RS Aggarwal Solutions: Presentation of Data in Tabular Form | Mathematics (Maths) Class 9 PDF Download

 Page 1


Question:1
Define statistics as a subject.
Solution:
Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data.
Question:2
Define some fundamental characteristics of statistics.
Solution:
The fundamental characteristics of data statistics
are as follows:
i
Numerical facts alone constitute data.
ii
Qualitative characteristics like intelligence and poverty, which cannot be measured numerically, do not form data.
iii
Data are aggregate of facts. A single observation does not form data.
iv
Data collected for a definite purpose may not be suited for another purpose.
v
Data in different experiments are comparable.
Question:3
What are primary data and secondary data? Which of the two is more reliable and why?
Solution:
Primary data: The data collected by the investigator himself with a definite plan in mind are known as primary data.
Secondary data: The data collected by someone other than the investigator are known as secondary data.
Primary data are highly reliable and relevant because they are collected by the investigator himself with a definite plan in
mind,  whereas secondary data are collected with a purpose different from that of the investigator and may not be fully relevant
to the investigation.
Question:4
Explain the meaning of each of the following terms:
i
Variate
ii
Class interval
iii
Class size
iv
Class mark
v
Class limit
vi
True class limits
vii
Frequency of a class
viii
Cumulative frequency of a class
Solution:
i
Variate : Any character which is capable of taking several different values is called a variant or a variable.
ii
Class interval : Each group into which the raw data is condensed is called class interval .
iii
Class size: The difference between the true upper limit and the true lower limit of a class is called its class size.
iv
( )
Page 2


Question:1
Define statistics as a subject.
Solution:
Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data.
Question:2
Define some fundamental characteristics of statistics.
Solution:
The fundamental characteristics of data statistics
are as follows:
i
Numerical facts alone constitute data.
ii
Qualitative characteristics like intelligence and poverty, which cannot be measured numerically, do not form data.
iii
Data are aggregate of facts. A single observation does not form data.
iv
Data collected for a definite purpose may not be suited for another purpose.
v
Data in different experiments are comparable.
Question:3
What are primary data and secondary data? Which of the two is more reliable and why?
Solution:
Primary data: The data collected by the investigator himself with a definite plan in mind are known as primary data.
Secondary data: The data collected by someone other than the investigator are known as secondary data.
Primary data are highly reliable and relevant because they are collected by the investigator himself with a definite plan in
mind,  whereas secondary data are collected with a purpose different from that of the investigator and may not be fully relevant
to the investigation.
Question:4
Explain the meaning of each of the following terms:
i
Variate
ii
Class interval
iii
Class size
iv
Class mark
v
Class limit
vi
True class limits
vii
Frequency of a class
viii
Cumulative frequency of a class
Solution:
i
Variate : Any character which is capable of taking several different values is called a variant or a variable.
ii
Class interval : Each group into which the raw data is condensed is called class interval .
iii
Class size: The difference between the true upper limit and the true lower limit of a class is called its class size.
iv
( )
Class mark of a class: The class mark is given by 
Upper limit+Lower limit
2
.
v
Class limit: Each class is bounded by two figures, which are called class limits.
vi
True class limits: In the exclusive form, the upper and lower limits of a class are respectively known as true upper limit and
true lower limit.
In the inclusive form of frequency distribution, the true lower limit of a class is obtained by subtracting 0.5 from the lower limit
and the true upper limit of the class is obtained by adding 0.5 to the upper limit.
vii
Frequency of a class: Frequency of a class is the number of times an observation occurs in that class.
viii
Cumulative frequency of a class: Cummulative frequency of a class is the sum total of all the frequencies up to and including
that class.
Question:5
The blood groups of 30 students of a class are recorded as under:
A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
i
Represent this data in the form of a frequency distribution table.
ii
Find out which is the most common and which is the rarest blood group among these students.
Solution:
i
 
Blood group tally marks Number of students
A 9
B 6
O 12
AB 3
ii
AB is rarest and O is most common. 
Question:6
Three coins are tossed 30 times. Each time the number of heads occurring was noted down as follows:
0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 0, 3, 0, 2, 1, 1, 3, 2, 0, 2.
Prepare a frequency distribution table.
Solution:
Number of heads tally marks Frequency
0 6
1 10
2 9
3 5
Question:7
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, taking classes 0-2, 1-4, etc.
Solution:
The minimum observation is 0 and the maximum observation is 8.
Therefore, classes of  the same size covering the given data are 0-2, 2-4, 4-6 and 6-8.          .
( )
Page 3


Question:1
Define statistics as a subject.
Solution:
Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data.
Question:2
Define some fundamental characteristics of statistics.
Solution:
The fundamental characteristics of data statistics
are as follows:
i
Numerical facts alone constitute data.
ii
Qualitative characteristics like intelligence and poverty, which cannot be measured numerically, do not form data.
iii
Data are aggregate of facts. A single observation does not form data.
iv
Data collected for a definite purpose may not be suited for another purpose.
v
Data in different experiments are comparable.
Question:3
What are primary data and secondary data? Which of the two is more reliable and why?
Solution:
Primary data: The data collected by the investigator himself with a definite plan in mind are known as primary data.
Secondary data: The data collected by someone other than the investigator are known as secondary data.
Primary data are highly reliable and relevant because they are collected by the investigator himself with a definite plan in
mind,  whereas secondary data are collected with a purpose different from that of the investigator and may not be fully relevant
to the investigation.
Question:4
Explain the meaning of each of the following terms:
i
Variate
ii
Class interval
iii
Class size
iv
Class mark
v
Class limit
vi
True class limits
vii
Frequency of a class
viii
Cumulative frequency of a class
Solution:
i
Variate : Any character which is capable of taking several different values is called a variant or a variable.
ii
Class interval : Each group into which the raw data is condensed is called class interval .
iii
Class size: The difference between the true upper limit and the true lower limit of a class is called its class size.
iv
( )
Class mark of a class: The class mark is given by 
Upper limit+Lower limit
2
.
v
Class limit: Each class is bounded by two figures, which are called class limits.
vi
True class limits: In the exclusive form, the upper and lower limits of a class are respectively known as true upper limit and
true lower limit.
In the inclusive form of frequency distribution, the true lower limit of a class is obtained by subtracting 0.5 from the lower limit
and the true upper limit of the class is obtained by adding 0.5 to the upper limit.
vii
Frequency of a class: Frequency of a class is the number of times an observation occurs in that class.
viii
Cumulative frequency of a class: Cummulative frequency of a class is the sum total of all the frequencies up to and including
that class.
Question:5
The blood groups of 30 students of a class are recorded as under:
A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
i
Represent this data in the form of a frequency distribution table.
ii
Find out which is the most common and which is the rarest blood group among these students.
Solution:
i
 
Blood group tally marks Number of students
A 9
B 6
O 12
AB 3
ii
AB is rarest and O is most common. 
Question:6
Three coins are tossed 30 times. Each time the number of heads occurring was noted down as follows:
0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 0, 3, 0, 2, 1, 1, 3, 2, 0, 2.
Prepare a frequency distribution table.
Solution:
Number of heads tally marks Frequency
0 6
1 10
2 9
3 5
Question:7
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, taking classes 0-2, 1-4, etc.
Solution:
The minimum observation is 0 and the maximum observation is 8.
Therefore, classes of  the same size covering the given data are 0-2, 2-4, 4-6 and 6-8.          .
( )
Frequency distribution table:
        Class              Tally mark         Frequency
        0-2
 
           11
        2-4           17
        4-6            9
        6-8            3
Question:8
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were
found as under:
8, 4, 8, 5, 1, 6, 2, 5, 3, 12, 3, 10, 4, 12, 2, 8, 15, 1, 6, 17, 5, 8, 2, 3, 9, 6, 7, 8, 14, 12.
i
Make a grouped frequency distribution table for this data, taking class width 5 and one of the class interval as 5 –10.
ii
How many children watched television for 15 or more hours a week?
Solution:
i
 
Class interval tally marks Frequency
0-5 10
5-10 13
10-15 5
15-20 2
ii
As we can see from the table, there are 2 children who watched tv for 15 hours or more. 
Question:9
The marks obtained by 40 students of a class in an examination are given below.
3,20,13,1,21,13,3,23,16,13,18,12,5,12,5,24,9,2,7,18,20,3,10,12,7,18,2,5,7,10,16,8,16,17,8,23,24,6,23, 15.
Present the data in the form of a frequency distribution using equal class size, one such class being 10-15
15notincluded.
Solution:
The minimum observation is 0 and the maximum observation is 25.
Therefore, classes of the same size covering the given data are 0-5, 5-10, 10-15, 15-20 and 20-25.
Frequency distribution table:
                 Class Tally mark Frequency
                  0-5        6
                5-10      10
               10-15        8
               15-20        8
               20-25        8
Question:10
Construct a frequency table for the following ages inyears
of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.
18,12,7,6,11,15,21,9,8,13,15,17,22,19,14,21,23,8,12,17,15,6,18,23,22,16,9,21,11,16.
Solution:
The minimum observation is 6 and the maximum observation is 24.
Therefore, classes of the same size covering the given data are 6-9, 9-12, 12-15, 15-18, 18-21 and 21-24.
Frequency distribution table:
Page 4


Question:1
Define statistics as a subject.
Solution:
Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data.
Question:2
Define some fundamental characteristics of statistics.
Solution:
The fundamental characteristics of data statistics
are as follows:
i
Numerical facts alone constitute data.
ii
Qualitative characteristics like intelligence and poverty, which cannot be measured numerically, do not form data.
iii
Data are aggregate of facts. A single observation does not form data.
iv
Data collected for a definite purpose may not be suited for another purpose.
v
Data in different experiments are comparable.
Question:3
What are primary data and secondary data? Which of the two is more reliable and why?
Solution:
Primary data: The data collected by the investigator himself with a definite plan in mind are known as primary data.
Secondary data: The data collected by someone other than the investigator are known as secondary data.
Primary data are highly reliable and relevant because they are collected by the investigator himself with a definite plan in
mind,  whereas secondary data are collected with a purpose different from that of the investigator and may not be fully relevant
to the investigation.
Question:4
Explain the meaning of each of the following terms:
i
Variate
ii
Class interval
iii
Class size
iv
Class mark
v
Class limit
vi
True class limits
vii
Frequency of a class
viii
Cumulative frequency of a class
Solution:
i
Variate : Any character which is capable of taking several different values is called a variant or a variable.
ii
Class interval : Each group into which the raw data is condensed is called class interval .
iii
Class size: The difference between the true upper limit and the true lower limit of a class is called its class size.
iv
( )
Class mark of a class: The class mark is given by 
Upper limit+Lower limit
2
.
v
Class limit: Each class is bounded by two figures, which are called class limits.
vi
True class limits: In the exclusive form, the upper and lower limits of a class are respectively known as true upper limit and
true lower limit.
In the inclusive form of frequency distribution, the true lower limit of a class is obtained by subtracting 0.5 from the lower limit
and the true upper limit of the class is obtained by adding 0.5 to the upper limit.
vii
Frequency of a class: Frequency of a class is the number of times an observation occurs in that class.
viii
Cumulative frequency of a class: Cummulative frequency of a class is the sum total of all the frequencies up to and including
that class.
Question:5
The blood groups of 30 students of a class are recorded as under:
A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
i
Represent this data in the form of a frequency distribution table.
ii
Find out which is the most common and which is the rarest blood group among these students.
Solution:
i
 
Blood group tally marks Number of students
A 9
B 6
O 12
AB 3
ii
AB is rarest and O is most common. 
Question:6
Three coins are tossed 30 times. Each time the number of heads occurring was noted down as follows:
0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 0, 3, 0, 2, 1, 1, 3, 2, 0, 2.
Prepare a frequency distribution table.
Solution:
Number of heads tally marks Frequency
0 6
1 10
2 9
3 5
Question:7
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, taking classes 0-2, 1-4, etc.
Solution:
The minimum observation is 0 and the maximum observation is 8.
Therefore, classes of  the same size covering the given data are 0-2, 2-4, 4-6 and 6-8.          .
( )
Frequency distribution table:
        Class              Tally mark         Frequency
        0-2
 
           11
        2-4           17
        4-6            9
        6-8            3
Question:8
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were
found as under:
8, 4, 8, 5, 1, 6, 2, 5, 3, 12, 3, 10, 4, 12, 2, 8, 15, 1, 6, 17, 5, 8, 2, 3, 9, 6, 7, 8, 14, 12.
i
Make a grouped frequency distribution table for this data, taking class width 5 and one of the class interval as 5 –10.
ii
How many children watched television for 15 or more hours a week?
Solution:
i
 
Class interval tally marks Frequency
0-5 10
5-10 13
10-15 5
15-20 2
ii
As we can see from the table, there are 2 children who watched tv for 15 hours or more. 
Question:9
The marks obtained by 40 students of a class in an examination are given below.
3,20,13,1,21,13,3,23,16,13,18,12,5,12,5,24,9,2,7,18,20,3,10,12,7,18,2,5,7,10,16,8,16,17,8,23,24,6,23, 15.
Present the data in the form of a frequency distribution using equal class size, one such class being 10-15
15notincluded.
Solution:
The minimum observation is 0 and the maximum observation is 25.
Therefore, classes of the same size covering the given data are 0-5, 5-10, 10-15, 15-20 and 20-25.
Frequency distribution table:
                 Class Tally mark Frequency
                  0-5        6
                5-10      10
               10-15        8
               15-20        8
               20-25        8
Question:10
Construct a frequency table for the following ages inyears
of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.
18,12,7,6,11,15,21,9,8,13,15,17,22,19,14,21,23,8,12,17,15,6,18,23,22,16,9,21,11,16.
Solution:
The minimum observation is 6 and the maximum observation is 24.
Therefore, classes of the same size covering the given data are 6-9, 9-12, 12-15, 15-18, 18-21 and 21-24.
Frequency distribution table:
         Class           Tally mark         Frequency
          6-9
             
               5
         9-12
              
               4
       12-15
              
               4
       15-18
              
               7
       18-21
              
               3
       21-24
              
               7
Question:11
Construct a frequency table with equal class intervals from the following data on the monthly wages inrupees
of 28 labourers working in a factory, taking one of the class intervals as 210-230
230notincluded.
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 minimum observation is 210 and the maximum observation is 330.
Therefore, classes of the same size covering the given data are 210-230, 230-250,250-270,270-290,290-310 and 310-330.
Frequency distribution table:
 
            Class       Tally mark          Frequency
           210-230
            
               4
           230-250
            
               4
          250-270
           
               5
          270-290
             
               3
          290-310
           
               7
          310-330
           
               5
Question:12
The weights ingrams
of 40 oranges picked at random from a basket are as follows:
40,50,60,65,45,55,30,90,75,85,70,85,75,80,100,110,70,55,30,35,45,70,80,85,95,70,60,70,75,100,65,60,40,100,75,110,30,45,84.
Construct a frequency table as well as a cumulative frequency table.
Solution:
The minimum observation is 30 and the maximum observation is 120.
                                                
Frequency distribution table:
           Class                Tally mark           Frequency
30-40
                    
                4
40-50
                   
                6
50-60
                    
                3
60-70
                   
                5
70-80
                   
                9
80-90
                    
                6
90-100
                      
                2
100-110
                    
                3
110-120
                     
                2
                                     
Cumulative frequency table:
   Class   Tally mark   Frequency     Cumulative frequency
Page 5


Question:1
Define statistics as a subject.
Solution:
Statistics is the science which deals with the collection, presentation, analysis and interpretation of numerical data.
Question:2
Define some fundamental characteristics of statistics.
Solution:
The fundamental characteristics of data statistics
are as follows:
i
Numerical facts alone constitute data.
ii
Qualitative characteristics like intelligence and poverty, which cannot be measured numerically, do not form data.
iii
Data are aggregate of facts. A single observation does not form data.
iv
Data collected for a definite purpose may not be suited for another purpose.
v
Data in different experiments are comparable.
Question:3
What are primary data and secondary data? Which of the two is more reliable and why?
Solution:
Primary data: The data collected by the investigator himself with a definite plan in mind are known as primary data.
Secondary data: The data collected by someone other than the investigator are known as secondary data.
Primary data are highly reliable and relevant because they are collected by the investigator himself with a definite plan in
mind,  whereas secondary data are collected with a purpose different from that of the investigator and may not be fully relevant
to the investigation.
Question:4
Explain the meaning of each of the following terms:
i
Variate
ii
Class interval
iii
Class size
iv
Class mark
v
Class limit
vi
True class limits
vii
Frequency of a class
viii
Cumulative frequency of a class
Solution:
i
Variate : Any character which is capable of taking several different values is called a variant or a variable.
ii
Class interval : Each group into which the raw data is condensed is called class interval .
iii
Class size: The difference between the true upper limit and the true lower limit of a class is called its class size.
iv
( )
Class mark of a class: The class mark is given by 
Upper limit+Lower limit
2
.
v
Class limit: Each class is bounded by two figures, which are called class limits.
vi
True class limits: In the exclusive form, the upper and lower limits of a class are respectively known as true upper limit and
true lower limit.
In the inclusive form of frequency distribution, the true lower limit of a class is obtained by subtracting 0.5 from the lower limit
and the true upper limit of the class is obtained by adding 0.5 to the upper limit.
vii
Frequency of a class: Frequency of a class is the number of times an observation occurs in that class.
viii
Cumulative frequency of a class: Cummulative frequency of a class is the sum total of all the frequencies up to and including
that class.
Question:5
The blood groups of 30 students of a class are recorded as under:
A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
i
Represent this data in the form of a frequency distribution table.
ii
Find out which is the most common and which is the rarest blood group among these students.
Solution:
i
 
Blood group tally marks Number of students
A 9
B 6
O 12
AB 3
ii
AB is rarest and O is most common. 
Question:6
Three coins are tossed 30 times. Each time the number of heads occurring was noted down as follows:
0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 0, 3, 0, 2, 1, 1, 3, 2, 0, 2.
Prepare a frequency distribution table.
Solution:
Number of heads tally marks Frequency
0 6
1 10
2 9
3 5
Question:7
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, taking classes 0-2, 1-4, etc.
Solution:
The minimum observation is 0 and the maximum observation is 8.
Therefore, classes of  the same size covering the given data are 0-2, 2-4, 4-6 and 6-8.          .
( )
Frequency distribution table:
        Class              Tally mark         Frequency
        0-2
 
           11
        2-4           17
        4-6            9
        6-8            3
Question:8
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were
found as under:
8, 4, 8, 5, 1, 6, 2, 5, 3, 12, 3, 10, 4, 12, 2, 8, 15, 1, 6, 17, 5, 8, 2, 3, 9, 6, 7, 8, 14, 12.
i
Make a grouped frequency distribution table for this data, taking class width 5 and one of the class interval as 5 –10.
ii
How many children watched television for 15 or more hours a week?
Solution:
i
 
Class interval tally marks Frequency
0-5 10
5-10 13
10-15 5
15-20 2
ii
As we can see from the table, there are 2 children who watched tv for 15 hours or more. 
Question:9
The marks obtained by 40 students of a class in an examination are given below.
3,20,13,1,21,13,3,23,16,13,18,12,5,12,5,24,9,2,7,18,20,3,10,12,7,18,2,5,7,10,16,8,16,17,8,23,24,6,23, 15.
Present the data in the form of a frequency distribution using equal class size, one such class being 10-15
15notincluded.
Solution:
The minimum observation is 0 and the maximum observation is 25.
Therefore, classes of the same size covering the given data are 0-5, 5-10, 10-15, 15-20 and 20-25.
Frequency distribution table:
                 Class Tally mark Frequency
                  0-5        6
                5-10      10
               10-15        8
               15-20        8
               20-25        8
Question:10
Construct a frequency table for the following ages inyears
of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.
18,12,7,6,11,15,21,9,8,13,15,17,22,19,14,21,23,8,12,17,15,6,18,23,22,16,9,21,11,16.
Solution:
The minimum observation is 6 and the maximum observation is 24.
Therefore, classes of the same size covering the given data are 6-9, 9-12, 12-15, 15-18, 18-21 and 21-24.
Frequency distribution table:
         Class           Tally mark         Frequency
          6-9
             
               5
         9-12
              
               4
       12-15
              
               4
       15-18
              
               7
       18-21
              
               3
       21-24
              
               7
Question:11
Construct a frequency table with equal class intervals from the following data on the monthly wages inrupees
of 28 labourers working in a factory, taking one of the class intervals as 210-230
230notincluded.
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 minimum observation is 210 and the maximum observation is 330.
Therefore, classes of the same size covering the given data are 210-230, 230-250,250-270,270-290,290-310 and 310-330.
Frequency distribution table:
 
            Class       Tally mark          Frequency
           210-230
            
               4
           230-250
            
               4
          250-270
           
               5
          270-290
             
               3
          290-310
           
               7
          310-330
           
               5
Question:12
The weights ingrams
of 40 oranges picked at random from a basket are as follows:
40,50,60,65,45,55,30,90,75,85,70,85,75,80,100,110,70,55,30,35,45,70,80,85,95,70,60,70,75,100,65,60,40,100,75,110,30,45,84.
Construct a frequency table as well as a cumulative frequency table.
Solution:
The minimum observation is 30 and the maximum observation is 120.
                                                
Frequency distribution table:
           Class                Tally mark           Frequency
30-40
                    
                4
40-50
                   
                6
50-60
                    
                3
60-70
                   
                5
70-80
                   
                9
80-90
                    
                6
90-100
                      
                2
100-110
                    
                3
110-120
                     
                2
                                     
Cumulative frequency table:
   Class   Tally mark   Frequency     Cumulative frequency
30-40
         
           4                  4
40-50
        
           6                 10
50-60
         
           3                 13
60-70 
       
           5                 18
70-80
    
           9                 27
80-90
      
           6                 33
90-100
         
           2                 35
100-110
        
           3                 38
110-120
         
           2                 40
Question:13
The heights inAnscm
of 30 students of a class are given below:
161, 155, 159, 153, 150, 158, 154, 158, 160, 148, 149, 162, 163, 159, 148,
153, 157, 151, 154, 157, 153, 156, 152, 156, 160, 152, 147, 155, 155, 157.
Prepare a frequency table as well as a cumulative frequency table with 160 – 165  165notincluded
as one of the class intervals.
Solution:
Class tally marks Frequency Cumulative frequency
145-150 4 4
150-155 9 4 + 9 = 13
155-160 12 13 + 12 = 25
160-165 5 25 + 5 = 30
Question:14
Following are the ages inyears
of 360 patients, getting medical treatment in a hospital:
Ages inyears 10-20 20-30 30-40 40-50 50-60 60-70
Number of patients 90 50 60 80 50 30
Construct the cumulative frequency table for the above data.
Solution:
The cumulative frequency table can be presented as given below:
 
      Age inyears No. of patients     Cumulative frequency
          10-20 90                90         
          20-30 50       140
          30-40 60        200
          40-50 80        280
          50-60 50        330
          60-70 30        360
Question:15
Present the following as an ordinary grouped frequency table:
Marks below 10 20 30 40 50 60
Number of students 5 12 32 40 45 48
Solution:
The grouped frequency table can be presented as given below: