# Finding the Median of a Set of Numbers

### Learning Outcomes

- Find the median of a set of numbers

When Ann, Bianca, Dora, Eve, and Francine sing together on stage, they line up in order of their heights. Their heights, in inches, are shown in the table below.

Ann | Bianca | Dora | Eve | Francine |
---|---|---|---|---|

[latex]59[/latex] | [latex]60[/latex] | [latex]65[/latex] | [latex]68[/latex] | [latex]70[/latex] |

*median*of the girls’ heights. Half of the heights are less than or equal to Dora’s height, and half are greater than or equal. The median is the middle value.

### Median

The median of a set of data values is the middle value.- Half the data values are less than or equal to the median.
- Half the data values are greater than or equal to the median.

[latex]59,60,62,65,68,70[/latex]

There is no single middle value. The heights of the six girls can be divided into two equal parts. Statisticians have agreed that in cases like this the median is the mean of the two values closest to the middle. So the median is the mean of [latex]62\text{ and }65,{\Large\frac{62+65}{2}}[/latex]. The median height is [latex]63.5[/latex] inches. Notice that when the number of girls was [latex]5[/latex], the median was the third height, but when the number of girls was [latex]6[/latex], the median was the mean of the third and fourth heights. In general, when the number of values is odd, the median will be the one value in the middle, but when the number is even, the median is the mean of the two middle values.### Find the median of a set of numbers.

- List the numbers from smallest to largest.
- Count how many numbers are in the set. Call this [latex]n[/latex].
- Is [latex]n[/latex] odd or even?
- If [latex]n[/latex] is an odd number, the median is the middle value.
- If [latex]n[/latex] is an even number, the median is the mean of the two middle values.

### example

Find the median of [latex]12,13,19,9,11,15,\text{and }18[/latex]. SolutionList the numbers in order from smallest to largest. | [latex]9, 11, 12, 13, 15, 18, 19[/latex] |

Count how many numbers are in the set. Call this [latex]n[/latex] . | [latex]n=7[/latex] |

Is [latex]n[/latex] odd or even? | odd |

The median is the middle value. | |

The middle is the number in the [latex]4[/latex]th position. | So the median of the data is [latex]13[/latex]. |

### try it

[ohm_question]146418[/ohm_question]### example

Kristen received the following scores on her weekly math quizzes: [latex]83,79,85,86,92,100,76,90,88,\text{and }64[/latex]. Find her median score.Answer: Solution

Find the median of [latex]83, 79, 85, 86, 92, 100, 76, 90, 88,\text{ and }64[/latex]. | |

List the numbers in order from smallest to largest. | [latex]64, 76, 79, 83, 85, 86, 88, 90, 92, 100[/latex] |

Count the number of data values in the set. Call this [latex]\mathrm{n.}[/latex] | [latex]n=10[/latex] |

Is [latex]n[/latex] odd or even? | even |

The median is the mean of the two middle values, the 5th and 6th numbers. | |

Find the mean of [latex]85[/latex] and [latex]86[/latex]. | [latex]\text{mean}={\Large\frac{85+86}{2}}[/latex] |

[latex]\text{mean}=85.5[/latex] | |

Kristen's median score is [latex]85.5[/latex]. |

### try it

[ohm_question]146419[/ohm_question]## Licenses & Attributions

### CC licensed content, Original

- Question ID 146419, 146418.
**Authored by:**Lumen Learning.**License:**CC BY: Attribution. - Revision and Adaptation.
**Provided by:**Lumen Learning**License:**CC BY: Attribution.

### CC licensed content, Shared previously

- Ex: Find the Median of a Data Set.
**Authored by:**James Sousa (Mathispower4u.com).**License:**CC BY: Attribution.

### CC licensed content, Specific attribution

- Prealgebra.
**Provided by:**OpenStax**License:**CC BY: Attribution.**License terms:**Download for free at http://cnx.org/contents/[email protected].