CUMULATIVE DISTRIBUTION FUNCTION (CDF)

1. The number of observed data values below or equal to a stated value of X _k .

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

3. The probability of data values less than or equal to this threshold is the sum or "cumulation" of probabilities:

   

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

Example of Car Pool Observations

Cell (X k )	Frequency	Threshold	Cumulation, F(X k )
X 1 = 2	f 1 = 0.40	T(X 1 )	0.40
X 2 = 3	f 2 = 0.25	T(X 2 )	0.40 + 0.25 = 0.65
X 3 = 4	f 3 = 0.20	T(X 3 )	0.40 + 0.25 + 0.20 = 0.85
X 4 = 5	f 4 = 0.10	T(X 4 )	0.40 + 0.25 + 0.20 + 0.10 = 0.95
X 5 = 6	f 5 = 0.05	T(X 5 )	0.40 + 0.25 + 0.20 + 0.10 + 0.05 = 1.0