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Data Handling – I (Classification and Tabulation of Data) Exercise 23.2 | Mathematics (Maths) Class 8 PDF Download

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1. The marks obtained by 40 students of class VIII in an examination are given
below :
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 3, 23, 5, 12, 18, 8, 12,
6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23.
Divide the data into five groups namely 0-5, 5-10, 10-15, 15-20 and 20-25 and
prepare a grouped frequency table.
Solution:
The frequency table for the marks of 40 students of class VIII in an examination is shown
below:
Range of Marks No: of Students 
0-5 9 
5-10 9 
10-15 7 
15-20 9 
20-25 6 
2. The marks scored by 20 students in a test are given below:
54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57.
Complete the following frequency table:
What is the class interval in which the greatest frequency occurs? 
Solution: 
The frequency table can be completed as follows: 
Marks in Class Interval Tally Marks No: of Children 
40 - 50 | | | | 4 
Page 2


 
   
1. The marks obtained by 40 students of class VIII in an examination are given
below :
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 3, 23, 5, 12, 18, 8, 12,
6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23.
Divide the data into five groups namely 0-5, 5-10, 10-15, 15-20 and 20-25 and
prepare a grouped frequency table.
Solution:
The frequency table for the marks of 40 students of class VIII in an examination is shown
below:
Range of Marks No: of Students 
0-5 9 
5-10 9 
10-15 7 
15-20 9 
20-25 6 
2. The marks scored by 20 students in a test are given below:
54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57.
Complete the following frequency table:
What is the class interval in which the greatest frequency occurs? 
Solution: 
The frequency table can be completed as follows: 
Marks in Class Interval Tally Marks No: of Children 
40 - 50 | | | | 4 
 
   
50 - 60 
| | | 
8 
60 - 70 | | | 3 
70 - 80 | | | 3 
80 - 90 | |  2 
The class interval with the greatest frequency (8) is 50-60. 
3. The following is the distribution of weights (in kg) of 52 persons:
Weight in kg Persons 
30 – 40 10 
40 – 50 15 
50 – 60 17 
60 – 70 6 
70 – 80 4 
(i) What is the lower limit of class 50-60?
(ii) Find the class marks of the classes 40-50, 50-60.
(iii) What is the class size?
Solution:
(i) The lower limit of the class 50-60 is 50.
(ii) Class mark for the class 40-50:
i.e., (40+50) / 2 = 90/2 = 45
Again, Class mark for the class 50-60: 
i.e., (50+60) / 2 = 110/2 = 55
(iii) Here the class size is 40-30, i.e. 10.
4. Construct a frequency table for the following weights (in gm) of 35 mangoes using
the equal class intervals, one of them is 40-45 (45 not included) :
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74,
45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
(i) What is the class mark of the class interval 40-45?
(ii) What is the range of the above weights?
(iii) How many classes are there?
Solution:
Weight (in grams) No: of Mangoes 
Page 3


 
   
1. The marks obtained by 40 students of class VIII in an examination are given
below :
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 3, 23, 5, 12, 18, 8, 12,
6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23.
Divide the data into five groups namely 0-5, 5-10, 10-15, 15-20 and 20-25 and
prepare a grouped frequency table.
Solution:
The frequency table for the marks of 40 students of class VIII in an examination is shown
below:
Range of Marks No: of Students 
0-5 9 
5-10 9 
10-15 7 
15-20 9 
20-25 6 
2. The marks scored by 20 students in a test are given below:
54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57.
Complete the following frequency table:
What is the class interval in which the greatest frequency occurs? 
Solution: 
The frequency table can be completed as follows: 
Marks in Class Interval Tally Marks No: of Children 
40 - 50 | | | | 4 
 
   
50 - 60 
| | | 
8 
60 - 70 | | | 3 
70 - 80 | | | 3 
80 - 90 | |  2 
The class interval with the greatest frequency (8) is 50-60. 
3. The following is the distribution of weights (in kg) of 52 persons:
Weight in kg Persons 
30 – 40 10 
40 – 50 15 
50 – 60 17 
60 – 70 6 
70 – 80 4 
(i) What is the lower limit of class 50-60?
(ii) Find the class marks of the classes 40-50, 50-60.
(iii) What is the class size?
Solution:
(i) The lower limit of the class 50-60 is 50.
(ii) Class mark for the class 40-50:
i.e., (40+50) / 2 = 90/2 = 45
Again, Class mark for the class 50-60: 
i.e., (50+60) / 2 = 110/2 = 55
(iii) Here the class size is 40-30, i.e. 10.
4. Construct a frequency table for the following weights (in gm) of 35 mangoes using
the equal class intervals, one of them is 40-45 (45 not included) :
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74,
45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
(i) What is the class mark of the class interval 40-45?
(ii) What is the range of the above weights?
(iii) How many classes are there?
Solution:
Weight (in grams) No: of Mangoes 
 
   
30 - 35 5 
35 - 40 2 
40 - 45 4 
45 - 50 3 
50 - 55 5 
55 - 60 3 
60 - 65 5 
65 - 70 5 
70 - 75 3 
(i) Class mark for the class interval 40 – 45:
Class mark = (40+45) / 2 = 85/2 = 42.5
(ii) Range of the above weights:
Range = Highest value – Lowest value
Range = 74 – 30 = 44
(iii) Number of classes = 9
5. Construct a frequency table with class-intervals 0-5 (5 not included) of the
following marks obtained by a group of 30 students in an examination :
0, 5, 7, 10, 12, 15, 20, 22, 25, 27, 8, 11, 17, 3, 6, 9, 17, 19, 21, 29, 31, 35, 37, 40, 42, 45,
49, 4, 50, 16.
Solution:
The frequency table with class intervals 0 – 5, 5 – 10, 10 – 15, . . . , 45 – 50 is shown
below:
Marks No: of Students 
0 – 5 3 
5 – 10 5 
10 – 15 3 
15 – 20 5 
20 – 25 3 
25 – 30 3 
30 – 35 1 
35 – 40 2 
40 – 45 2 
45 – 50 2 
50 - 55                                     1
Page 4


 
   
1. The marks obtained by 40 students of class VIII in an examination are given
below :
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 3, 23, 5, 12, 18, 8, 12,
6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23.
Divide the data into five groups namely 0-5, 5-10, 10-15, 15-20 and 20-25 and
prepare a grouped frequency table.
Solution:
The frequency table for the marks of 40 students of class VIII in an examination is shown
below:
Range of Marks No: of Students 
0-5 9 
5-10 9 
10-15 7 
15-20 9 
20-25 6 
2. The marks scored by 20 students in a test are given below:
54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57.
Complete the following frequency table:
What is the class interval in which the greatest frequency occurs? 
Solution: 
The frequency table can be completed as follows: 
Marks in Class Interval Tally Marks No: of Children 
40 - 50 | | | | 4 
 
   
50 - 60 
| | | 
8 
60 - 70 | | | 3 
70 - 80 | | | 3 
80 - 90 | |  2 
The class interval with the greatest frequency (8) is 50-60. 
3. The following is the distribution of weights (in kg) of 52 persons:
Weight in kg Persons 
30 – 40 10 
40 – 50 15 
50 – 60 17 
60 – 70 6 
70 – 80 4 
(i) What is the lower limit of class 50-60?
(ii) Find the class marks of the classes 40-50, 50-60.
(iii) What is the class size?
Solution:
(i) The lower limit of the class 50-60 is 50.
(ii) Class mark for the class 40-50:
i.e., (40+50) / 2 = 90/2 = 45
Again, Class mark for the class 50-60: 
i.e., (50+60) / 2 = 110/2 = 55
(iii) Here the class size is 40-30, i.e. 10.
4. Construct a frequency table for the following weights (in gm) of 35 mangoes using
the equal class intervals, one of them is 40-45 (45 not included) :
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74,
45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
(i) What is the class mark of the class interval 40-45?
(ii) What is the range of the above weights?
(iii) How many classes are there?
Solution:
Weight (in grams) No: of Mangoes 
 
   
30 - 35 5 
35 - 40 2 
40 - 45 4 
45 - 50 3 
50 - 55 5 
55 - 60 3 
60 - 65 5 
65 - 70 5 
70 - 75 3 
(i) Class mark for the class interval 40 – 45:
Class mark = (40+45) / 2 = 85/2 = 42.5
(ii) Range of the above weights:
Range = Highest value – Lowest value
Range = 74 – 30 = 44
(iii) Number of classes = 9
5. Construct a frequency table with class-intervals 0-5 (5 not included) of the
following marks obtained by a group of 30 students in an examination :
0, 5, 7, 10, 12, 15, 20, 22, 25, 27, 8, 11, 17, 3, 6, 9, 17, 19, 21, 29, 31, 35, 37, 40, 42, 45,
49, 4, 50, 16.
Solution:
The frequency table with class intervals 0 – 5, 5 – 10, 10 – 15, . . . , 45 – 50 is shown
below:
Marks No: of Students 
0 – 5 3 
5 – 10 5 
10 – 15 3 
15 – 20 5 
20 – 25 3 
25 – 30 3 
30 – 35 1 
35 – 40 2 
40 – 45 2 
45 – 50 2 
50 - 55                                     1
 
   
6. The marks scored by 40 students of class VIII in mathematics are given below :
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54,
70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.
Prepare a frequency distribution with class size of 10 marks.
Solution:
The frequency table of the marks scored by 40 students of class VIII in mathematics is
shown below:
Marks Frequency Distribution 
20 – 30 1 
30 – 40 3 
40 – 50 5 
50 – 60 8 
60 – 70 9 
70 – 80 8 
80 – 90 34 
90 – 100 2 
7. The heights (in cm) of 30 students of class VIII are given below :
155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151,
154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153.
Prepare a frequency distribution table with 160-164 as one of the class intervals.
Solution:
The frequency distribution table is shown below:
Height (in cm) No: of Students 
145 – 149 4 
150 – 154 9 
155 – 159 12 
160 – 164 5 
8. The monthly wages of 30 workers in a factory are given below:
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 
812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890. 
Represent the data in the form of a frequency distribution with class size 10. 
Solution: 
The frequency table of the monthly wages of 30 workers in a factory is shown below: 
Page 5


 
   
1. The marks obtained by 40 students of class VIII in an examination are given
below :
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24, 16, 3, 23, 5, 12, 18, 8, 12,
6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23.
Divide the data into five groups namely 0-5, 5-10, 10-15, 15-20 and 20-25 and
prepare a grouped frequency table.
Solution:
The frequency table for the marks of 40 students of class VIII in an examination is shown
below:
Range of Marks No: of Students 
0-5 9 
5-10 9 
10-15 7 
15-20 9 
20-25 6 
2. The marks scored by 20 students in a test are given below:
54, 42, 68, 56, 62, 71, 78, 51, 72, 53, 44, 58, 47, 64, 41, 57, 89, 53, 84, 57.
Complete the following frequency table:
What is the class interval in which the greatest frequency occurs? 
Solution: 
The frequency table can be completed as follows: 
Marks in Class Interval Tally Marks No: of Children 
40 - 50 | | | | 4 
 
   
50 - 60 
| | | 
8 
60 - 70 | | | 3 
70 - 80 | | | 3 
80 - 90 | |  2 
The class interval with the greatest frequency (8) is 50-60. 
3. The following is the distribution of weights (in kg) of 52 persons:
Weight in kg Persons 
30 – 40 10 
40 – 50 15 
50 – 60 17 
60 – 70 6 
70 – 80 4 
(i) What is the lower limit of class 50-60?
(ii) Find the class marks of the classes 40-50, 50-60.
(iii) What is the class size?
Solution:
(i) The lower limit of the class 50-60 is 50.
(ii) Class mark for the class 40-50:
i.e., (40+50) / 2 = 90/2 = 45
Again, Class mark for the class 50-60: 
i.e., (50+60) / 2 = 110/2 = 55
(iii) Here the class size is 40-30, i.e. 10.
4. Construct a frequency table for the following weights (in gm) of 35 mangoes using
the equal class intervals, one of them is 40-45 (45 not included) :
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74,
45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
(i) What is the class mark of the class interval 40-45?
(ii) What is the range of the above weights?
(iii) How many classes are there?
Solution:
Weight (in grams) No: of Mangoes 
 
   
30 - 35 5 
35 - 40 2 
40 - 45 4 
45 - 50 3 
50 - 55 5 
55 - 60 3 
60 - 65 5 
65 - 70 5 
70 - 75 3 
(i) Class mark for the class interval 40 – 45:
Class mark = (40+45) / 2 = 85/2 = 42.5
(ii) Range of the above weights:
Range = Highest value – Lowest value
Range = 74 – 30 = 44
(iii) Number of classes = 9
5. Construct a frequency table with class-intervals 0-5 (5 not included) of the
following marks obtained by a group of 30 students in an examination :
0, 5, 7, 10, 12, 15, 20, 22, 25, 27, 8, 11, 17, 3, 6, 9, 17, 19, 21, 29, 31, 35, 37, 40, 42, 45,
49, 4, 50, 16.
Solution:
The frequency table with class intervals 0 – 5, 5 – 10, 10 – 15, . . . , 45 – 50 is shown
below:
Marks No: of Students 
0 – 5 3 
5 – 10 5 
10 – 15 3 
15 – 20 5 
20 – 25 3 
25 – 30 3 
30 – 35 1 
35 – 40 2 
40 – 45 2 
45 – 50 2 
50 - 55                                     1
 
   
6. The marks scored by 40 students of class VIII in mathematics are given below :
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54,
70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.
Prepare a frequency distribution with class size of 10 marks.
Solution:
The frequency table of the marks scored by 40 students of class VIII in mathematics is
shown below:
Marks Frequency Distribution 
20 – 30 1 
30 – 40 3 
40 – 50 5 
50 – 60 8 
60 – 70 9 
70 – 80 8 
80 – 90 34 
90 – 100 2 
7. The heights (in cm) of 30 students of class VIII are given below :
155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151,
154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153.
Prepare a frequency distribution table with 160-164 as one of the class intervals.
Solution:
The frequency distribution table is shown below:
Height (in cm) No: of Students 
145 – 149 4 
150 – 154 9 
155 – 159 12 
160 – 164 5 
8. The monthly wages of 30 workers in a factory are given below:
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 
812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890. 
Represent the data in the form of a frequency distribution with class size 10. 
Solution: 
The frequency table of the monthly wages of 30 workers in a factory is shown below: 
 
 
 
 
 
   
 
 
Wages No: of Workers 
800 – 809 3 
810 – 819 2 
820 – 829 1 
830 – 839 8 
840 – 849 5 
850 – 859 1 
860 – 869 3 
870 – 879 1 
880 – 889 1 
890 – 899 5 
 
9. Construct a frequency table with equal class intervals from the following data on 
the monthly wages (in rupees) of 28 labourers working in a factory, taking one of 
the class intervals as 210-230 (230 not included) : 
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 
254, 278, 210, 240, 280, 316, 306, 215, 256, 236. 
Solution: 
The frequency table of the monthly wages of 28 laborers working in a factory is shown 
below: 
Wages No: of Workers 
210 – 230 4 
230 – 250 4 
250 – 270 5 
270 – 290 3 
290 – 310 7 
310 – 330 5 
 
10. The daily minimum temperatures in degrees Celsius recorded in a certain Arctic 
region are as follows : 
- 12.5, -10.8, -18.6, -8.4, -10.8, -4.2, -4.8, -6.7, -13.2, -11.8, -2.3, 1.2, 2.6, 0, -2.4, 0, 3.2, 
2.7, 3.4, 0, -2.4, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -5.8, -8.9, -14.6, -12.3, -11.5, -7.8, -2.9 
Represent them as frequency distribution table taking -19.9 to -15 as the first class 
interval. 
Solution: 
The frequency table of the daily minimum temperatures is shown below: 
 
Temperature Frequency Distribution

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