Data Handling – I (Classification and Tabulation of Data) Exercise 23.1 | Mathematics (Maths) Class 8 PDF Download

 Page 1


 
 
 
 
 
   
 
 
                                                     
 
1. Define the following terms : 
(i) Observations 
(ii) Raw data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
(v) Discrete frequency distribution 
(vi) Grouped frequency distribution 
(vii) Class-interval 
(viii) Class-size 
(ix) Class limits 
(x) True class limits 
Solution: 
(i) Observations: 
Observation is the value at a particular period of a particular variable. 
 
(ii) Raw data: 
Raw data is the data collected in its original form. 
 
(iii) Frequency of an observation: 
Frequency of an observation is the number of times a certain value or a class of values 
occurs. 
 
(iv) Frequency distribution: 
Frequency distribution is the organization of raw data in table form with classes and 
frequencies. 
 
(v) Discrete frequency distribution: 
Discrete frequency distribution is a frequency distribution where sufficiently great 
numbers are grouped into one class. 
 
(vi) Grouped frequency distribution: 
Grouped frequency distribution is a frequency distribution where several numbers are 
grouped into one class. 
 
(vii) Class-interval: 
Class interval is a group under which large number of data is grouped to analyse its 
Range and Distribution. 
Page 2


 
 
 
 
 
   
 
 
                                                     
 
1. Define the following terms : 
(i) Observations 
(ii) Raw data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
(v) Discrete frequency distribution 
(vi) Grouped frequency distribution 
(vii) Class-interval 
(viii) Class-size 
(ix) Class limits 
(x) True class limits 
Solution: 
(i) Observations: 
Observation is the value at a particular period of a particular variable. 
 
(ii) Raw data: 
Raw data is the data collected in its original form. 
 
(iii) Frequency of an observation: 
Frequency of an observation is the number of times a certain value or a class of values 
occurs. 
 
(iv) Frequency distribution: 
Frequency distribution is the organization of raw data in table form with classes and 
frequencies. 
 
(v) Discrete frequency distribution: 
Discrete frequency distribution is a frequency distribution where sufficiently great 
numbers are grouped into one class. 
 
(vi) Grouped frequency distribution: 
Grouped frequency distribution is a frequency distribution where several numbers are 
grouped into one class. 
 
(vii) Class-interval: 
Class interval is a group under which large number of data is grouped to analyse its 
Range and Distribution. 
 
   
(viii) Class-size:
Class size is the difference between the upper and the lower values of a class.
(ix) Class limits:
Class limits are the smallest and the largest observations (data, events, etc.) in a class.
(x) True class limits:
True class limits are the actual class limits of a class.
2. The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84,
58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60
(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second
group etc.
Now answer the following:
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?
Solution:
The given raw data can be arranged in an ascending order.
The class intervals are 30 – 39, 40 – 49, …, 100 – 109.
Then, take the raw data and place it in the appropriate class intervals.
(i) The marks can be arranged in an ascending order as shown below:
Page 3


 
 
 
 
 
   
 
 
                                                     
 
1. Define the following terms : 
(i) Observations 
(ii) Raw data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
(v) Discrete frequency distribution 
(vi) Grouped frequency distribution 
(vii) Class-interval 
(viii) Class-size 
(ix) Class limits 
(x) True class limits 
Solution: 
(i) Observations: 
Observation is the value at a particular period of a particular variable. 
 
(ii) Raw data: 
Raw data is the data collected in its original form. 
 
(iii) Frequency of an observation: 
Frequency of an observation is the number of times a certain value or a class of values 
occurs. 
 
(iv) Frequency distribution: 
Frequency distribution is the organization of raw data in table form with classes and 
frequencies. 
 
(v) Discrete frequency distribution: 
Discrete frequency distribution is a frequency distribution where sufficiently great 
numbers are grouped into one class. 
 
(vi) Grouped frequency distribution: 
Grouped frequency distribution is a frequency distribution where several numbers are 
grouped into one class. 
 
(vii) Class-interval: 
Class interval is a group under which large number of data is grouped to analyse its 
Range and Distribution. 
 
   
(viii) Class-size:
Class size is the difference between the upper and the lower values of a class.
(ix) Class limits:
Class limits are the smallest and the largest observations (data, events, etc.) in a class.
(x) True class limits:
True class limits are the actual class limits of a class.
2. The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84,
58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60
(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second
group etc.
Now answer the following:
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?
Solution:
The given raw data can be arranged in an ascending order.
The class intervals are 30 – 39, 40 – 49, …, 100 – 109.
Then, take the raw data and place it in the appropriate class intervals.
(i) The marks can be arranged in an ascending order as shown below:
 
   
(ii) The Highest score is 100.
(iii) The Lowest score is 37.
(iv) The Range is 100 – 37 i.e., 63.
(v) If 40 is the passing mark, then the number of students who failed is 2 (i.e. 37, 39).
(vi) The number of students scoring 75 and above is 8 (i.e. 75, 77, 78, 84, 88, 90, 98,
100).
(vii) The marks 51, 54, and 57 do not actually appear between 50 and 60.
(viii) The number of students scoring less than 50 is 5 (i.e. 37, 39, 44, 48, 48).
3. The weights of new born babies (in kg) in a hospital on a particular day are as
follows:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
(i) Rearrange the weights in descending order.
(ii) Determine the highest weight.
(iii) Determine the lowest weight.
(iv) Determine the range.
(v) How many babies were born on that day?
(vi) How many babies weigh below 2.5 kg?
(vii) How many babies weigh more than 2.8 kg?
(viii) How many babies weigh 2.8 kg?
Solution:
(i) The weights of the newly born babies in descending order are as follows: 3.1, 3.0, 2.9,
2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.4, 2.4, 2.3, 2.2, 2.1
(ii) The highest weight is 3.1 kg
(iii) The lowest weight is 2.1 kg
(iv) The range is 3.1-2.1, i.e. 1 kg
(v) The number of babies born on that day is 15
(vi) The number of babies whose weights are below 2.5 kg is 4 (i.e. 2.4, 2.3, 2.2, 2.1)
Page 4


 
 
 
 
 
   
 
 
                                                     
 
1. Define the following terms : 
(i) Observations 
(ii) Raw data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
(v) Discrete frequency distribution 
(vi) Grouped frequency distribution 
(vii) Class-interval 
(viii) Class-size 
(ix) Class limits 
(x) True class limits 
Solution: 
(i) Observations: 
Observation is the value at a particular period of a particular variable. 
 
(ii) Raw data: 
Raw data is the data collected in its original form. 
 
(iii) Frequency of an observation: 
Frequency of an observation is the number of times a certain value or a class of values 
occurs. 
 
(iv) Frequency distribution: 
Frequency distribution is the organization of raw data in table form with classes and 
frequencies. 
 
(v) Discrete frequency distribution: 
Discrete frequency distribution is a frequency distribution where sufficiently great 
numbers are grouped into one class. 
 
(vi) Grouped frequency distribution: 
Grouped frequency distribution is a frequency distribution where several numbers are 
grouped into one class. 
 
(vii) Class-interval: 
Class interval is a group under which large number of data is grouped to analyse its 
Range and Distribution. 
 
   
(viii) Class-size:
Class size is the difference between the upper and the lower values of a class.
(ix) Class limits:
Class limits are the smallest and the largest observations (data, events, etc.) in a class.
(x) True class limits:
True class limits are the actual class limits of a class.
2. The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84,
58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60
(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second
group etc.
Now answer the following:
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?
Solution:
The given raw data can be arranged in an ascending order.
The class intervals are 30 – 39, 40 – 49, …, 100 – 109.
Then, take the raw data and place it in the appropriate class intervals.
(i) The marks can be arranged in an ascending order as shown below:
 
   
(ii) The Highest score is 100.
(iii) The Lowest score is 37.
(iv) The Range is 100 – 37 i.e., 63.
(v) If 40 is the passing mark, then the number of students who failed is 2 (i.e. 37, 39).
(vi) The number of students scoring 75 and above is 8 (i.e. 75, 77, 78, 84, 88, 90, 98,
100).
(vii) The marks 51, 54, and 57 do not actually appear between 50 and 60.
(viii) The number of students scoring less than 50 is 5 (i.e. 37, 39, 44, 48, 48).
3. The weights of new born babies (in kg) in a hospital on a particular day are as
follows:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
(i) Rearrange the weights in descending order.
(ii) Determine the highest weight.
(iii) Determine the lowest weight.
(iv) Determine the range.
(v) How many babies were born on that day?
(vi) How many babies weigh below 2.5 kg?
(vii) How many babies weigh more than 2.8 kg?
(viii) How many babies weigh 2.8 kg?
Solution:
(i) The weights of the newly born babies in descending order are as follows: 3.1, 3.0, 2.9,
2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.4, 2.4, 2.3, 2.2, 2.1
(ii) The highest weight is 3.1 kg
(iii) The lowest weight is 2.1 kg
(iv) The range is 3.1-2.1, i.e. 1 kg
(v) The number of babies born on that day is 15
(vi) The number of babies whose weights are below 2.5 kg is 4 (i.e. 2.4, 2.3, 2.2, 2.1)
 
   
(vii) The number of babies whose weights are more than 2.8 kg is 4 (i.e. 3.1, 3.0, 2.9, 2.9)
(viii) The number of babies whose weight is 2.8 kg is 2.
4. Following data gives the number of children in 41 families :
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 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:
The data can be put in the form of frequency distribution in the following manner:
Children No: of Families 
0 5 
1 7 
2 12 
3 5 
4 6 
5 3 
6 3 
5. Prepare a frequency table of the following scores obtained by 50 students in a
test:
42, 51, 21, 42, 37, 37, 42, 49, 38, 52, 7, 33, 17,44, 39, 7, 14, 27, 39, 42, 42, 62, 37, 39, 67,
51,53, 53, 59, 41, 29, 38, 27, 31, 54, 19, 53, 51, 22,61, 42, 39, 59, 47, 33, 34, 16, 37, 57,
43
Solution: The frequency table of 50 students is given below:
Marks No: of Students Marks No: of Students Marks No: of Students 
7 2 33 2 49 1 
14 1 34 1 51 3 
16 1 37 4 52 1 
17 1 38 2 53 3 
19 1 39 4 54 1 
21 1 41 1 57 1 
22 1 42 6 59 2 
27 2 43 1 61 1 
29 1 44 1 62 1 
31 1 47 1 67 1 
Page 5


 
 
 
 
 
   
 
 
                                                     
 
1. Define the following terms : 
(i) Observations 
(ii) Raw data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
(v) Discrete frequency distribution 
(vi) Grouped frequency distribution 
(vii) Class-interval 
(viii) Class-size 
(ix) Class limits 
(x) True class limits 
Solution: 
(i) Observations: 
Observation is the value at a particular period of a particular variable. 
 
(ii) Raw data: 
Raw data is the data collected in its original form. 
 
(iii) Frequency of an observation: 
Frequency of an observation is the number of times a certain value or a class of values 
occurs. 
 
(iv) Frequency distribution: 
Frequency distribution is the organization of raw data in table form with classes and 
frequencies. 
 
(v) Discrete frequency distribution: 
Discrete frequency distribution is a frequency distribution where sufficiently great 
numbers are grouped into one class. 
 
(vi) Grouped frequency distribution: 
Grouped frequency distribution is a frequency distribution where several numbers are 
grouped into one class. 
 
(vii) Class-interval: 
Class interval is a group under which large number of data is grouped to analyse its 
Range and Distribution. 
 
   
(viii) Class-size:
Class size is the difference between the upper and the lower values of a class.
(ix) Class limits:
Class limits are the smallest and the largest observations (data, events, etc.) in a class.
(x) True class limits:
True class limits are the actual class limits of a class.
2. The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84,
58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60
(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second
group etc.
Now answer the following:
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?
Solution:
The given raw data can be arranged in an ascending order.
The class intervals are 30 – 39, 40 – 49, …, 100 – 109.
Then, take the raw data and place it in the appropriate class intervals.
(i) The marks can be arranged in an ascending order as shown below:
 
   
(ii) The Highest score is 100.
(iii) The Lowest score is 37.
(iv) The Range is 100 – 37 i.e., 63.
(v) If 40 is the passing mark, then the number of students who failed is 2 (i.e. 37, 39).
(vi) The number of students scoring 75 and above is 8 (i.e. 75, 77, 78, 84, 88, 90, 98,
100).
(vii) The marks 51, 54, and 57 do not actually appear between 50 and 60.
(viii) The number of students scoring less than 50 is 5 (i.e. 37, 39, 44, 48, 48).
3. The weights of new born babies (in kg) in a hospital on a particular day are as
follows:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
(i) Rearrange the weights in descending order.
(ii) Determine the highest weight.
(iii) Determine the lowest weight.
(iv) Determine the range.
(v) How many babies were born on that day?
(vi) How many babies weigh below 2.5 kg?
(vii) How many babies weigh more than 2.8 kg?
(viii) How many babies weigh 2.8 kg?
Solution:
(i) The weights of the newly born babies in descending order are as follows: 3.1, 3.0, 2.9,
2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.4, 2.4, 2.3, 2.2, 2.1
(ii) The highest weight is 3.1 kg
(iii) The lowest weight is 2.1 kg
(iv) The range is 3.1-2.1, i.e. 1 kg
(v) The number of babies born on that day is 15
(vi) The number of babies whose weights are below 2.5 kg is 4 (i.e. 2.4, 2.3, 2.2, 2.1)
 
   
(vii) The number of babies whose weights are more than 2.8 kg is 4 (i.e. 3.1, 3.0, 2.9, 2.9)
(viii) The number of babies whose weight is 2.8 kg is 2.
4. Following data gives the number of children in 41 families :
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 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:
The data can be put in the form of frequency distribution in the following manner:
Children No: of Families 
0 5 
1 7 
2 12 
3 5 
4 6 
5 3 
6 3 
5. Prepare a frequency table of the following scores obtained by 50 students in a
test:
42, 51, 21, 42, 37, 37, 42, 49, 38, 52, 7, 33, 17,44, 39, 7, 14, 27, 39, 42, 42, 62, 37, 39, 67,
51,53, 53, 59, 41, 29, 38, 27, 31, 54, 19, 53, 51, 22,61, 42, 39, 59, 47, 33, 34, 16, 37, 57,
43
Solution: The frequency table of 50 students is given below:
Marks No: of Students Marks No: of Students Marks No: of Students 
7 2 33 2 49 1 
14 1 34 1 51 3 
16 1 37 4 52 1 
17 1 38 2 53 3 
19 1 39 4 54 1 
21 1 41 1 57 1 
22 1 42 6 59 2 
27 2 43 1 61 1 
29 1 44 1 62 1 
31 1 47 1 67 1 
 
 
 
 
 
   
 
 
6. A die was thrown 25 times and following scores were obtained : 
1, 5, 2, 4, 3, 6, 1, 4, 2, 5, 1, 6, 2, 6, 3, 5, 4, 1, 3, 2, 3, 6, 1, 5, 2 
Prepare a frequency table of the scores. 
Solution: 
The frequency of the scores of the die is shown below: 
 
The Die Frequency 
1 5 
2 5 
3 4 
4 3 
5 4 
6 4 
 
7. In a study of number of accidents per day, the observations for 30 days were 
obtained as follows : 
6, 3, 5, 6, 4, 3, 2, 5, 4, 2, 4, 2, 1, 2, 2, 
0, 5, 4, 6, 1, 6, 0, 5, 3, 6, 1, 5, 5, 2, 6 
Prepare a frequency distribution table. 
Solution: 
Given that, 
6, 3, 5, 6, 4, 3, 2, 5, 4, 2, 4, 2, 1, 2, 2, 
0, 5, 4, 6, 1, 6, 0, 5, 3, 6, 1, 5, 5, 2, 6 
From the above set we can observe that 0 occurs for 2 times,1 occurs for 3times, 2 occurs 
for 6times, 3 occurs for 3times, 4 occurs for 4times, 5 occurs for 6times, 6 occurs for 6 
times. 
The frequency table for the number of accidents per day for a period of 30 days is shown 
below: 
Number of Accidents Frequency 
0 2 
1 3 
2 6 
3 3 
4 4 
5 6 
6 6 
 
8. Prepare a frequency table of the following ages (in years) of 30 students of class 
VIII in your school :