Question 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

**Answer:**

Sulphur dioxide (ppm) | Number of days |
---|---|

0.00 – 0.04 | 4 |

0.04 – 0.08 | 9 |

0.08 – 0.12 | 9 |

0.12 – 0.16 | 2 |

0.16 – 0.20 | 4 |

0.20 – 0.24 | 2 |

Total | 30 |

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

**Answer:** 6 days

Question 6: 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.

**Answer:**

Number of heads | Frequency |
---|---|

0 | 6 |

1 | 10 |

2 | 9 |

3 | 5 |

Total | 30 |

Question 7: The value of π upto 50 decimal places is given below:

3.14159265358979323846264338327950288419716939937510

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

**Answer:**

Digits | Frequency |
---|---|

0 | 2 |

1 | 5 |

2 | 5 |

3 | 8 |

4 | 4 |

5 | 5 |

6 | 4 |

7 | 4 |

8 | 5 |

9 | 8 |

Total | 50 |

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

**Answer:** Most frequent digit = 3 and 9

Least frequent digit = 0

Question 8: 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.

**Answer:**

Number of hours | Frequency |
---|---|

0 – 5 | 10 |

5 – 10 | 13 |

10 – 15 | 5 |

15 – 20 | 2 |

Total | 30 |

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

**Answer:** Two children

Question 9: 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 interval 2 - 2.5.

**Answer:**

Class Interval | Frequency |
---|---|

2 – 2.5 | 2 |

2.5 – 3 | 6 |

3 – 3.5 | 14 |

3.5 – 4 | 11 |

4 – 4.5 | 4 |

4.5 – 5 | 3 |

Total | 40 |

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