Data Handling | Mathematics (Maths) Class 8 PDF Download

 Page 1


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.
Solution:
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 f r e q u e n c y
3 | | | | 4
4 | | | | 4
5
| | | |
 ||
7
6 | | | 3
7 || 2
Total 20
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.
Solution:
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 | | | | 5
5 | | | | 4
6 | | | | 5
Total 30
Page 2


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.
Solution:
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 f r e q u e n c y
3 | | | | 4
4 | | | | 4
5
| | | |
 ||
7
6 | | | 3
7 || 2
Total 20
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.
Solution:
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 | | | | 5
5 | | | | 4
6 | | | | 5
Total 30
Marks Tally marks Frequency
0-10 ||| 3
10-20 |||| ||| 8
20-30 ||||  |||| |||| 14
30-40 |||| |||| 9
40-50 |||| | 6
      Total 40
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.
Solution:
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
f r e q u e n c y
0 | | | | 4
1 | | | | | | 7
2 | | | | | | | | | | 12
3 | | | | 5
4
| | | |
 |
6
5 | | | 3
6 | | | 3
 Total 40
Question:4
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 w h e r e10 n o t i n c l u d e d
.
Solution:
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:
Question:5
The electricity bills i n r u p e e s
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.
Page 3


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.
Solution:
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 f r e q u e n c y
3 | | | | 4
4 | | | | 4
5
| | | |
 ||
7
6 | | | 3
7 || 2
Total 20
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.
Solution:
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 | | | | 5
5 | | | | 4
6 | | | | 5
Total 30
Marks Tally marks Frequency
0-10 ||| 3
10-20 |||| ||| 8
20-30 ||||  |||| |||| 14
30-40 |||| |||| 9
40-50 |||| | 6
      Total 40
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.
Solution:
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
f r e q u e n c y
0 | | | | 4
1 | | | | | | 7
2 | | | | | | | | | | 12
3 | | | | 5
4
| | | |
 |
6
5 | | | 3
6 | | | 3
 Total 40
Question:4
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 w h e r e10 n o t i n c l u d e d
.
Solution:
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:
Question:5
The electricity bills i n r u p e e s
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.
Electricity bills
i n R u p e e s
Tally marks Frequency
300-400 |||| 5
400-500 ||| 3
500-600 |||| | 6
600-700 |||| 4
700-800 |||| || 7
 Total 25
Weekly wages
i n R u p e e s
Tally marks Frequency
610-630 |||| 4
630-650 |||| 4
650-670 |||| 5
670-690 ||| 3
690-710 |||| || 7
710-730 |||| 5
 Total 28
Weekly pocket expenses
i n R u p e e s
Tally marks Frequency
60-70 |||| | 6
70-80 |||| 5
80-90 |||| || 7
90-100 |||| 5
100-110 ||| 3
110-120 |||| 4
 Total 30
Solution:
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:
 
Question:6
The weekly wages i n r u p e e s
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.
Solution:
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:
 
Question:7
The weekly pocket expenses i n r u p e e s
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 w h e r e70 i s n o t i n c l u d e d
, 70-80, 80-90, etc.
Solution:
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:
 
Question:8
The daily earnings i n r u p e e s
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.
Solution:
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:
Page 4


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.
Solution:
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 f r e q u e n c y
3 | | | | 4
4 | | | | 4
5
| | | |
 ||
7
6 | | | 3
7 || 2
Total 20
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.
Solution:
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 | | | | 5
5 | | | | 4
6 | | | | 5
Total 30
Marks Tally marks Frequency
0-10 ||| 3
10-20 |||| ||| 8
20-30 ||||  |||| |||| 14
30-40 |||| |||| 9
40-50 |||| | 6
      Total 40
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.
Solution:
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
f r e q u e n c y
0 | | | | 4
1 | | | | | | 7
2 | | | | | | | | | | 12
3 | | | | 5
4
| | | |
 |
6
5 | | | 3
6 | | | 3
 Total 40
Question:4
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 w h e r e10 n o t i n c l u d e d
.
Solution:
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:
Question:5
The electricity bills i n r u p e e s
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.
Electricity bills
i n R u p e e s
Tally marks Frequency
300-400 |||| 5
400-500 ||| 3
500-600 |||| | 6
600-700 |||| 4
700-800 |||| || 7
 Total 25
Weekly wages
i n R u p e e s
Tally marks Frequency
610-630 |||| 4
630-650 |||| 4
650-670 |||| 5
670-690 ||| 3
690-710 |||| || 7
710-730 |||| 5
 Total 28
Weekly pocket expenses
i n R u p e e s
Tally marks Frequency
60-70 |||| | 6
70-80 |||| 5
80-90 |||| || 7
90-100 |||| 5
100-110 ||| 3
110-120 |||| 4
 Total 30
Solution:
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:
 
Question:6
The weekly wages i n r u p e e s
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.
Solution:
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:
 
Question:7
The weekly pocket expenses i n r u p e e s
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 w h e r e70 i s n o t i n c l u d e d
, 70-80, 80-90, etc.
Solution:
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:
 
Question:8
The daily earnings i n r u p e e s
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.
Solution:
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
i n R u p e e s
Tally marks Frequency
500-550 ||||| || 7
550-600 ||||| 5
600-650 |||| 4
650-700 ||| 3
700-750 ||||| 5
 Total 24
Heights i n c m Tally marks Frequency
125-130 |||| 5
130-135 |||| || 7
135-140 |||| | 6
140-145 |||| 4
 Total 22
 
Question:9
The heights i n c m
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.
Solution:
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:
 
Question:10
The top speeds of 30 different land animals have
been organised into a frequency table given below:
Maximum speed 
i n k m/ h
10–20
20–
30
30–
40
40–
50
50–
60
60–
70
Number of animals 3 5 10 8 0 2
Draw a histogram for the given data.
Solution:
Question:11
The ages i n y e a r s
of 360 patients treated in a hospital on a particular day are given below:
Age i n y e a r s
10–
20
20–
30
30–
40
40–
50
50–
60
60–
70
Page 5


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.
Solution:
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 f r e q u e n c y
3 | | | | 4
4 | | | | 4
5
| | | |
 ||
7
6 | | | 3
7 || 2
Total 20
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.
Solution:
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 | | | | 5
5 | | | | 4
6 | | | | 5
Total 30
Marks Tally marks Frequency
0-10 ||| 3
10-20 |||| ||| 8
20-30 ||||  |||| |||| 14
30-40 |||| |||| 9
40-50 |||| | 6
      Total 40
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.
Solution:
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
f r e q u e n c y
0 | | | | 4
1 | | | | | | 7
2 | | | | | | | | | | 12
3 | | | | 5
4
| | | |
 |
6
5 | | | 3
6 | | | 3
 Total 40
Question:4
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 w h e r e10 n o t i n c l u d e d
.
Solution:
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:
Question:5
The electricity bills i n r u p e e s
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.
Electricity bills
i n R u p e e s
Tally marks Frequency
300-400 |||| 5
400-500 ||| 3
500-600 |||| | 6
600-700 |||| 4
700-800 |||| || 7
 Total 25
Weekly wages
i n R u p e e s
Tally marks Frequency
610-630 |||| 4
630-650 |||| 4
650-670 |||| 5
670-690 ||| 3
690-710 |||| || 7
710-730 |||| 5
 Total 28
Weekly pocket expenses
i n R u p e e s
Tally marks Frequency
60-70 |||| | 6
70-80 |||| 5
80-90 |||| || 7
90-100 |||| 5
100-110 ||| 3
110-120 |||| 4
 Total 30
Solution:
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:
 
Question:6
The weekly wages i n r u p e e s
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.
Solution:
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:
 
Question:7
The weekly pocket expenses i n r u p e e s
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 w h e r e70 i s n o t i n c l u d e d
, 70-80, 80-90, etc.
Solution:
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:
 
Question:8
The daily earnings i n r u p e e s
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.
Solution:
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
i n R u p e e s
Tally marks Frequency
500-550 ||||| || 7
550-600 ||||| 5
600-650 |||| 4
650-700 ||| 3
700-750 ||||| 5
 Total 24
Heights i n c m Tally marks Frequency
125-130 |||| 5
130-135 |||| || 7
135-140 |||| | 6
140-145 |||| 4
 Total 22
 
Question:9
The heights i n c m
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.
Solution:
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:
 
Question:10
The top speeds of 30 different land animals have
been organised into a frequency table given below:
Maximum speed 
i n k m/ h
10–20
20–
30
30–
40
40–
50
50–
60
60–
70
Number of animals 3 5 10 8 0 2
Draw a histogram for the given data.
Solution:
Question:11
The ages i n y e a r s
of 360 patients treated in a hospital on a particular day are given below:
Age i n y e a r s
10–
20
20–
30
30–
40
40–
50
50–
60
60–
70
Number of
patients
90 40 60 20 120 30
Draw a histogram for the given data.
Hint. Take 10 small divisions = 10 patients.
Solution:
Question:12
Draw a histogram for the frequency distribution of following data:
Class
interval
8–13
13–
18
18–
23
23–
28
28–
33
33–
38
38–
43
Frequency 320 780 160 540 260 100 80
Hint. Take 1 small division = 10.
Solution: