Skewness Author: Buenaflor

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