Cumulative Frequency Analysis - Histogram

Histogram

The observed data can be arranged in classes or groups with serial number k. Each group has a lower limit (L_k) and an upper limit (U_k). When the class (k) contains m_k data and the total number of data is N, then the relative class or group frequency is found from:

• Fg(L_k<X≤U_k) = m_k / N

or briefly:

• Fg_k = m/N

or in percentage:

• Fg(%) = 100m/N

The presentation of all class frequencies gives a frequency distribution, or histogram. Histograms, even when made from the same record, are different for different class limits.

The histogram can also be derived from the fitted cumulative probability distribution:

• Pg_k = Pc(U_k) − Pc(L_k)

There may be a difference between Fg_k and Pg_k due to the deviations of the observed data from the fitted distribution (see figure).