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#### Page No 234:

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 $||||$ 4 4 $||||$ 4 5 $\overline{)||||}$ $||$ 7 6 $|||$ 3 7 $||$ 2 Total 20

#### Page No 234:

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 6 2 6 3 $||||$ 4 4 $\overline{)||||}$ 5 5 $||||$ 4 6 $\overline{)||||}$ 5 Total 30

#### Page No 234:

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 $||||$ 4 1 7 2 12 3 $\overline{)||||}$ 5 4 $\overline{)||||}$ $|$ 6 5 $|||$ 3 6 $|||$ 3 Total 40

#### Page No 235:

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:

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:

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:

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:

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:

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

ans

#### Page No 240:

Frequency distribution table

 Marks Tally Marks Number of students 3-8 $||$ 2 8-13 $\overline{)||||}$ $|||$ 8 13-18 $\overline{)||||}$ $\overline{)||||}$ $\overline{)||||}$ $|$ 16 18-23 $||||$ 4 Total = 30

#### Page No 240:

Frequency distriubution table

 Weight(in kg) Tally Marks Number of students 25-30 $||$ 2 30-35 $\overline{)||||}$ $||$ 7 35-40 $\overline{)||||}$ $\overline{)||||}$ $|$ 11 40-45 $\overline{)||||}$ $||$ 7 45-50 $|||$ 3 Total = 30

#### Page No 240:

(i) Number of students = $14+18+10=42$
(ii) Class interval with least number of students = 150−155
(iii) Class size = 130 − 125 = 5
(iv) Number of students with height less than 140 = $14+8+6=28$

#### Page No 241:

(i) The given histogram tells about the number of teachers in a school from the age group 25-30 to 55-60.
(ii) Number of teachers with age less than 45 years = $3+5+7+6=21$
(iii) Number of teachers with age more than 40 years but less than 55 years = $6+4+3=13$

#### Page No 241:

(i) Age group =10 to 40
Given all the classes are of equal width
Number of class interval of equal width = 6
Class width = $\frac{40-10}{6}=5$
Classes are 10-15,15-20,20-25,25-30,30-35,35-40

(ii) Class width = $\frac{40-10}{6}=5$

(iii)Age group with least literate females = 10-15
(iv)Age group with highest literate females = 15-20

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