frequency

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A frequency is the number of events, i.e. the result of a counting process . The foreign word “frequency”, borrowed from the Latin “frequentia” = “frequency”, is also used as a synonym for “frequency”. This original term, frequency understood as frequency, can be confused with the physical term frequency derived from it , especially in the case of translations from foreign-language texts. The stochastics puts the term " absolute frequency " are available, can take over the user.

Further terms are derived from the term “absolute frequency”, namely in relation to the number of data ( relative frequency ), a period of time (frequency in the physical sense) or in relation to another comparative value (for example number of particles per unit volume). (See below)

If objects are selected randomly from a population , their characteristic values ​​are also referred to as random events in the statistics. This is why the number of randomly selected objects with the same characteristics is also referred to as frequency in the statistics.

Examples: If you randomly draw the ball with the number 1 three times from an urn and put it back, the absolute frequency of this event (having drawn a 1) is three. Similarly, if one selects residents of a city in a random sample and three of them are women, the absolute frequency of this event (having selected a woman) is also three in this case.

Frequency concept

Definition

Stochastics introduces the term "absolute frequency":

The term “absolute frequency” can be used in all applications in which the result of a counting process is to be described. It is not tied to the typical stochastic requirement of performing and documenting random experiments. If one wishes to use the absolute frequency for a prognosis before an examination, one also speaks of the expected frequency or expected absolute frequency , which can be compared with the observed frequency or observed absolute frequency after the examination . Reference is made below to some applications in special contexts.

The graphical representation of the frequency as a function of a quantifiable characteristic is the frequency distribution .

Derived terms

If you want to compare absolute frequencies with one another, you usually relate them to one or more reference values. A new concept is then created, derived from the concept of absolute frequency.

  • relative frequency : absolute frequency divided by the sample size.
  • Frequency in physics: number (absolute frequency) of periods divided by the observation period.

use

The following questions and answers are intended to show the diversity in use, combined with derived terms. (Whether the answers are confirmed by real investigations is not relevant here.)

  • “How often does a person move in Germany?” - On average every 7 years (in relation to a period of time) or eight times in their life (number in a given period of time; the period is often omitted).
  • “How often does an accident happen ?” - In Germany 8.5 million times a year (number in a given period of time and with a fixed basic amount (population in Germany)) or in 2004 10% of the population (ratio to a comparative figure, with defined period of time).
  • "How often does a malformation occur in newborns ?" - Two percent (relative frequency, since it is related to the number of all newborns).
  • “What lightning frequency is to be expected?” - In Central Europe about 2 lightning strikes per square kilometer and year , however, regionally and seasonally very different (relationship to a time span and to an area).

Word origin

The adjective often actually meant “heaps” in the 16th century and “often” since the 18th century. So it means something like “occurring in large numbers, occurring repeatedly” or “numerous in large numbers, in large quantities”. Heap also means “in heaps, in masses” or “in droves, in masses”.

The same applies to the word accumulation , which can mean something like “storage in large quantities”, but also “accumulation, frequent occurrence (of phenomena, events)”. The word cluster can also refer to as the "act of heaping" of earth or the accumulation of business, as well as the word ridging .

The word frequency is also used in the sense of frequency . In the context of linguistics , the Brockhaus Encyclopedia refers to the lemma frequency for the word frequency . Here we find that the word frequency in Latin stands for frequency . The frequency of a word means the frequency with which a word occurs within a certain text or a text corpus . Because of the frequency can sverteilungen Frequency dictionaries are created that provide information on the use of frequency of giving a word.

The word frequency is technical language in the 17th century and borrowed from the Latin “frequentia” meaning “frequency”. This is an abstraction from the Latin “frequentis” = “frequently” and related to the Latin fracīare for “stuffing”.

Special frequency terms

Examples of special applications of the frequency concept:

  • Under natural frequency is defined as the relative abundance of chemical elements or their isotopic ratio .
  • The frequency of errors is a special area of ​​consideration for quality management.
  • The error calculation deals with the frequency distribution of measured values ​​if they are scattered.
  • The cumulative frequency : If the values of an ordinal or metrically scaled characteristic are arranged according to size (in ascending order), the cumulative frequency is the sum of all frequencies up to and including the respective characteristic value .

Web links

Wiktionary: Frequency  - explanations of meanings, word origins, synonyms, translations

Individual evidence

  1. ↑ Peter Zöfel, Statistics in Practice. UTB Taschenbuch 1293, Gustav Fischer Verlag, Stuttgart and Jena, 1992, ISBN 3-8252-1293-9 , p. 23.
  2. ↑ Zöfel points this out on p. 23.
  3. ^ Zöfel, p. 23
  4. ↑ Ingrid Andrea Uhlemann: Introduction to Statistics for Communication Scientists: Descriptive and Inductive Methods for the Bachelor's Degree . Springer-Verlag, 2014, ISBN 978-3-658-05769-5 , pp. 174 ( limited preview in Google Book Search [accessed July 27, 2016]).
  5. ^ Andreas Büchter, Hans-Wolfgang Henn: Elementare Stochastik. Springer Verlag, Berlin / Heidelberg / New York 2005, ISBN 3-540-22250-2 , p. 25.
  6. ↑ Wolfgang Kohn, Riza Öztürk: Statistics for Economists: Data Analysis with R and SPSS. Springer, 2010, p. 24 ff.
  7. ^ Rainer Diaz-Bone, Christoph Weischer (ed.): Lexicon of methods for the social sciences. Springer VS, 2015, p. 171.
  8. ↑ Büchter / Henn, p. 25.
  9. ↑ Robert Wichard Pohl: Pohl's introduction to physics . 20th edition. tape 1 . Springer-Verlag, 2008, ISBN 3-540-76337-6 , pp. 8 .
  10. ↑ Günther Strohrmann: Automation of procedural processes. Oldenbourg, 2002, p. 434
  11. ^ Elmar Seebold (editor): Kluge: Etymological dictionary of the German language. Walter de Gruyter, Berlin / New York: 2002, p. 396, ISBN 3-11-017473-1 .
  12. ↑ a b Werner Scholze-Stubenrecht: Duden. The large dictionary of the German language in 10 volumes. Volume 4, Bibliographisches Institut & FF Brockhaus AG, Mannheim 1999, p. 1690. ISBN 978-3-411-04773-4 .
  13. ^ Joachim Heinrich Campe: Dictionary of the German language . Volume 2. School bookshop, Braunschweig 1808, p. 563
  14. ↑ Renate Wahrig-Burfeind: Illustrated dictionary of the German language. ADAC Verlag, Munich 2004, p. 362. ISBN 3-577-10051-6 .
  15. ↑ Moriz Heyne: German Dictionary. (Volume 2), S. Hirzel, Leipzig 1906, p. 70.
  16. ↑ a b Annette Zwahr : Brockhaus Enzyklopädie, 21st edition . FF Brockhaus, Mannheim 2006, volume 12.
  17. ↑ Elmar Seebold (editor): Kluge: Etymological dictionary of the German language. Walter de Gruyter, Berlin / New York 2002, p. 396. ISBN 3-11-017473-1 .