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#### Question

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?

#### Solution

#### Similar questions

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:-

1 | 6 | 2 | 3 | 5 | 12 | 5 | 8 | 4 | 8 |

10 | 3 | 4 | 12 | 2 | 8 | 15 | 1 | 17 | 6 |

3 | 2 | 8 | 5 | 9 | 6 | 8 | 7 | 14 | 12 |

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.

(ii) How many children watched television for 15 or more hours a week?

A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:-

0.03 | 0.08 | 0.08 | 0.09 | 0.04 | 0.17 |

0.16 | 0.05 | 0.02 | 0.06 | 0.18 | 0.20 |

0.11 | 0.08 | 0.12 | 0.13 | 0.22 | 0.07 |

0.08 | 0.01 | 0.10 | 0.06 | 0.09 | 0.18 |

0.11 | 0.07 | 0.05 | 0.07 | 0.01 | 0.04 |

(i) Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04, 0.04 - 0.08, and so on.

(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?

The blood groups of 30 students of Class VIII are recorded as follows:-

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.

Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?

The heights of 50 students, measured to the nearest centimeters, have been found to be as follows:-

161 | 150 | 154 | 165 | 168 | 161 | 154 | 162 | 150 | 151 |

162 | 164 | 171 | 165 | 158 | 154 | 156 | 172 | 160 | 170 |

153 | 159 | 161 | 170 | 162 | 165 | 166 | 168 | 165 | 164 |

154 | 152 | 153 | 156 | 158 | 162 | 160 | 161 | 173 | 166 |

161 | 159 | 162 | 167 | 168 | 159 | 158 | 153 | 154 | 159 |

(i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc.

(ii) What can you conclude bout their heights from the table?

The value of π up to50 decimal places is given below:-

3.14159265358979323846264338327950288419716939937510

(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.

(ii) What are the most and the least frequently occurring digits?