Cumulative frequency analysis

The cumulative (also cumulative ) frequency or cumulative frequency is a measure of descriptive statistics. It indicates, in which the number of carriers of the trait in an empirical study, the characteristic value is smaller than a certain limit. The cumulative frequency is calculated as the sum of the frequencies of the characteristic values ​​of the smallest expression to the respectively considered barrier.

Explanation

The standards they require at least ordinally scaled features that forms can then be sorted by size. Is considered the rate of occurrence of the characteristics to a certain upper limit. Depending on whether absolute or relative frequencies are summed, one speaks of absolute cumulative frequency or relative cumulative frequency.

A question that could be solved using the cumulative frequency, the question of the number of notes is not worse than 4 in an exam. Here we would all ones, twos, threes and fours (or their frequencies ) and include add up to calculate the cumulative frequency of the characteristic school grade to the upper limit four.

The representation of the cumulative frequency in the theory of probability is a distribution function.

Defined in formula notation

The readings are divided into selected for a suitable criterion classes and organized the classes and numbered up. The absolute frequency of associated with these classes measured values ​​are denoted by. The corresponding relative frequencies are denoted by. The barrier, to which the frequencies are to be summed, is referred to.

Thus, the absolute cumulative frequency is defined by

And the relative cumulative frequency by