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### Description

frequency distribution table

#### Questions

A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:-

2.6 | 3.0 | 3.7 | 3.2 | 2.2 | 4.1 | 3.5 | 4.5 |

3.5 | 2.3 | 3.2 | 3.4 | 3.8 | 3.2 | 4.6 | 3.7 |

2.5 | 4.4 | 3.4 | 3.3 | 2.9 | 3.0 | 4.3 | 2.8 |

3.5 | 3.2 | 3.9 | 3.2 | 3.2 | 3.1 | 3.7 | 3.4 |

4.6 | 3.8 | 3.2 | 2.6 | 3.5 | 4.2 | 2.9 | 3.6 |

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2 − 2.5.

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 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?

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?

The relative humidity (in %) of a certain city for a month of 30 days was as follows:-

98.1 | 98.6 | 99.2 | 90.3 | 86.5 | 95.3 | 92.9 | 96.3 | 94.2 | 95.1 |

89.2 | 92.3 | 97.1 | 93.5 | 92.7 | 95.1 | 97.2 | 93.3 | 95.2 | 97.3 |

96.2 | 92.1 | 84.9 | 90.2 | 95.7 | 98.3 | 97.3 | 96.1 | 92.1 | 89 |

(i) Construct a grouped frequency distribution table with classes

84 - 86, 86 - 88

(ii) Which month or season do you think this data is about?

(iii) What is the range of this data?

Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:-

0 | 1 | 2 | 2 | 1 | 2 | 3 | 1 | 3 | 0 |

1 | 3 | 1 | 1 | 2 | 2 | 0 | 1 | 2 | 1 |

3 | 0 | 0 | 1 | 1 | 2 | 3 | 2 | 2 | 0 |

Prepare a frequency distribution table for the data given above.

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?