# Statistical Sequences and Frequencies

### From MM*Stat International

English |

Português |

Français |

Español |

Italiano |

Nederlands |

## Statistical Sequence

In recording data we generate a statistical sequence. The original, unprocessed sequence is called *raw data*. Given an appropriate scale level (i.e. at least an ordinal scale), we can sort the raw data, thus creating an *ordered sequence*.
Data collected at the same point in time or for the same period of time on different elements are called cross-section data.
Data collected at different points in time or for different periods of time on the same element are called time-series data. The sequence of observations is ordered along the time axis.

## Frequency

The number of observations falling into a given class is called the frequency.
Classes are constructed to summarize continuous or quasi-continuous data by means of frequencies.
In discrete data one regularly encounters so-called ties, i.e. two or more observations taking on the same value. Thus, discrete data may not require grouping in order to calculate frequencies.
*Absolute frequency*
Counting the number of observations taking on a specific value yields the absolute frequency:
When data are grouped, the *absolute frequencies of classes* are calculated as follows:
Properties:
*Relative frequency*
The proportion of observations taking on a specific value or falling into a specific class is called the relative frequency, the absolute frequency standardized by the total number of observations.

*Frequency distribution*
By standardizing class frequencies for grouped data by their respective class widths, frequencies for differently sized classes are made comparable. The resulting frequencies can be compiled to form a frequency distribution.
where are the upper and lower class boundaries with .

150 persons have been asked for their marital status: 88 of them are married, 41 single and 21 divorced. The four conceivable responses have been assigned categories as follows:

- single:
- married:
- divorced:
- widowed:

The number of statistical elements is . The absolute frequencies given above are:

Dividing by the sample size yields the relative frequencies:

Thus, 59 per cent of the persons surveyed are married, 27 per cent are single and 15 per cent divorced. No one is widowed.