Tabular Representation of Statistical Data- 1 RD Sharma Solutions | Mathematics (Maths) Class 9 PDF Download

 Page 1


Question:1
What do you understand by the word ''statistics'' in
i
singular form       ii
plural form?
Solution:
i In singular form statistics may be defined as the science of collection, presentation, analysis and interpretation of
numerical data.
ii In plural form statistics means numerical facts or observations collected with definite purpose.
For examples, the income and expenditure of persons in a particular locality, number of males and females in a
particular town are statistics.
Question:2
Describe some fundamental characteristic of statistics.
Solution:
The plural form statistics has the simplest structure and the singular form statistics has many components. There
is only structural difference between singular and plural form statistics. Some of the characteristics of a statistics
are
1. Statistics is a collection of observations. So, clearly a single observation cannot form a statistics.
2. Statistics are collected with definite purpose.
3. Statistics are comparable and classified into various types depending on their properties.
4. Statistics are expressed quantitatively and not qualitatively. 
Question:3
What are i
primary data? ii
secondary data? Which of the two - the primary or the secondary data - is more reliable and why?
Solution:
i When an investigator collects data himself with a definite plan or designs in his
her mind, it is called primary data.
ii Data which are not originally collected rather obtained from published or unpublished sources are known as
secondary data.
 
Question:4
Why do we group data?
Solution:
To study the features of a collected data, the data must be arranged in a condensed form. There are a number of
ways to arrange the data in condensed form, namely,
1. Serial order or alphabetical order
Page 2


Question:1
What do you understand by the word ''statistics'' in
i
singular form       ii
plural form?
Solution:
i In singular form statistics may be defined as the science of collection, presentation, analysis and interpretation of
numerical data.
ii In plural form statistics means numerical facts or observations collected with definite purpose.
For examples, the income and expenditure of persons in a particular locality, number of males and females in a
particular town are statistics.
Question:2
Describe some fundamental characteristic of statistics.
Solution:
The plural form statistics has the simplest structure and the singular form statistics has many components. There
is only structural difference between singular and plural form statistics. Some of the characteristics of a statistics
are
1. Statistics is a collection of observations. So, clearly a single observation cannot form a statistics.
2. Statistics are collected with definite purpose.
3. Statistics are comparable and classified into various types depending on their properties.
4. Statistics are expressed quantitatively and not qualitatively. 
Question:3
What are i
primary data? ii
secondary data? Which of the two - the primary or the secondary data - is more reliable and why?
Solution:
i When an investigator collects data himself with a definite plan or designs in his
her mind, it is called primary data.
ii Data which are not originally collected rather obtained from published or unpublished sources are known as
secondary data.
 
Question:4
Why do we group data?
Solution:
To study the features of a collected data, the data must be arranged in a condensed form. There are a number of
ways to arrange the data in condensed form, namely,
1. Serial order or alphabetical order
2. Ascending order
3. Descending order
But, if the number of observations is large, then arranging data in ascending or descending or serial order is a
tedious job and it does not tell us much except perhaps the minimums
and maximums
of data. So to make it easily understandable and clear we condense the data into groups or table form.
Question:5
Explain the meaning of the following terms:
i
variate
ii
class-integral
iii
class-size
iv
class-mark
v
frequency
vi
class limits
vii
true class limits.
Solution:
i A name which takes different values is called variates. For example, the mark obtained by students of class IX in
mathematics is variates.
ii In a grouped data, the groups are called class-intervals. For example, 0-5, 5-10, 10-15… are class intervals.
iii The difference between the true upper limit and the true lower limit of a class is called its class size. For
example, the class size of the class-interval 10-15 is
iv The mid value of a class is called the class mark. For example, the mid value of the class 10-15 is
v The number of observation falling in a particular class is called the frequency of that class or class frequency.
For example, if the number of students obtaining marks 60-70 in a particular subject is 60, then the frequency of the
class 60-70 is 60.
vi Class limits are the boundaries of a class. The left boundary of a class is called the lower limit and the right
boundary of a class is called the upper limit. For example, for the class interval 60-70 the lower limit is 60 and the
upper limit is 70.
vii The class limits of a continuous grouped frequency distribution are called true class limits. For example, 5-10,
10-15, 15-20, 20-25, 25-30 are continuous class intervals, then the true lower and upper limits
classlimits of the class 15-20 are 15 and 20 respectively. If the classes are not continuous, then adjust the class
Page 3


Question:1
What do you understand by the word ''statistics'' in
i
singular form       ii
plural form?
Solution:
i In singular form statistics may be defined as the science of collection, presentation, analysis and interpretation of
numerical data.
ii In plural form statistics means numerical facts or observations collected with definite purpose.
For examples, the income and expenditure of persons in a particular locality, number of males and females in a
particular town are statistics.
Question:2
Describe some fundamental characteristic of statistics.
Solution:
The plural form statistics has the simplest structure and the singular form statistics has many components. There
is only structural difference between singular and plural form statistics. Some of the characteristics of a statistics
are
1. Statistics is a collection of observations. So, clearly a single observation cannot form a statistics.
2. Statistics are collected with definite purpose.
3. Statistics are comparable and classified into various types depending on their properties.
4. Statistics are expressed quantitatively and not qualitatively. 
Question:3
What are i
primary data? ii
secondary data? Which of the two - the primary or the secondary data - is more reliable and why?
Solution:
i When an investigator collects data himself with a definite plan or designs in his
her mind, it is called primary data.
ii Data which are not originally collected rather obtained from published or unpublished sources are known as
secondary data.
 
Question:4
Why do we group data?
Solution:
To study the features of a collected data, the data must be arranged in a condensed form. There are a number of
ways to arrange the data in condensed form, namely,
1. Serial order or alphabetical order
2. Ascending order
3. Descending order
But, if the number of observations is large, then arranging data in ascending or descending or serial order is a
tedious job and it does not tell us much except perhaps the minimums
and maximums
of data. So to make it easily understandable and clear we condense the data into groups or table form.
Question:5
Explain the meaning of the following terms:
i
variate
ii
class-integral
iii
class-size
iv
class-mark
v
frequency
vi
class limits
vii
true class limits.
Solution:
i A name which takes different values is called variates. For example, the mark obtained by students of class IX in
mathematics is variates.
ii In a grouped data, the groups are called class-intervals. For example, 0-5, 5-10, 10-15… are class intervals.
iii The difference between the true upper limit and the true lower limit of a class is called its class size. For
example, the class size of the class-interval 10-15 is
iv The mid value of a class is called the class mark. For example, the mid value of the class 10-15 is
v The number of observation falling in a particular class is called the frequency of that class or class frequency.
For example, if the number of students obtaining marks 60-70 in a particular subject is 60, then the frequency of the
class 60-70 is 60.
vi Class limits are the boundaries of a class. The left boundary of a class is called the lower limit and the right
boundary of a class is called the upper limit. For example, for the class interval 60-70 the lower limit is 60 and the
upper limit is 70.
vii The class limits of a continuous grouped frequency distribution are called true class limits. For example, 5-10,
10-15, 15-20, 20-25, 25-30 are continuous class intervals, then the true lower and upper limits
classlimits of the class 15-20 are 15 and 20 respectively. If the classes are not continuous, then adjust the class
intervals to form continuous grouped class intervals.
Question:6
The ages of ten students of a group are given below. The ages have been recorded in years and months:
8 - 6, 9 - 0, 8 - 0,4, 9 - 3, 7 - 8, 8 - 11, 8 - 7, 9 - 2, 7 - 10, 8 - 8
i
What is the lowest age?
ii
What is the highest age?
iii
Determine the range?
Solution:
After arranging in ascending order, the ages of the students are 7 years 8 months, 7 years 10 months, 8 years 4
months, 8 years 6 months, 8 years 7 months, 8 years 8 months, 8 years 11 months, 9 years, 9 years 2 months, and
9 years 3 months.
i The lowest age is 7 years 8 months.
ii The highest age is 9 years 3 months.
iii The range of the ages is
Question:7
The monthly pocket money of six friends is given below:
Rs 45, Rs 30, Rs 50, Rs 25, Rs 45
a
What is the highest pocket money?
b
What is the lowest pocket money?
c
What is the range?
d
Arrange the amounts of pocket money in ascending order.
Solution:
i After arranging in ascending order, the pocket money’s in Rs. are 25, 30, 40, 45, 45 and 50. The highest pocket
money is Rs 50.
ii The lowest pocket money is Rs 25.
iii The range of the pocket money’s is
iv The given data
Page 4


Question:1
What do you understand by the word ''statistics'' in
i
singular form       ii
plural form?
Solution:
i In singular form statistics may be defined as the science of collection, presentation, analysis and interpretation of
numerical data.
ii In plural form statistics means numerical facts or observations collected with definite purpose.
For examples, the income and expenditure of persons in a particular locality, number of males and females in a
particular town are statistics.
Question:2
Describe some fundamental characteristic of statistics.
Solution:
The plural form statistics has the simplest structure and the singular form statistics has many components. There
is only structural difference between singular and plural form statistics. Some of the characteristics of a statistics
are
1. Statistics is a collection of observations. So, clearly a single observation cannot form a statistics.
2. Statistics are collected with definite purpose.
3. Statistics are comparable and classified into various types depending on their properties.
4. Statistics are expressed quantitatively and not qualitatively. 
Question:3
What are i
primary data? ii
secondary data? Which of the two - the primary or the secondary data - is more reliable and why?
Solution:
i When an investigator collects data himself with a definite plan or designs in his
her mind, it is called primary data.
ii Data which are not originally collected rather obtained from published or unpublished sources are known as
secondary data.
 
Question:4
Why do we group data?
Solution:
To study the features of a collected data, the data must be arranged in a condensed form. There are a number of
ways to arrange the data in condensed form, namely,
1. Serial order or alphabetical order
2. Ascending order
3. Descending order
But, if the number of observations is large, then arranging data in ascending or descending or serial order is a
tedious job and it does not tell us much except perhaps the minimums
and maximums
of data. So to make it easily understandable and clear we condense the data into groups or table form.
Question:5
Explain the meaning of the following terms:
i
variate
ii
class-integral
iii
class-size
iv
class-mark
v
frequency
vi
class limits
vii
true class limits.
Solution:
i A name which takes different values is called variates. For example, the mark obtained by students of class IX in
mathematics is variates.
ii In a grouped data, the groups are called class-intervals. For example, 0-5, 5-10, 10-15… are class intervals.
iii The difference between the true upper limit and the true lower limit of a class is called its class size. For
example, the class size of the class-interval 10-15 is
iv The mid value of a class is called the class mark. For example, the mid value of the class 10-15 is
v The number of observation falling in a particular class is called the frequency of that class or class frequency.
For example, if the number of students obtaining marks 60-70 in a particular subject is 60, then the frequency of the
class 60-70 is 60.
vi Class limits are the boundaries of a class. The left boundary of a class is called the lower limit and the right
boundary of a class is called the upper limit. For example, for the class interval 60-70 the lower limit is 60 and the
upper limit is 70.
vii The class limits of a continuous grouped frequency distribution are called true class limits. For example, 5-10,
10-15, 15-20, 20-25, 25-30 are continuous class intervals, then the true lower and upper limits
classlimits of the class 15-20 are 15 and 20 respectively. If the classes are not continuous, then adjust the class
intervals to form continuous grouped class intervals.
Question:6
The ages of ten students of a group are given below. The ages have been recorded in years and months:
8 - 6, 9 - 0, 8 - 0,4, 9 - 3, 7 - 8, 8 - 11, 8 - 7, 9 - 2, 7 - 10, 8 - 8
i
What is the lowest age?
ii
What is the highest age?
iii
Determine the range?
Solution:
After arranging in ascending order, the ages of the students are 7 years 8 months, 7 years 10 months, 8 years 4
months, 8 years 6 months, 8 years 7 months, 8 years 8 months, 8 years 11 months, 9 years, 9 years 2 months, and
9 years 3 months.
i The lowest age is 7 years 8 months.
ii The highest age is 9 years 3 months.
iii The range of the ages is
Question:7
The monthly pocket money of six friends is given below:
Rs 45, Rs 30, Rs 50, Rs 25, Rs 45
a
What is the highest pocket money?
b
What is the lowest pocket money?
c
What is the range?
d
Arrange the amounts of pocket money in ascending order.
Solution:
i After arranging in ascending order, the pocket money’s in Rs. are 25, 30, 40, 45, 45 and 50. The highest pocket
money is Rs 50.
ii The lowest pocket money is Rs 25.
iii The range of the pocket money’s is
iv The given data
pocketmoneyinRs. in ascending order is 25, 30, 40, 45, 45 and 50.
Question:8
Write the class-size in each of the following:
a
0-4, 5-9, 10-14
b
10-19, 20-29, 30-39
c
100-120, 120-140, 160-180
d
0-0.25, 0.25-0, 0.50-0.75
e
5-5.01, 5.01-5.02, 5.02-5.03
Solution:
i The given classes are 0-4, 5-9 and 10-14. The classes can be written in continuous form as
-0.5-4.5, 4.5-9.5, and 9.5-14.5. The upper and lower limits of the first class are 4.5 and
-0.5 respectively. Hence, the class size is
ii The given classes are 10-19, 20-29, and 30-39. The classes can be written in continuous form as 9.5-19.5, 19.5-
29.5, 29.5-39.5. The upper and lower limits of the first class are 19.5 and 9.5 respectively. Hence, the class size is
iii The given classes are 100-120, 120-140, 160-180, are in continuous form. The upper and lower limits of the first
class are 120 and 100 respectively. Hence, the class size is
iv The given classes are 0-0.25, 0.25-0.50, 0.50-0.75, are in continuous form. The upper and lower limits of the first
class are 0.25 and 0 respectively. Hence, the class size is
v The given classes are 5-5.01, 5.01-5.02, 5.02-5.03, are in continuous form. The upper and lower limits of the first
class are 5.01 and 5 respectively. Hence, the class size is
Page 5


Question:1
What do you understand by the word ''statistics'' in
i
singular form       ii
plural form?
Solution:
i In singular form statistics may be defined as the science of collection, presentation, analysis and interpretation of
numerical data.
ii In plural form statistics means numerical facts or observations collected with definite purpose.
For examples, the income and expenditure of persons in a particular locality, number of males and females in a
particular town are statistics.
Question:2
Describe some fundamental characteristic of statistics.
Solution:
The plural form statistics has the simplest structure and the singular form statistics has many components. There
is only structural difference between singular and plural form statistics. Some of the characteristics of a statistics
are
1. Statistics is a collection of observations. So, clearly a single observation cannot form a statistics.
2. Statistics are collected with definite purpose.
3. Statistics are comparable and classified into various types depending on their properties.
4. Statistics are expressed quantitatively and not qualitatively. 
Question:3
What are i
primary data? ii
secondary data? Which of the two - the primary or the secondary data - is more reliable and why?
Solution:
i When an investigator collects data himself with a definite plan or designs in his
her mind, it is called primary data.
ii Data which are not originally collected rather obtained from published or unpublished sources are known as
secondary data.
 
Question:4
Why do we group data?
Solution:
To study the features of a collected data, the data must be arranged in a condensed form. There are a number of
ways to arrange the data in condensed form, namely,
1. Serial order or alphabetical order
2. Ascending order
3. Descending order
But, if the number of observations is large, then arranging data in ascending or descending or serial order is a
tedious job and it does not tell us much except perhaps the minimums
and maximums
of data. So to make it easily understandable and clear we condense the data into groups or table form.
Question:5
Explain the meaning of the following terms:
i
variate
ii
class-integral
iii
class-size
iv
class-mark
v
frequency
vi
class limits
vii
true class limits.
Solution:
i A name which takes different values is called variates. For example, the mark obtained by students of class IX in
mathematics is variates.
ii In a grouped data, the groups are called class-intervals. For example, 0-5, 5-10, 10-15… are class intervals.
iii The difference between the true upper limit and the true lower limit of a class is called its class size. For
example, the class size of the class-interval 10-15 is
iv The mid value of a class is called the class mark. For example, the mid value of the class 10-15 is
v The number of observation falling in a particular class is called the frequency of that class or class frequency.
For example, if the number of students obtaining marks 60-70 in a particular subject is 60, then the frequency of the
class 60-70 is 60.
vi Class limits are the boundaries of a class. The left boundary of a class is called the lower limit and the right
boundary of a class is called the upper limit. For example, for the class interval 60-70 the lower limit is 60 and the
upper limit is 70.
vii The class limits of a continuous grouped frequency distribution are called true class limits. For example, 5-10,
10-15, 15-20, 20-25, 25-30 are continuous class intervals, then the true lower and upper limits
classlimits of the class 15-20 are 15 and 20 respectively. If the classes are not continuous, then adjust the class
intervals to form continuous grouped class intervals.
Question:6
The ages of ten students of a group are given below. The ages have been recorded in years and months:
8 - 6, 9 - 0, 8 - 0,4, 9 - 3, 7 - 8, 8 - 11, 8 - 7, 9 - 2, 7 - 10, 8 - 8
i
What is the lowest age?
ii
What is the highest age?
iii
Determine the range?
Solution:
After arranging in ascending order, the ages of the students are 7 years 8 months, 7 years 10 months, 8 years 4
months, 8 years 6 months, 8 years 7 months, 8 years 8 months, 8 years 11 months, 9 years, 9 years 2 months, and
9 years 3 months.
i The lowest age is 7 years 8 months.
ii The highest age is 9 years 3 months.
iii The range of the ages is
Question:7
The monthly pocket money of six friends is given below:
Rs 45, Rs 30, Rs 50, Rs 25, Rs 45
a
What is the highest pocket money?
b
What is the lowest pocket money?
c
What is the range?
d
Arrange the amounts of pocket money in ascending order.
Solution:
i After arranging in ascending order, the pocket money’s in Rs. are 25, 30, 40, 45, 45 and 50. The highest pocket
money is Rs 50.
ii The lowest pocket money is Rs 25.
iii The range of the pocket money’s is
iv The given data
pocketmoneyinRs. in ascending order is 25, 30, 40, 45, 45 and 50.
Question:8
Write the class-size in each of the following:
a
0-4, 5-9, 10-14
b
10-19, 20-29, 30-39
c
100-120, 120-140, 160-180
d
0-0.25, 0.25-0, 0.50-0.75
e
5-5.01, 5.01-5.02, 5.02-5.03
Solution:
i The given classes are 0-4, 5-9 and 10-14. The classes can be written in continuous form as
-0.5-4.5, 4.5-9.5, and 9.5-14.5. The upper and lower limits of the first class are 4.5 and
-0.5 respectively. Hence, the class size is
ii The given classes are 10-19, 20-29, and 30-39. The classes can be written in continuous form as 9.5-19.5, 19.5-
29.5, 29.5-39.5. The upper and lower limits of the first class are 19.5 and 9.5 respectively. Hence, the class size is
iii The given classes are 100-120, 120-140, 160-180, are in continuous form. The upper and lower limits of the first
class are 120 and 100 respectively. Hence, the class size is
iv The given classes are 0-0.25, 0.25-0.50, 0.50-0.75, are in continuous form. The upper and lower limits of the first
class are 0.25 and 0 respectively. Hence, the class size is
v The given classes are 5-5.01, 5.01-5.02, 5.02-5.03, are in continuous form. The upper and lower limits of the first
class are 5.01 and 5 respectively. Hence, the class size is
Question:9
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:
i The frequency distribution table of grouped frequency such as 30-39, 40-49… is the following:
ii The highest score is 100.
iii The lowest score is 37.
iv The range of the scores is
v If 40 is the pass mark, then the number of students failed is 2.
vi The number of students scored more than 75 is 8.
vii The observations 51, 54 and 57 in between 50-60 have not actually appeared.
viii Number of students scored less than 50 is 5.