## 1.3 Mode

The * mode* is the most commonly occurring value in a given set of values. For example, suppose \(n=10\) randomly selected students were asked the question,

*how many siblings do you have?*, with responses as follows: \[2, 0, 1, 1, 3, 1, 2, 3, 4, 0\]

Arranging these responses into a frequency table allows us to more easily see what the mode is:

Number of Siblings | Frequency |
---|---|

0 | 2 |

1 | 3 |

2 | 2 |

3 | 2 |

4 | 1 |

Since the most commonly occurring response was \(1\) *sibling*, with \(3\) responses, we can say that the * mode* is \(1\), with a frequency of \(3\).

The mode does not always exist. Consider again, for example, the five income values from our previous example: \(1740, 6940, 25000, 1170, 66300\). Since every value is unique, the mode does not exist for this data set.

Another way to determine the mode is to view a histogram. For example, now suppose \(n=100\) randomly selected students were asked the question, *how many siblings do you have?*, with responses represented in the below histogram:

As we can see, the mode is now \(2\) siblings, with a frequency of \(33\).

Sometimes, there is more than one mode, which can lead to either a * bi-modal* or

*distribution. We will consider these concepts shortly.*

**multi-modal**