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5 3 10 20 25 11 13 7 12 31

19 10 12 17 18 11 32 16 2 7

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?

Answer :

Let us make the classes as 0-5, 5-10, 10-15, 15-20, 20-25, 25-30 and 30-35.

The frequency distribution table will be as follows:

Distance from residence | Distance values and No. of entries (Tally Marks) | No. of engineers(frequency) |

0 - 5 | 3, 2, 3, 3, 2 = 5 entries | 5 |

5 - 10 | 5, 7, 7, 9, 7, 8, 5, 9, 6, 7, 6 = 11 entries | 11 |

10 - 15 | 10, 11, 13, 12, 10, 12, 11, 12, 12, 14, 12 = 11 entries | 11 |

15 - 20 | 19, 17, 18, 17, 16, 15, 18, 15, 15 = 9 entries | 9 |

20 - 25 | 20 = 1 entry | 1 |

25 - 30 | 25 = 1 entry | 1 |

30 - 35 | 31, 32 = 2 entries | 2 |

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- 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 value of ? upto 50 decimal places is given below: 3.14159265358979323846264338327950288419716939937510i) 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?
- 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 12i) 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 company manufactures car batteries of particular type. The lives of 4 sch 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 3.6Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 - 2.5.

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