Six Sigma and Beyond: Statistics and Probability, Volume III

  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

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