### Frequencies

Frequency, or observed frequency, is the number of times that a particular value occurs in a data set.

For grouped data, it is the number of observations that lie in that group or class interval.

An expected frequency is the number of times that a particular event is expected to occur when a chance experiment is repeated a number of times. For example, If the experiment is repeated n times, and on each of those times the probability that the event occurs is p, then the expected frequency of the event is np.

For example, suppose that a fair coin is tossed 5 times and the number of heads showing recorded. Then the expected frequency of ‘heads’ is 5/2.

This example shows that the expected frequency is not necessarily an observed frequency, which in this case is one of the numbers 0,1,2,3,4 or 5.

A frequency table lists the frequency (number of occurrences) of observations in different ranges, called class intervals.

The frequency distribution of the heights (in cm) of a sample of 42 people is displayed in the frequency table below

Height (cm)

Class intervalFrequency
155-<1603
160-<1652
165-<1709
170-<1757
175-<18010
180-<1855
185-<1905
185-<1905

A frequency distribution is the division of a set of observations into a number of classes, together with a listing of the number of observations (the frequency) in that class.

Frequency distributions can be displayed in tabular or graphical form.

Frequency, or observed frequency, is the number of times that a particular value occurs in a data set.

For grouped data, it is the number of observations that lie in that group or class interval.

Relative frequency is given by the ratio , where f is the frequency of occurrence of a particular data value or group of data values in a data set and n is the number of data values in the data set.