Frequency (statistics)

Number of occurrences in an experiment or study

In statistics, the frequency or absolute frequency of an event is the number of times the observation has occurred/recorded in an experiment or study. These frequencies are often depicted graphically or in tabular form.

A histogram is a representation of tabulated frequencies, shown as adjacent rectangles or squares (in some of situations), erected over discrete intervals (bins), with an area proportional to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i. e., the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data. A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the total area equaling 1. The categories are usually specified as consecutive, non overlapping intervals of a variable. The categories (intervals) must be adjacent, and often are chosen to be of the same size. The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous.

A bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column bar chart.

Under the frequency interpretation of probability, it is assumed that as the length of a series of trials increases without bound, the fraction of experiments in which a given event occurs will approach a fixed value, known as the limiting relative frequency. This interpretation is often contrasted with Bayesian probability. In fact, the term 'frequentist' was first used by M. G. Kendall in 1949, to contrast with Bayesians, whom he called "non frequentists". He observed
3 we may broadly distinguish two main attitudes. One takes probability as 'a degree of rational belief', or some similar idea the second defines probability in terms of frequencies of occurrence of events, or by relative proportions in 'populations' or 'collectives'; (p. 101)

12. It might be thought that the differences between the frequentists and the non frequentists (if I may call them such) are largely due to the differences of the domains which they purport to cover. (p. 104)

I assert that this is not so The essential distinction between the frequentists and the non frequentists is, I think, that the former, in an effort to avoid anything savouring of matters of opinion, seek to define probability in terms of the objective properties of a population, real or hypothetical, whereas the latter do not. [emphasis in original]

Managing and operating on frequency tabulated data is much simpler than operation on raw data. There are simple algorithms to calculate median, mean, standard deviation etc. from these tables. Statistical hypothesis testing is founded on the assessment of differences and similarities between frequency distributions. This assessment involves measures of central tendency or averages, such as the mean and median, and measures of variability or statistical dispersion, such as the standard deviation or variance. A frequency distribution is said to be skewed when its mean and median are significantly different, or more generally when it is asymmetric. The kurtosis of a frequency distribution is a measure of the proportion of extreme values (outliers), which appear at either end of the histogram. If the distribution is more outlier prone than the normal distribution it is said to be leptokurtic; if less outlier prone it is said to be platykurtic. Letter frequency distributions are also used in frequency analysis to crack ciphers, and are used to compare the relative frequencies of letters in different languages and other languages are often used like Greek, Latin, etc.