Data can be grouped into **class intervals**. A survey of companies found the number of employees for each company was:

The **Modal Class** is the class with the highest frequency: in this case, the modal class is 11 - 15.

The median is the class that contains the *middle member*. Create a running count (**cumulative frequency**) and find the middle number. In this example there are 25 companies so the middle number is the 13th:

The 13th company is found in the class 11 - 15; this is the class interval of the median.

The **Estimated Mean** can be found by multiplying the *midpoint* of the class interval by the frequency. The mean is estimated because we are using the midpoint value rather than actual values:

The estimated mean is 330 ÷ 25 = 13.2 employees.

The **Range** is the difference between the lowest *possible* value and the highest *possible* values: 25 - 1 = 24

A table may show class intervals with a simple range (e.g. 1 - 6) when the data is discrete; or as an inequality (e.g. 1 < *x* ≤ 6) when the data is continuous.

The information, below, shows how long employees took to travel to work. Give an estimated mean of the travel time to work.

Travel Time (mins) | Employees |
---|---|

0 < m ≤ 20 | 22 |

20 < m ≤ 40 | 15 |

40 < m ≤ 60 | 8 |

60 < m ≤ 80 | 2 |

From the table below, estimated total number of minutes for all employees = 1210. Number of employees = 27.

Travel Time (mins) | Employees (e) |
Midpoint (m) |
m x e |
---|---|---|---|

0 < m ≤ 20 | 22 | 10 | 220 |

20 < m ≤ 40 | 15 | 30 | 450 |

40 < m ≤ 60 | 8 | 50 | 400 |

60 < m ≤ 80 | 2 | 70 | 140 |

TOTALS | 27 | 1210 |

Estimated mean = 1210 ÷ 27 = 44.81 minutes

Answer: 44.81 minutes

The table below shows the journey time for employees arriving at work for a company. What is the modal class?

Travel Time (mins) | Employees |
---|---|

0 < m ≤ 20 | 22 |

20 < m ≤ 40 | 15 |

40 < m ≤ 60 | 8 |

60 < m ≤ 80 | 2 |

The modal class is the class interval with the highest frequency (22).

Answer: 0 < *m* < 20

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