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1
If the absolute value of any observation is greater than 1013 , no calculations are done. For sorting of the observations, see Appendix 6. For information on percentiles for grouped data, see Appendix 8.
Notation
The following notation is used throughout this chapter unless otherwise stated: X (^) k Value of the variable for case^ k w (^) k Weight for case^ k NV Number of distinct values the variable assumes N Number of cases W Sum of weights of the cases
Basic Statistics
The values are sorted into ascending order and the following calculated:
Sum of Weights of Cases Having Each Value of X
f (^) j w ki i j NV i
N = = =
∑ 1
where
k
X X
i = RS i^ = j T
if otherwise
where X (^) j is the jth largest distinct value of X.
Relative Frequency (Percentage) for each Value of X
Rf
f j W = j ′
F HG^
I KJ^
× 100
where
=
W (^) ∑f (^) i i
NV
1
(sum over all categories including those declared as missing values)
Adjusted Frequency (Percentage)
Af
f j W = F j HG^
I KJ^
× 100
where
W f ki i i
NV
=
∑ 1
(sum over nonmissing categories)
and
k (^) i = RS Xi T
0 if has been declared missing 1 otherwise
For all X (^) j declared missing, an adjusted frequency is not printed.
Cumulative Frequency (Percentage)
Cf (^) j fi i
j
=
∑ 1
Mean
X
f X
W
j j j
NV
∑ 1
Moments about the mean are calculated as:
M (^) j f (^) i X (^) i X j j i
NV = − = =
∑ d^ i 1
Variance
S M
W
2 2 1
b − g
Standard Deviation
S = S^2
Standard Error of the Mean
SEM S
W
Skewness (computed if W ≥ 3 and S^2 > 0 ) (Bliss, 1967, p. 144)
g WM W W S
se g W W (^1) W W W 3 1 2 3 1
a fa f b g^ −^ +^ +
a f a fa fa f
Kurtosis (computed if W ≥ 4 and S^2 > 0 )
g W W^ M^ W^ M W W W S
se g
W se g (^2) W W 4 22 4 2
2 12 1 3 1 1 2 3
a f a f a fa fa f
b g
e j b g a fa f
References
Blalock, H. M. 1972. Social statistics. New York: McGraw-Hill.
Bliss, C. I. 1967. Statistics in biology, Volume 1. New York: McGraw-Hill.
