# Frequency tables

## In a nutshell

Frequency tables are used to display the quantities of different data. They are extremely useful for calculating mean, median and mode as averages of a set of data, as well as the range to determine the spread of the data.

## Frequency

### Definition

Frequency represents the quantity of an outcome and it answers the question, 'How many?' An outcome occurs more frequently than another if it has happened more times than the other.

##### Example 1

*Alice flips a coin $50$ times. The outcome heads has a frequency of $17$. What is the frequency of tails?*

*The only two outcomes of a coin flip are heads and tails. Hence, as the frequencies of heads and tails sum to $50$ the frequency of tails is:*

*$50 - 17 = \underline{33}$.*

*Tails occurs $\underline{33}$ times.*

## Table representation

When there are several different categories of the data, frequency tables can be used to display the respective frequencies of the categories. A frequency table that lists data items and shows the number of times the items occur.

##### Example 2

*Mark creates a frequency table after asking his classmates which sport they prefer to play. His results are as follows:*

#### Sport | #### Frequency |

Badminton | $3$ |

Football | $13$ |

Hockey | $9$ |

Tennis | $5$ |

*Which sport is most popular?*

**

*Read the table and identify that $3$ people prefer badminton, $13$ people prefer football, $9$ people prefer hockey and $5$ people prefer tennis. The most popular sport has the highest frequency.*

*Football** is the most popular sport.*

*How many classmates did Mark get data from?*

*Sum the frequencies of each category to find how many people Mark asked in total. Hence, Mark asked: *

*$3+13+9+5 = \underline{30}$ classmates*