Measures Of Skewness
 These are numerical values such assist in evaluating the degree of deviation of a frequency distribution from the general distribution.
 Given are the normally used measures of skewness.
1. Coefficient Skewness
= 3 * {(mean  median)/standard deviation}
2. Coefficient of skewness
= (mean  median)/standard deviation
NB: These 2 coefficients above are also termed as Pearsonian measures of skewness.
1. Quartile Coefficient of skewness
= (Q3 + Q1  2Q2)/(Q3 + Q1)
Whereas: Q1 = 1st quartile
Q2 = 2nd quartile
Q3 = 3rd quartile
NB: The Pearsonian coefficients of skewness generally range between ve (negative) 3 and +ve (positive) 3. These are extreme value that is +ve (positive) 3 and ve(negative) 3 which hence indicate that a given frequency is negatively skewed and the amount of skewness is quite high.
Correspondingly if the coefficient of skewness is +ve or positive it can be concluded that the amount of skewness of deviation from the general distribution is quite high and the degree of frequency distribution also is positively skewed.
Illustration
The given information was acquired from an NGO which was providing small loans to some small scale business enterprises in year 1996 the loans are in the form of thousands of Kshs.
Loans

Units (f)

Midpoints(x)

xa=d

d/c= u

fu

Fu^{2}

UCB

cf

46  50

32

48

15

3

96

288

50.5

32

51  55

62

53

10

2

124

248

55.5

94

56  60

97

58

5

1

97

97

60.5

191

61 65

120

63 (A)

0

0

0

0

0

0

66 70

92

68

5

+1

92

92

70.5

403

71 75

83

73

10

+2

166

332

75.5

486

76  80

52

78

15

+3

156

468

80.5

538

81  85

40

83

20

+4

160

640

85.5

57.8

86  90

21

88

25

+5

105

525

90.5

599

91  95

11

93

30

+6

66

396

95.5

610

Total

610




428

3086



Required
By using the Pearsonian measure of skewness, estimate the coefficients of skewness and thus comment briefly on the nature of the distribution of the loans.
Arithmetic mean = Assumed mean +
= 63 + {(428 * 5)/610}
= 66.51
This is very significant to note that the method of acquiring arithmetic mean or any other statistic by misusing assumed mean (A) from X and then dividing by c can be a bit confusing, if this is the case then just employ the straight forward method of:
=5 ×
= 10.68
The Position of the median lies m = (n + 1)/2
= (610 + 1)/2= 305.5
= 60.5 + {(305.5  191 )/120} × 5
= 60.5 + (114.4/120) × 5
Median = 65.27
Hence the Pearsonian coefficient
= 3 * {(66.51  64.27)/10.68}
= 0.348