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The distance (in km) of 40 engineers from their residence to their place of work were found as follows:-

5 | 3 | 10 | 20 | 25 | 11 | 13 | 7 | 12 | 31 |

19 | 10 | 12 | 17 | 18 | 11 | 32 | 17 | 16 | 2 |

7 | 9 | 7 | 8 | 3 | 5 | 12 | 15 | 18 | 3 |

12 | 14 | 2 | 9 | 6 | 15 | 15 | 7 | 6 | 12 |

Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?

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#### Solution

It is given that a grouped frequency distribution table of class size 5 has to be constructed. Therefore, the class intervals will be 0 − 5, 5 − 10, 10 − 15, 15 −20…

By observing the data given as above, a grouped frequency distribution table can be constructed as follows.

Distance (in km) |
Tally mark |
Number of engineers |

0 − 5 | 5 | |

5 − 10 | 11 | |

10 −15 | 11 | |

15 − 20 | 9 | |

20 − 25 | | | 1 |

25 − 30 | | | 1 |

30 − 35 | || | 2 |

Total | 40 |

It can be observed that there are very few engineers whose homes are at more than or equal to 20 km distance from their work place. Most of the engineers have their workplace up to 15 km distance from their homes.

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