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

 Page 1


Q u e s t i o n : 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
S o l u t i o n :
i
Observation is the value at a particular period of a particular variable.
ii
Raw data is the data collected in its original form.
iii
Frequency of an observation is the number of times a certain value or a class of values occurs.
iv
Frequency distribution is the organisation of raw data in table form with classes and frequencies.
v
Discrete frequency distribution is a frequency distribution where sufficiently great numbers are grouped into one
class.
vi
Grouped frequency distribution is a frequency distribution where several numbers are grouped into one class.
vii
Class interval is the width of such a class. 
viii
Class size is the difference between the upper and the lower values of a class.
ix
Class limits are the smallest and the largest observations data, events, etc.
in a class.
x
True class limits are the actual class limits of a class.
Q u e s t i o n : 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?
Page 2


Q u e s t i o n : 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
S o l u t i o n :
i
Observation is the value at a particular period of a particular variable.
ii
Raw data is the data collected in its original form.
iii
Frequency of an observation is the number of times a certain value or a class of values occurs.
iv
Frequency distribution is the organisation of raw data in table form with classes and frequencies.
v
Discrete frequency distribution is a frequency distribution where sufficiently great numbers are grouped into one
class.
vi
Grouped frequency distribution is a frequency distribution where several numbers are grouped into one class.
vii
Class interval is the width of such a class. 
viii
Class size is the difference between the upper and the lower values of a class.
ix
Class limits are the smallest and the largest observations data, events, etc.
in a class.
x
True class limits are the actual class limits of a class.
Q u e s t i o n : 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?
S o l u t i o n :
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:
    30 to 39 ?
37, 39
    40 to 49 ?
44, 48, 48
    50 to 59 ?
50, 52, 53,
55, 56, 58, 58, 59
    60 to 69 ?
60, 60, 60, 61, 62, 64, 67, 68
    70 to 79 ?
70, 75, 77, 78
    80 to 89 ?
84, 88
    90 to 99 ?
90, 98
    100 to 109 ?
100
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
.
Q u e s t i o n : 3
The weights of new born babies inkg
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
Page 3


Q u e s t i o n : 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
S o l u t i o n :
i
Observation is the value at a particular period of a particular variable.
ii
Raw data is the data collected in its original form.
iii
Frequency of an observation is the number of times a certain value or a class of values occurs.
iv
Frequency distribution is the organisation of raw data in table form with classes and frequencies.
v
Discrete frequency distribution is a frequency distribution where sufficiently great numbers are grouped into one
class.
vi
Grouped frequency distribution is a frequency distribution where several numbers are grouped into one class.
vii
Class interval is the width of such a class. 
viii
Class size is the difference between the upper and the lower values of a class.
ix
Class limits are the smallest and the largest observations data, events, etc.
in a class.
x
True class limits are the actual class limits of a class.
Q u e s t i o n : 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?
S o l u t i o n :
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:
    30 to 39 ?
37, 39
    40 to 49 ?
44, 48, 48
    50 to 59 ?
50, 52, 53,
55, 56, 58, 58, 59
    60 to 69 ?
60, 60, 60, 61, 62, 64, 67, 68
    70 to 79 ?
70, 75, 77, 78
    80 to 89 ?
84, 88
    90 to 99 ?
90, 98
    100 to 109 ?
100
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
.
Q u e s t i o n : 3
The weights of new born babies inkg
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?
S o l u t i o n :
The frequency distribution of the weights of new born babies in a hospital on a particular day is represented in the
following table:
i
The weights of the newly born babies in descending order are as follows:
 
Weight Tally marks Frequency
3.1 I 1
3.0 I 1
2.9 II 2
2.8 II 2
2.7 II 2
2.6 I 1
2.5 II 2
2.4 I 1
2.3 I 1
2.2 I 1
2.1 I 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.
Page 4


Q u e s t i o n : 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
S o l u t i o n :
i
Observation is the value at a particular period of a particular variable.
ii
Raw data is the data collected in its original form.
iii
Frequency of an observation is the number of times a certain value or a class of values occurs.
iv
Frequency distribution is the organisation of raw data in table form with classes and frequencies.
v
Discrete frequency distribution is a frequency distribution where sufficiently great numbers are grouped into one
class.
vi
Grouped frequency distribution is a frequency distribution where several numbers are grouped into one class.
vii
Class interval is the width of such a class. 
viii
Class size is the difference between the upper and the lower values of a class.
ix
Class limits are the smallest and the largest observations data, events, etc.
in a class.
x
True class limits are the actual class limits of a class.
Q u e s t i o n : 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?
S o l u t i o n :
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:
    30 to 39 ?
37, 39
    40 to 49 ?
44, 48, 48
    50 to 59 ?
50, 52, 53,
55, 56, 58, 58, 59
    60 to 69 ?
60, 60, 60, 61, 62, 64, 67, 68
    70 to 79 ?
70, 75, 77, 78
    80 to 89 ?
84, 88
    90 to 99 ?
90, 98
    100 to 109 ?
100
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
.
Q u e s t i o n : 3
The weights of new born babies inkg
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?
S o l u t i o n :
The frequency distribution of the weights of new born babies in a hospital on a particular day is represented in the
following table:
i
The weights of the newly born babies in descending order are as follows:
 
Weight Tally marks Frequency
3.1 I 1
3.0 I 1
2.9 II 2
2.8 II 2
2.7 II 2
2.6 I 1
2.5 II 2
2.4 I 1
2.3 I 1
2.2 I 1
2.1 I 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.
Q u e s t i o n : 4
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, 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.
S o l u t i o n :
The data can be put in the form of frequency distribution in the following manner:
Number of Children Tally marks Frequency
0 |||| 5
1 |||| || 7
2 |||| |||| || 12
3 |||| 5
4 |||| | 6
5 ||| 3
6 ||| 3
Q u e s t i o n : 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, 64, 19, 53, 51, 22,
61, 42, 39, 59, 47, 33, 34, 16, 37, 57, 43,  
S o l u t i o n :
The frequency table of 50 students is given below:
Marks
Number of
Students
Marks
Number of
Students
Marks
Number 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
Q u e s t i o n : 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.
S o l u t i o n :
The frequency of the scores of the die is shown below:
The Die Tally Marks Frequency
1 |||| 5
2 |||| 5
3 |||| 4
4 ||| 3
5 |||| 4
Page 5


Q u e s t i o n : 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
S o l u t i o n :
i
Observation is the value at a particular period of a particular variable.
ii
Raw data is the data collected in its original form.
iii
Frequency of an observation is the number of times a certain value or a class of values occurs.
iv
Frequency distribution is the organisation of raw data in table form with classes and frequencies.
v
Discrete frequency distribution is a frequency distribution where sufficiently great numbers are grouped into one
class.
vi
Grouped frequency distribution is a frequency distribution where several numbers are grouped into one class.
vii
Class interval is the width of such a class. 
viii
Class size is the difference between the upper and the lower values of a class.
ix
Class limits are the smallest and the largest observations data, events, etc.
in a class.
x
True class limits are the actual class limits of a class.
Q u e s t i o n : 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?
S o l u t i o n :
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:
    30 to 39 ?
37, 39
    40 to 49 ?
44, 48, 48
    50 to 59 ?
50, 52, 53,
55, 56, 58, 58, 59
    60 to 69 ?
60, 60, 60, 61, 62, 64, 67, 68
    70 to 79 ?
70, 75, 77, 78
    80 to 89 ?
84, 88
    90 to 99 ?
90, 98
    100 to 109 ?
100
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
.
Q u e s t i o n : 3
The weights of new born babies inkg
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?
S o l u t i o n :
The frequency distribution of the weights of new born babies in a hospital on a particular day is represented in the
following table:
i
The weights of the newly born babies in descending order are as follows:
 
Weight Tally marks Frequency
3.1 I 1
3.0 I 1
2.9 II 2
2.8 II 2
2.7 II 2
2.6 I 1
2.5 II 2
2.4 I 1
2.3 I 1
2.2 I 1
2.1 I 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.
Q u e s t i o n : 4
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, 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.
S o l u t i o n :
The data can be put in the form of frequency distribution in the following manner:
Number of Children Tally marks Frequency
0 |||| 5
1 |||| || 7
2 |||| |||| || 12
3 |||| 5
4 |||| | 6
5 ||| 3
6 ||| 3
Q u e s t i o n : 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, 64, 19, 53, 51, 22,
61, 42, 39, 59, 47, 33, 34, 16, 37, 57, 43,  
S o l u t i o n :
The frequency table of 50 students is given below:
Marks
Number of
Students
Marks
Number of
Students
Marks
Number 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
Q u e s t i o n : 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.
S o l u t i o n :
The frequency of the scores of the die is shown below:
The Die Tally Marks Frequency
1 |||| 5
2 |||| 5
3 |||| 4
4 ||| 3
5 |||| 4
6 |||| 4
Q u e s t i o n : 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.
S o l u t i o n :
The frequency table for the number of accidents per day for a period of 30 days is given below:
Number of
Accidents
Tally Marks Frequency
0 || 2
1 ||| 3
2 |||| | 6
3 ||| 3
4 |||| 4
5 |||| | 6
6 |||| | 6
 
Q u e s t i o n : 8
Prepare a frequency table of the following ages inyears
of 30 students of class VIII in your school:
13, 14, 13, 12, 14, 13, 14, 15, 13, 14, 13, 14, 16, 12, 14, 13, 14, 15, 16, 13, 14, 13, 12, 17, 13, 12, 13, 13, 13, 14
S o l u t i o n :
The frequency table of the ages of 30 students of class VII in the school is given below:
Age Tally Marks Frequency
12 |||| 4
13 |||| |||| || 12
14 |||| |||| 9
15 || 2
16 || 2
17 | 1
Q u e s t i o n : 9
Following figures relate to the weekly wages inRs
of 15 workers in a factory:
300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250
Prepare a frequency table.
i
What is the range in wages inRs
?
ii
How many workers are getting Rs 350?
iii