# measures of location

**Mean **(or arithmetic mean, or average): It is calculated by adding all the numbers of the list and dividing by N (the sample size or the number of elements in the list).

** Median**: If you order the data from lower to greater, the median is the middle number, if the list has an odd number of elements, or the mean of the two middle numbers, if the list has an even number of elements. The number in the middle is:

**Mode**: It is the number (or numbers) that occur more often.

*Example 1*: 20 families are asked about how many children they have:

x_{i} |
f_{i } |

0 | 1 |

1 | 2 |

2 | 6 |

3 | 6 |

4 | 3 |

5 | 2 |

We order the data to calculate the median:

0,1,1,2,2,2,2,2,2,**3,3**,3,3,3,3,4,4,4,5,5

Mo = 2 and 3

*Example 2*: We ask 40 people about the number of times that they went to the cinema last year, and the answers are:

3, 15, 24, 28, 33, 35, 38, 42, 43, 38, 36, 34, 29, 25, 17, 7, 34, 36, 39, 44, 31, 26, 20, 11, 13, 22, 27, 47, 39, 37, 34, 32, 35, 28, 38, 41, 58, 15, 32, 13

I_{i } |
mark class | f_{i} |

[0,10) | 5 | 2 |

[10,20) | 15 | 6 |

[20,30) | 25 | 9 |

[30,40) | 35 | 17 |

[40,50) | 45 | 5 |

[50,60) | 55 | 1 |

Σ | 40 |

We use the mark class to calculate:

Mo = 35 or [30,40)

*Example 3*: Try to find out the mean in these graphs:

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