GCSE(F),

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

Employees | Number of Companies |
---|---|

1 - 5 | 1 |

6 - 10 | 3 |

11 - 15 | 16 |

16 - 20 | 4 |

21 - 25 | 1 |

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*. There are 25 companies; the middle company will be the 13th:

Employees | Number of Companies | Running count of companies |
---|---|---|

1 - 5 | 1 | 1 |

6 - 10 | 3 | 4 |

11 - 15 | 16 | 20 |

16 - 20 | 4 | |

21 - 25 | 1 |

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 any actual values are replaced by the midpoint value:

Employees | Frequency f | midpoint m | f x m |
---|---|---|---|

1 - 5 | 1 | 3 | 3 |

6 - 10 | 3 | 8 | 24 |

11 - 15 | 16 | 13 | 208 |

16 - 20 | 4 | 18 | 72 |

21 - 25 | 1 | 23 | 23 |

TOTALS | 25 | 330 |

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.

1. 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 |

Answer: 44.81 minutes

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

Estimated mean = 1210 ÷ 27 = 44.81 minutes

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

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 |

2. 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 |

Answer: 0 < *m* < 20

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

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