CUMULATIVE FREQUENCY FUNCTION

1. The number of observed data values that are below or equal to a stated value of X _k . (Think of a sieve.)

2. The stated value of X _k is often called the threshold: T(X _k ).

3. The number of observed data values less than or equal to this threshold are summed or "cumulated."

   

   where n _T is the cell number k( ‰ n _c ) set by the threshold T(X _nT ).

Note  

Cumulative distribution has the advantage that data do not need to be rank ordered before proceeding.

Example of Car Pool Observations

Cell (X k )	Frequency	Threshold	Cumulation, F k
X 1 = 2	f 1 = 8	T(X 1 )	8
X 2 = 3	f 2 = 5	T(X 2 )	8 + 5 = 13
X 3 = 4	f 3 = 4	T(X 3 )	8 + 5 + 4 = 17
X 4 = 5	f 4 = 2	T(X 4 )	8 + 5 + 4 + 2 = 19
X 5 = 6	f 5 = 1	T(X 5 )	8 + 5 + 4 + 2+1 = 20