Frequency distribution

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In statistics, a frequency distribution is a table that displays the frequency of various outcomes in a sample.[1] Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample.

Univariate frequency tables[edit]

An example of a univariate (i.e. single variable) frequency table. The frequency of each response to a survey question is depicted.

Rank Degree of agreement Number
1 Strongly agree 20
2 Agree somewhat 30
3 Not sure 20
4 Disagree somewhat 15
5 Strongly disagree 15


Height range Number of students Cumulative number
less than 5.0 feet 25 25
5.0–5.5 feet 35 60
5.5–6.0 feet 20 80
6.0–6.5 feet 20 100


Construction of frequency distributions[edit]

  1. Decide about the number of classes. Too many classes or too few classes might not reveal the basic shape of the data set, also it will be difficult to interpret such frequency distribution. The maximum number of classes may be determined by formula: or where n is the total number of observations in the data.
  2. Calculate the range of the data (Range = Max – Min) by finding minimum and maximum data value. Range will be used to determine the class interval or class width.
  3. Decide about width of the class denote by h and obtained by .

Generally the class interval or class width is the same for all classes. The classes all taken together must cover at least the distance from the lowest value (minimum) in the data set up to the highest (maximum) value. Also note that equal class intervals are preferred in frequency distribution, while unequal class interval may be necessary in certain situations to avoid a large number of empty, or almost empty classes.[2]

  1. Decide the individual class limits and select a suitable starting point of the first class which is arbitrary, it may be less than or equal to the minimum value. Usually it is started before the minimum value in such a way that the midpoint (the average of lower and upper class limits of the first class) is properly placed.
  2. Take an observation and mark a vertical bar (|) for a class it belongs. A running tally is kept till the last observation.
  3. Find the frequencies, relative frequency, cumulative frequency etc. as required.

Joint frequency distributions[edit]


Two-way contingency table with marginal frequencies
Dance Sports TV Total
Men 2 10 8 20
Women 16 6 8 30
Total 18 16 16 50





A frequency distribution is said to be skewed when its mean and median are different, or the same, depending on the textbook. The kurtosis of a frequency distribution is the concentration of scores at the mean, or how peaked the distribution appears if depicted graphically—for example, in a histogram. If the distribution is more peaked than the normal distribution it is said to be leptokurtic; if less peaked it is said to be platykurtic.

Letter frequency distributions are also used in frequency analysis to crack codes and are referred to the relative frequency of letters in different languages.

See also[edit]


  1. ^ Australian Bureau of Statistics,
  2. ^ Manikandan, S (1 January 2011). "Frequency distribution". Journal of Pharmacology & Pharmacotherapeutics. 2 (1): 54–55. doi:10.4103/0976-500X.77120. ISSN 0976-500X. PMC 3117575Freely accessible. 
  3. ^ Stat Trek, Statistics and Probability Glossary, s.v. Joint frequency

External links[edit]