Frequency
Frequency, in statistics, is the number of times a particular value, category, or class of values occurs in a dataset — the raw count of observations that fall into a given bin. If 14 of 40 surveyed customers choose "blue" as a favourite colour, the frequency of blue is 14. It is the most elementary summary of data there is: before any average, spread, or model, someone has counted how often each outcome happened, and nearly every later statistical idea is built by rearranging, scaling, or accumulating those counts. This is the statistical sense of the word, a tally of occurrences in data, and has nothing to do with the frequency of a wave or signal measured in cycles per second.
The defining property of frequency is that it is an absolute count, so it depends on the size of the dataset as much as on the underlying pattern: 14 blue answers out of 40 and 140 blue answers out of 400 describe the same preference but carry frequencies ten times apart. Because of this, a bare frequency is meaningful only alongside the total number of observations n, and the frequencies of all categories in a dataset must add up to n exactly — a built-in check that catches miscounted or double-counted data. Dividing each frequency by n produces the relative frequency, adding frequencies progressively produces the cumulative frequency, and laying them all out per category produces a frequency distribution; each of those has its own entry, and frequency itself is the raw material they all share.
Frequencies are obtained differently depending on the type of variable. For categorical data (eye colour, product type, survey response) each distinct category is simply counted. For discrete numeric data with few distinct values (number of children, goals per match) each value can be counted directly. For continuous or finely-grained data (heights, incomes, response times) individual values almost never repeat, so the range is first cut into class intervals and the frequency of a class is the number of observations falling inside it, which is the step that turns a list of measurements into a histogram. The historical root is the tally mark: the five-bar gate of four strokes crossed by a fifth is a centuries-old way to count by hand, and John Graunt's analysis of London's Bills of Mortality in 1662, tabulating deaths by cause, is often cited as an early landmark in treating counts as evidence about a population.
Frequency counts are the inputs to a surprising amount of applied work. In data science, a value_counts call on a column is usually the first step of exploratory analysis, exposing rare categories, data-entry variants ("NY" versus "New York"), and class imbalance before any model is trained. In machine learning, word frequency drives bag-of-words and TF-IDF text representations, and class frequencies decide whether accuracy is a trustworthy metric or whether a classifier that always predicts the majority class looks deceptively good. In science, Pearson's 1900 chi-square test compares observed frequencies with the frequencies a hypothesis predicts, so a hypothesis about a population is tested directly against counts. In industry, defect counts per batch and incident counts per week are frequencies that control charts monitor.
The most common pitfall is comparing raw frequencies across groups of different size. A city reporting 300 burglaries and a town reporting 30 has not necessarily the more dangerous streets; per-capita rates, which are relative frequencies, are the fair comparison. A second pitfall is confusing frequency with probability: an observed frequency is a fact about one dataset, while a probability is a property of the process generating it, and the two converge only as the number of observations grows, as the law of large numbers describes. A third is treating a zero frequency as proof that something is impossible when it may only reflect a small sample, and a fourth is binning continuous data so coarsely, or so finely, that the frequencies hide or invent structure.
Frequency is deliberately kept apart from the measures that summarise a distribution's centre and spread. The mean, median, and mode are computed from the data a frequency table describes, and the mode in particular is defined directly as the value with the highest frequency, but none of them is itself a frequency. The same is true of variance and standard deviation, which can be computed from a frequency table without listing every observation, by weighting each value by how often it occurred. Keeping the count, its rescaled forms, and the statistics derived from them conceptually separate is what keeps later formulas readable.
Read frequency as the answer to the first question anyone asks of data — how many? — a plain count of occurrences that is only meaningful against the total, which is why relative, cumulative, and tabulated forms exist, and why almost every richer statistic is a count, rescaled or accumulated, in disguise.