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#### Page No 234:

#### Question 1:

The number of members in 20 families are given below:

4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7.

Prepare a frequency distribution of the data.

#### Answer:

First, we will arrange the data in increasing order.

3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7

Frequency table of the above data:

Number of members | Tally marks | Number of families (frequency) |

3 | $\left|\right|\left|\right|$ | 4 |

4 | $\left|\right|\left|\right|$ | 4 |

5 | $\overline{)\left|\right|\left|\right|}$ $\left|\right|$ | 7 |

6 | $\left|\right||$ | 3 |

7 | $\left|\right|$ | 2 |

Total | 20 |

#### Page No 234:

#### Question 2:

A dice was thrown 30 times and the following outcomes were noted:

2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4.

Prepare a frequency table.

#### Answer:

Arranging the outcomes in increasing order, we get:

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6

Now, we have:

1 was thrown 6 times

2 was thrown 6 times

3 was thrown 4 times

4 was thrown 5 times

5 was thrown 4 times

6 was thrown 5 times

Frequency distribution table of the above data:

Number | Tally mark | frequency |

1 | $\overline{)\left|\right|\left|\right|}|$ | 6 |

2 | $\overline{)\left|\right|\left|\right|}|$ | 6 |

3 | $\left|\right|\left|\right|$ | 4 |

4 | $\overline{)\left|\right|\left|\right|}$ | 5 |

5 | $\left|\right|\left|\right|$ | 4 |

6 | $\overline{)\left|\right|\left|\right|}$ | 5 |

Total | 30 |

#### Page No 234:

#### Question 3:

The following data gives the number of children in 40 families:

1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.

Represent it in the form of a frequency distribution.

#### Answer:

Arranging the dates in ascending order, we get:

0, 0 ,0 , 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2,2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6

There are:

4 families with no children

7 families with 1 child

12 families with 2 children

5 families with 3 children

6 families with 4 children

3 families with 5 children

3 families with 6 children

The frequency distribution table for the above data can be generated as below:

Number of children |
Tally mark |
Number of families (frequency) |

0 | $\left|\right|\left|\right|$ | 4 |

1 | $\overline{)\left|\right|\left|\right|}\left|\right|$ | 7 |

2 | $\overline{)\left|\right|\left|\right|}\overline{)\left|\right|\left|\right|}\left|\right|$ | 12 |

3 | $\overline{)\left|\right|\left|\right|}$ | 5 |

4 | $\overline{)\left|\right|\left|\right|}$ $|$ | 6 |

5 | $\left|\right||$ | 3 |

6 | $\left|\right||$ | 3 |

Total | 40 |

#### Page No 235:

#### Question 1:

The marks obtained by 40 students of a class in an examination are given below:

8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34.

Prepare a frequency distribution table with equal class intervals, starting from 0−10 (where 10 not included).

#### Answer:

Arranging the given observations in ascending order, we get:

3, 7, 8, 11, 13, 14, 15, 15, 17, 18, 19, 21, 21, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 29, 29, 31, 31, 34, 34, 34, 35, 37, 38, 38, 42, 45, 45, 47, 48, 49

Thus, the frequency distribution may be represented as shown below:

Marks | Tally marks | Frequency |
---|---|---|

0-10 | ||| | 3 |

10-20 | 8 | |

20-30 | 14 | |

30-40 | 9 | |

40-50 | 6 | |

Total | 40 |

#### Page No 235:

#### Question 2:

The electricity bills (in rupees) of 25 houses of a certain locality for a month are given below:

324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472.

Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300−400, where 400 is not included.

#### Answer:

Arranging the given observations in increasing order, we get:

312, 324, 356, 365, 378, 400, 435, 472, 506, 548, 565, 570, 584, 596, 617, 630, 674, 685, 700, 736, 745, 754, 763, 776, 786

Thus, the frequency distribution may be represented as shown below:

Electricity bills (in Rupees) |
Tally marks | Frequency |
---|---|---|

300-400 | 5 | |

400-500 | ||| | 3 |

500-600 | 6 | |

600-700 | |||| | 4 |

700-800 | 7 | |

Total | 25 |

#### Page No 235:

#### Question 3:

The weekly wages (in rupees) of 28 workers of a factory are given below:

668, 610, 642, 658, 668, 620, 719, 720, 700, 690, 710, 642, 672, 654, 692, 706, 718, 702, 704, 678, 615, 640, 680, 716, 705, 615, 636, 656.

Construct a frequency table with equal class intervals, taking the first of the class intervals as 610−630, where 630 is not included.

#### Answer:

Arranging the given observations in ascending order, we get:

610, 615, 615, 620, 636, 640, 642, 642, 654, 656, 658, 668, 668, 672, 678, 680, 690, 692, 700, 702, 704, 705, 706, 710, 716, 718, 719, 720

Thus, the frequency distribution may be represented as shown below:

Weekly wages (in Rupees) |
Tally marks | Frequency |
---|---|---|

610-630 | |||| | 4 |

630-650 | |||| | 4 |

650-670 | 5 | |

670-690 | ||| | 3 |

690-710 | 7 | |

710-730 | 5 | |

Total | 28 |

#### Page No 235:

#### Question 4:

The weekly pocket expenses (in rupees) of 30 students of a class are given below:

62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115.

Construct a frequency table with class intervals 60−70 (where 70 is not included), 70−80, 80−90, etc.

#### Answer:

Arranging the given observations in increasing order, we get:

60, 62, 62, 64, 65, 68, 72, 72, 73, 75, 78, 80, 80, 84, 85, 86, 87, 87, 90, 94, 94, 95, 96, 100, 103, 105, 110, 115, 117, 118

Thus, the frequency distribution may be represented as given below:

Weekly pocket expenses (in Rupees) |
Tally marks | Frequency |
---|---|---|

60-70 | 6 | |

70-80 | 5 | |

80-90 | 7 | |

90-100 | 5 | |

100-110 | ||| | 3 |

110-120 | |||| | 4 |

Total | 30 |

#### Page No 236:

#### Question 5:

The daily earnings (in rupees) of 24 stores in a market was recorded as under:

715, 650, 685, 550, 573, 530, 610, 525, 742, 680, 736, 524, 500, 585, 723, 545, 532, 560, 580, 545, 625, 630, 645, 700.

Prepare a frequency table taking equal class sizes. One such class is 500−550, where 550 is not included.

#### Answer:

Arranging the given observations in increasing order, we get:

500, 524, 525, 530, 532, 545, 545, 550, 560, 573, 580, 585, 610, 625, 630, 645, 650, 680, 685, 700, 715, 723, 736, 742

Thus, the frequency distribution may be represented as given below:

Daily earnings (in Rupees) |
Tally marks | Frequency |
---|---|---|

500-550 | ||||| || | 7 |

550-600 | ||||| | 5 |

600-650 | |||| | 4 |

650-700 | ||| | 3 |

700-750 | ||||| | 5 |

Total | 24 |

#### Page No 236:

#### Question 6:

The heights (in cm) of 22 students were recorded as under:

125, 132, 138, 144, 142, 136, 134, 125, 135, 130, 126, 132, 135, 142, 143, 128, 126, 136, 135, 130, 130, 133.

Prepare a frequency distribution table, taking equal class intervals and starting from 125−130, where 130 is not included.

#### Answer:

Arranging the given observations in increasing order, we get 125, 125, 126, 126, 128, 130, 130, 130, 132, 132, 133, 134, 135, 135, 135, 136, 136, 138, 142, 142, 143 and 144.

Thus, the frequency distribution may be represented as given below:

Heights (in cm) | Tally marks | Frequency |
---|---|---|

125-130 | 5 | |

130-135 | 7 | |

135-140 | 6 | |

140-145 | |||| | 4 |

Total | 22 |

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