It is usual practice to choose a fairly small number of categories so that the relative frequencies within categories are not too small. If no definite upper or lower limits are known, all values above (or below) a certain value are grouped into a single category known as the upper (or lower) tail.
Frequency distributions may be summarized by computing statistics such as the mean (or other measures of location) and the standard deviation (or other measures of variation), and sometimes measures of asymmetry or skewness and of compactness (i.e. the proportion of the sample in the center and in the tails).
The term frequency distribution is applied to observed data in a sample. In contrast, probability distributions are theoretical formulas for the probability of observing each event. Fitting probability distributions to observed frequency distributions is a fundamental statistical method of data analysis.
Systematic representation of data, arranged so that the observed frequency of occurrence of data falling within certain ranges, classes, or categories, is shown.
When data is presented in a frequency distribution, the objective is to show the number of times a particular value or range of values occurs. Common forms of presentation of frequency distribution include the frequency polygon, the bar graph, and the frequency curve, which associate a number (the frequency) with each range, class, or category of data. A grouped frequency distribution is a kind of frequency distribution in which groups of ranges, classes, or categories are presented. Grouped frequency distributions are generally used when the number of different ranges, classes, or categories is large. A cumulative frequency distribution is a representation in which each successive division includes all of the items in previous divisions (so that, for example, the last division includes all of the data in the entire distribution). A probability distribution is similar to a frequency distribution, except that in a probability distribution the observed probability of occurrence is associated with each range, class, or category. The sum of the probabilities in a probability distribution is one, while the sum of the frequencies in a frequency distribution is the total number of data items.
Berman, Simeon M. Mathematical Statistics: An Introduction Based on the Normal Distribution. Scranton, PA: Intext Educational Publishers, 1971.
Peavy, J. Virgil. Descriptive Statistics: Measures of Central Tendency and Dispersion. Atlanta, GA: U.S. Dept. of Health and Human Services/Public Health Service, Centers for Disease Control, 1981.