
- 30. d3
- 31. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n fd2
- 32. fd3
- 33. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n
- 34. COMPUTATIONAL GROUPED DATA FOR SKEWNESS X M f fM X d d2 d3 fd2 fd3 84-90 87 2 174 49.71 37.29 1390.54 51853.39 2781.09 103706.78 77-83 80 5 400 49.71 30.29 917.48 27790.59 4587.42 138952.97 70-76 73 3 219 49.71 23.29 542.42 12633.06 1627.27 37899.17 63-69 66 7 462 49.71 16.29 265.36 4322.78 1857.55 30259.47 56-62 59 3 177 49.71 9.29 86.30 801.77 258.91 2405.30 49-55 52 6 312 49.71 2.29 5.24 12.01 31.46 72.05 42-47 45 8 360 49.71 -4.71 22.18 -104.49 177.47 -835.90 35-41 38 5 190 49.71 -11.71 137.12 -1605.72 685.62 -8028.62 28-34 31 4 124 49.71 -18.71 350.06 -6549.70 1400.26 -26198.80 21-27 24 5 120 49.71 -25.71 661.00 -16994.42 3305.02 -84972.08 14-20 17 1 17 49.71 -32.71 1069.94 -34997.87 1069.94 -34997.87 7-13 3 30 49.71 -39.71 1576.88 -62618.07 4730.65 -187854.20 52 2585 22512.67 -29591.73
- 35. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n
- 36. Formula: m2 = 푓(푀 − 푋)2/n and m3 = 푓(푋 − 푋)3/n