Figure 11-3.
The relative frequency function and cumulative relative frequency function
The results illustrated in the table 11.3 can be generalized. If X 1 , X 2 ,... , X kare
kdifferent numerical values in a sample of size Nwhere X 1 occurs f ̃ 1 times and X 2
occurs f ̃ 2 times,.. ., and Xkoccurs f ̃ktimes, then f ̃ 1 ,f ̃ 2 ,... , f ̃kare called the frequencies
associated with the data set and satisfy
f ̃ 1 +f ̃ 2 +···+f ̃k=N=sample size
The relative frequencies associated with the data are defined by
f 1 =
f ̃ 1
N
, f 2 =
f ̃ 2
N
,... , f k=
f ̃k
N
which satisfy the summation property
∑k
i=1
fi=f 1 +f 2 +···+fk= 1
Define a frequency function associated with the sample using
f(x) =
{f
j, when x=Xj
0 , otherwise
for j= 1,... , k
The frequency function determines how the numbers in the sample are distributed.
