[xmean,s2,s3,s4,n,ifail] = g01adf(x,ifreq<,ifail>)
The input data consist of a univariate frequency distribution,
denoted by f , for i=1,2,...,k-1, and the boundary values of the
i
classes x , for i=1,2,...,k. Thus the frequency associated with
i
the interval (x ,x ) is f , and the routine assumes that all
i i+1 i
the values in this interval are concentrated at the point
y =(x +x )/2, i=1,2,...,k-1
i i+1 i
.
The following quantities are calculated:
(a) total frequency,
k-1
--
n= > f .
-- i
i=1
(b) mean,
k-1
--
> f y
-- i i
_ i=1
y= --------.
n
(c) standard deviation,
______________
/ k-1
/ -- _ 2
/ > f (y -y)
/ -- i i
/ i=1
s = / -------------, n>=2.
2 \/ (n-1)
(d) coefficient of skewness,
k-1
-- _ 3
> f (y -y)
-- i i
i=1
s = -------------, n>=2.
3 3
(n-1)*s
2
(e) coefficient of kurtosis,
k-1
-- _ 4
> f (y -y)
-- i i
i=1
s = --------------3, n>=2.
4 4
(n-1)*s
2
The routine has been developed primarily for groupings of a
continuous variable. If, however, the routine is to be used on
the frequency distribution of a discrete variable, taking the
values y ,...,y , then the boundary values for the classes may
1 k-1
be defined as follows:
(i) for k>2, x = (3y -y )/2
1 1 2
x = (y +y )/2, j=2,...,k-1
j j-1 j
x = (3y -y )/2
k k-1 k-2
(ii) for k=2, x = y -a and x =y +a for any a>0.
1 1 2 1
g01adf Required Input Arguments: x (:) real ifreq (:) integer Optional Input Arguments: <Default> ifail integer -1 Output Arguments: xmean real s2 real s3 real s4 real n integer ifail integer