Where does frequency collide?

How many times a periodic phenomenon repeats in a unit of time, measured in hertz, where one hertz is one cycle per second. In the physics of waves and oscillation, set out in texts such as French's Vibrations and Waves and fixed by the SI definition of the hertz, frequency is the reciprocal of the period: a wave that completes a cycle every half second has a frequency of two hertz. The referent is a physical oscillation, a swinging pendulum, a vibrating string, an electromagnetic wave, and the quantity is a rate, cycles divided by time. This is not a tally of anything discrete; it is how fast a continuous repetition turns over, and it carries a unit of inverse seconds that the other meanings do not.[1][2]

Unit

Hertz (cycles per second)

Recovery means

Not applicable

Measured by

Counting cycles of an oscillation over a timed interval, or reading the period and inverting it

How many times a particular value or category shows up in a set of observations. In descriptive statistics, laid out in texts such as Yule and Kendall's An Introduction to the Theory of Statistics, the frequency of a value is its raw count, and arranging every value with its count gives a frequency distribution, the table or histogram that summarises the data. The referent is a data set, and the quantity is a whole number of occurrences, not a rate over time. A relative frequency divides that count by the total, giving a proportion between zero and one. Here frequency has no unit of time and no oscillation; it is simply a tally of how common a value is.[3]

Unit

A count of occurrences (dimensionless)

Recovery means

Not applicable

Measured by

Tallying how often each value appears in a sample, then tabulating the counts as a distribution

Probability defined as the limit a relative frequency approaches as a trial is repeated without end. In the frequentist interpretation, argued by Venn's The Logic of Chance and formalised by von Mises's Probability, Statistics and Truth, the probability of an event is not a degree of belief but the value its relative frequency settles toward in an unending sequence of like trials, what von Mises called a collective. The referent is a hypothetical endless run of experiments, and the quantity is a limiting proportion. This borrows the idea of counting but turns it into a theory of what probability is: the count of an outcome divided by the number of trials, taken to the limit, rather than a tally of a finite sample.[4][5]

Unit

A limiting proportion between 0 and 1

Recovery means

Not applicable

Measured by

Estimated by the relative frequency of an outcome across a long series of repeated trials

How many times a word form appears in a body of text, and how that count behaves across the whole vocabulary. In corpus linguistics, word frequency is the count of a token in a corpus, and Zipf's Human Behavior and the Principle of Least Effort observed that a word's frequency is roughly inversely proportional to its rank, so a handful of words are very common and a long tail are rare, a regularity reviewed by Piantadosi. The referent is a corpus of language, and the quantity is a count of occurrences, often reported per million words so corpora of different sizes can be compared. It shares the plain counting of descriptive statistics, but its object is words in text, and its signature is the skewed rank-frequency curve rather than any single number.[6][7]

Unit

Occurrences (often per million words)

Recovery means

Not applicable

Measured by

Counting token occurrences in a corpus, often normalised per million words and ranked