### 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 interval | Frequency |
---|---|

155-<160 | 3 |

160-<165 | 2 |

165-<170 | 9 |

170-<175 | 7 |

175-<180 | 10 |

180-<185 | 5 |

185-<190 | 5 |

185-<190 | 5 |

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.