Six Sigma and Beyond: Statistics and Probability, Volume III

  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

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