NCERT Textbook Chapter 14 - Statistics, Mathematics, Class 9 Class 9 Notes | EduRev

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Class 9 : NCERT Textbook Chapter 14 - Statistics, Mathematics, Class 9 Class 9 Notes | EduRev

 Page 1


238 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
CHAPTER 14
STATISTICS
14.1 Introduction
Everyday we come across a wide variety of informations in the form of facts, numerical
figures, tables, graphs, etc. These are provided by newspapers, televisions, magazines
and other means of communication. These may relate to cricket batting or bowling
averages, profits of a company, temperatures of cities, expenditures in various sectors
of a five year plan, polling results, and so on. These facts or figures, which are numerical
or otherwise, collected with a definite purpose are called data. Data is the plural form
of the Latin word datum. Of course, the word ‘data’ is not new for you. You have
studied about data and data handling in earlier classes.
Our world is becoming more and more information oriented. Every part of our
lives utilises data in one form or the other. So, it becomes essential for us to know how
to extract meaningful information from such data. This  extraction of meaningful
information is studied in a branch of mathematics called Statistics.
The word ‘statistics’ appears to have been derived from the Latin word ‘status’
meaning ‘a (political) state’. In its origin, statistics was simply the collection of data on
different aspects of the life of people, useful to the State. Over the period of time,
however, its scope broadened and statistics began to concern itself not only with the
collection and presentation of data but also with the interpretation and drawing of
inferences from the data. Statistics deals with collection, organisation, analysis and
interpretation of data. The word ‘statistics’ has different meanings in different contexts.
Let us observe the following sentences:
1. May I have the latest copy of ‘Educational Statistics of India’.
2. I like to study ‘Statistics’ because it is used in day-to-day life.
In the first sentence, statistics is used in a plural sense, meaning numerical data. These
may include a number of educational institutions of India, literacy rates of various
Page 2


238 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
CHAPTER 14
STATISTICS
14.1 Introduction
Everyday we come across a wide variety of informations in the form of facts, numerical
figures, tables, graphs, etc. These are provided by newspapers, televisions, magazines
and other means of communication. These may relate to cricket batting or bowling
averages, profits of a company, temperatures of cities, expenditures in various sectors
of a five year plan, polling results, and so on. These facts or figures, which are numerical
or otherwise, collected with a definite purpose are called data. Data is the plural form
of the Latin word datum. Of course, the word ‘data’ is not new for you. You have
studied about data and data handling in earlier classes.
Our world is becoming more and more information oriented. Every part of our
lives utilises data in one form or the other. So, it becomes essential for us to know how
to extract meaningful information from such data. This  extraction of meaningful
information is studied in a branch of mathematics called Statistics.
The word ‘statistics’ appears to have been derived from the Latin word ‘status’
meaning ‘a (political) state’. In its origin, statistics was simply the collection of data on
different aspects of the life of people, useful to the State. Over the period of time,
however, its scope broadened and statistics began to concern itself not only with the
collection and presentation of data but also with the interpretation and drawing of
inferences from the data. Statistics deals with collection, organisation, analysis and
interpretation of data. The word ‘statistics’ has different meanings in different contexts.
Let us observe the following sentences:
1. May I have the latest copy of ‘Educational Statistics of India’.
2. I like to study ‘Statistics’ because it is used in day-to-day life.
In the first sentence, statistics is used in a plural sense, meaning numerical data. These
may include a number of educational institutions of India, literacy rates of various
ST A TISTICS 239
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
states, etc. In the second sentence, the word ‘statistics’ is used as a singular noun,
meaning the subject which deals with the collection, presentation, analysis of data as
well as drawing of meaningful conclusions from the data.
In this chapter, we shall briefly discuss all these aspects regarding data.
14.2 Collection of Data
Let us begin with an exercise on gathering data by performing the following activity.
Activity 1 : Divide the students of your class into four groups. Allot each group the
work of collecting one of the following kinds of data:
(i) Heights of 20 students of your class.
(ii) Number of absentees in each day in your class for a month.
(iii) Number of members in the families of your classmates.
(iv) Heights of 15 plants in or around your school.
Let us move to the results students have gathered. How did they collect their data
in each group?
(i) Did they collect the information from each and every student, house or person
concerned for obtaining the information?
(ii) Did they get the information from some source like available school records?
In the first case, when the information was collected by the investigator herself or
himself with a definite objective in her or his mind, the data obtained is called primary
data.
In the second case, when the information was gathered from a source which
already had the information  stored, the data obtained is called secondary data. Such
data, which has been collected by someone else in another context, needs to be used
with great care ensuring that the source is reliable.
By now, you must have understood how to collect data and distinguish between
primary and secondary data.
EXERCISE 14.1
1. Give five examples of data that you can collect from your day-to-day life.
2. Classify the data in Q.1 above as primary or secondary data.
Page 3


238 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
CHAPTER 14
STATISTICS
14.1 Introduction
Everyday we come across a wide variety of informations in the form of facts, numerical
figures, tables, graphs, etc. These are provided by newspapers, televisions, magazines
and other means of communication. These may relate to cricket batting or bowling
averages, profits of a company, temperatures of cities, expenditures in various sectors
of a five year plan, polling results, and so on. These facts or figures, which are numerical
or otherwise, collected with a definite purpose are called data. Data is the plural form
of the Latin word datum. Of course, the word ‘data’ is not new for you. You have
studied about data and data handling in earlier classes.
Our world is becoming more and more information oriented. Every part of our
lives utilises data in one form or the other. So, it becomes essential for us to know how
to extract meaningful information from such data. This  extraction of meaningful
information is studied in a branch of mathematics called Statistics.
The word ‘statistics’ appears to have been derived from the Latin word ‘status’
meaning ‘a (political) state’. In its origin, statistics was simply the collection of data on
different aspects of the life of people, useful to the State. Over the period of time,
however, its scope broadened and statistics began to concern itself not only with the
collection and presentation of data but also with the interpretation and drawing of
inferences from the data. Statistics deals with collection, organisation, analysis and
interpretation of data. The word ‘statistics’ has different meanings in different contexts.
Let us observe the following sentences:
1. May I have the latest copy of ‘Educational Statistics of India’.
2. I like to study ‘Statistics’ because it is used in day-to-day life.
In the first sentence, statistics is used in a plural sense, meaning numerical data. These
may include a number of educational institutions of India, literacy rates of various
ST A TISTICS 239
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
states, etc. In the second sentence, the word ‘statistics’ is used as a singular noun,
meaning the subject which deals with the collection, presentation, analysis of data as
well as drawing of meaningful conclusions from the data.
In this chapter, we shall briefly discuss all these aspects regarding data.
14.2 Collection of Data
Let us begin with an exercise on gathering data by performing the following activity.
Activity 1 : Divide the students of your class into four groups. Allot each group the
work of collecting one of the following kinds of data:
(i) Heights of 20 students of your class.
(ii) Number of absentees in each day in your class for a month.
(iii) Number of members in the families of your classmates.
(iv) Heights of 15 plants in or around your school.
Let us move to the results students have gathered. How did they collect their data
in each group?
(i) Did they collect the information from each and every student, house or person
concerned for obtaining the information?
(ii) Did they get the information from some source like available school records?
In the first case, when the information was collected by the investigator herself or
himself with a definite objective in her or his mind, the data obtained is called primary
data.
In the second case, when the information was gathered from a source which
already had the information  stored, the data obtained is called secondary data. Such
data, which has been collected by someone else in another context, needs to be used
with great care ensuring that the source is reliable.
By now, you must have understood how to collect data and distinguish between
primary and secondary data.
EXERCISE 14.1
1. Give five examples of data that you can collect from your day-to-day life.
2. Classify the data in Q.1 above as primary or secondary data.
240 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
14.3 Presentation of Data
As soon as the work related to collection of data is over, the investigator has to find out
ways to present them in a form which is meaningful, easily understood and gives its
main features at a glance. Let us now recall the various ways of presenting the data
through some examples.
Example 1 : Consider the marks obtained by 10 students in a mathematics test as
given below:
55 36 95 73 60 42 25 78 75 62
The data in this form is called raw data.
By looking at it in this form, can you find the highest and the lowest marks?
Did it take you some time to search for the maximum and minimum scores? Wouldn’t
it be less time consuming if these scores were arranged in ascending or descending
order? So let us arrange the marks in ascending order as
25 36 42 55 60 62 73 75 78 95
Now, we can clearly see that the lowest marks are 25 and the highest marks are 95.
The difference of the highest and the lowest values in the data is called the range of the
data. So, the range in this case is 95 – 25 = 70.
Presentation of data in ascending or descending order can be quite time consuming,
particularly when the number of observations in an experiment is large, as in the case
of the next example.
Example 2 : Consider the marks obtained (out of 100 marks) by 30 students of Class
IX of a school:
10 20 36 92 95 40 50 56 60 70
92 88 80 70 72 70 36 40 36 40
92 40 50 50 56 60 70 60 60 88
Recall that the number of students who have obtained a certain number of marks is
called the frequency of those marks. For instance, 4 students got 70 marks. So the
frequency of 70 marks is 4. To make the data more easily understandable, we write it
Page 4


238 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
CHAPTER 14
STATISTICS
14.1 Introduction
Everyday we come across a wide variety of informations in the form of facts, numerical
figures, tables, graphs, etc. These are provided by newspapers, televisions, magazines
and other means of communication. These may relate to cricket batting or bowling
averages, profits of a company, temperatures of cities, expenditures in various sectors
of a five year plan, polling results, and so on. These facts or figures, which are numerical
or otherwise, collected with a definite purpose are called data. Data is the plural form
of the Latin word datum. Of course, the word ‘data’ is not new for you. You have
studied about data and data handling in earlier classes.
Our world is becoming more and more information oriented. Every part of our
lives utilises data in one form or the other. So, it becomes essential for us to know how
to extract meaningful information from such data. This  extraction of meaningful
information is studied in a branch of mathematics called Statistics.
The word ‘statistics’ appears to have been derived from the Latin word ‘status’
meaning ‘a (political) state’. In its origin, statistics was simply the collection of data on
different aspects of the life of people, useful to the State. Over the period of time,
however, its scope broadened and statistics began to concern itself not only with the
collection and presentation of data but also with the interpretation and drawing of
inferences from the data. Statistics deals with collection, organisation, analysis and
interpretation of data. The word ‘statistics’ has different meanings in different contexts.
Let us observe the following sentences:
1. May I have the latest copy of ‘Educational Statistics of India’.
2. I like to study ‘Statistics’ because it is used in day-to-day life.
In the first sentence, statistics is used in a plural sense, meaning numerical data. These
may include a number of educational institutions of India, literacy rates of various
ST A TISTICS 239
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
states, etc. In the second sentence, the word ‘statistics’ is used as a singular noun,
meaning the subject which deals with the collection, presentation, analysis of data as
well as drawing of meaningful conclusions from the data.
In this chapter, we shall briefly discuss all these aspects regarding data.
14.2 Collection of Data
Let us begin with an exercise on gathering data by performing the following activity.
Activity 1 : Divide the students of your class into four groups. Allot each group the
work of collecting one of the following kinds of data:
(i) Heights of 20 students of your class.
(ii) Number of absentees in each day in your class for a month.
(iii) Number of members in the families of your classmates.
(iv) Heights of 15 plants in or around your school.
Let us move to the results students have gathered. How did they collect their data
in each group?
(i) Did they collect the information from each and every student, house or person
concerned for obtaining the information?
(ii) Did they get the information from some source like available school records?
In the first case, when the information was collected by the investigator herself or
himself with a definite objective in her or his mind, the data obtained is called primary
data.
In the second case, when the information was gathered from a source which
already had the information  stored, the data obtained is called secondary data. Such
data, which has been collected by someone else in another context, needs to be used
with great care ensuring that the source is reliable.
By now, you must have understood how to collect data and distinguish between
primary and secondary data.
EXERCISE 14.1
1. Give five examples of data that you can collect from your day-to-day life.
2. Classify the data in Q.1 above as primary or secondary data.
240 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
14.3 Presentation of Data
As soon as the work related to collection of data is over, the investigator has to find out
ways to present them in a form which is meaningful, easily understood and gives its
main features at a glance. Let us now recall the various ways of presenting the data
through some examples.
Example 1 : Consider the marks obtained by 10 students in a mathematics test as
given below:
55 36 95 73 60 42 25 78 75 62
The data in this form is called raw data.
By looking at it in this form, can you find the highest and the lowest marks?
Did it take you some time to search for the maximum and minimum scores? Wouldn’t
it be less time consuming if these scores were arranged in ascending or descending
order? So let us arrange the marks in ascending order as
25 36 42 55 60 62 73 75 78 95
Now, we can clearly see that the lowest marks are 25 and the highest marks are 95.
The difference of the highest and the lowest values in the data is called the range of the
data. So, the range in this case is 95 – 25 = 70.
Presentation of data in ascending or descending order can be quite time consuming,
particularly when the number of observations in an experiment is large, as in the case
of the next example.
Example 2 : Consider the marks obtained (out of 100 marks) by 30 students of Class
IX of a school:
10 20 36 92 95 40 50 56 60 70
92 88 80 70 72 70 36 40 36 40
92 40 50 50 56 60 70 60 60 88
Recall that the number of students who have obtained a certain number of marks is
called the frequency of those marks. For instance, 4 students got 70 marks. So the
frequency of 70 marks is 4. To make the data more easily understandable, we write it
ST A TISTICS 241
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
in a table, as given below:
Table 14.1
Marks Number of students
(i.e., the frequency)
10 1
20 1
36 3
40 4
50 3
56 2
60 4
70 4
72 1
80 1
88 2
92 3
95 1
Total 30
Table 14.1 is called an ungrouped frequency distribution table, or simply a frequency
distribution table. Note that you can use also tally marks in preparing these tables,
as in the next example.
Example 3 : 100 plants each were planted in 100 schools during Van Mahotsava.
After one month, the number of plants that survived were recorded as :
95 67 28 32 65 65 69 33 98 96
76 42 32 38 42 40 40 69 95 92
75 83 76 83 85 62 37 65 63 42
89 65 73 81 49 52 64 76 83 92
93 68 52 79 81 83 59 82 75 82
86 90 44 62 31 36 38 42 39 83
87 56 58 23 35 76 83 85 30 68
69 83 86 43 45 39 83 75 66 83
92 75 89 66 91 27 88 89 93 42
53 69 90 55 66 49 52 83 34 36
Page 5


238 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
CHAPTER 14
STATISTICS
14.1 Introduction
Everyday we come across a wide variety of informations in the form of facts, numerical
figures, tables, graphs, etc. These are provided by newspapers, televisions, magazines
and other means of communication. These may relate to cricket batting or bowling
averages, profits of a company, temperatures of cities, expenditures in various sectors
of a five year plan, polling results, and so on. These facts or figures, which are numerical
or otherwise, collected with a definite purpose are called data. Data is the plural form
of the Latin word datum. Of course, the word ‘data’ is not new for you. You have
studied about data and data handling in earlier classes.
Our world is becoming more and more information oriented. Every part of our
lives utilises data in one form or the other. So, it becomes essential for us to know how
to extract meaningful information from such data. This  extraction of meaningful
information is studied in a branch of mathematics called Statistics.
The word ‘statistics’ appears to have been derived from the Latin word ‘status’
meaning ‘a (political) state’. In its origin, statistics was simply the collection of data on
different aspects of the life of people, useful to the State. Over the period of time,
however, its scope broadened and statistics began to concern itself not only with the
collection and presentation of data but also with the interpretation and drawing of
inferences from the data. Statistics deals with collection, organisation, analysis and
interpretation of data. The word ‘statistics’ has different meanings in different contexts.
Let us observe the following sentences:
1. May I have the latest copy of ‘Educational Statistics of India’.
2. I like to study ‘Statistics’ because it is used in day-to-day life.
In the first sentence, statistics is used in a plural sense, meaning numerical data. These
may include a number of educational institutions of India, literacy rates of various
ST A TISTICS 239
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
states, etc. In the second sentence, the word ‘statistics’ is used as a singular noun,
meaning the subject which deals with the collection, presentation, analysis of data as
well as drawing of meaningful conclusions from the data.
In this chapter, we shall briefly discuss all these aspects regarding data.
14.2 Collection of Data
Let us begin with an exercise on gathering data by performing the following activity.
Activity 1 : Divide the students of your class into four groups. Allot each group the
work of collecting one of the following kinds of data:
(i) Heights of 20 students of your class.
(ii) Number of absentees in each day in your class for a month.
(iii) Number of members in the families of your classmates.
(iv) Heights of 15 plants in or around your school.
Let us move to the results students have gathered. How did they collect their data
in each group?
(i) Did they collect the information from each and every student, house or person
concerned for obtaining the information?
(ii) Did they get the information from some source like available school records?
In the first case, when the information was collected by the investigator herself or
himself with a definite objective in her or his mind, the data obtained is called primary
data.
In the second case, when the information was gathered from a source which
already had the information  stored, the data obtained is called secondary data. Such
data, which has been collected by someone else in another context, needs to be used
with great care ensuring that the source is reliable.
By now, you must have understood how to collect data and distinguish between
primary and secondary data.
EXERCISE 14.1
1. Give five examples of data that you can collect from your day-to-day life.
2. Classify the data in Q.1 above as primary or secondary data.
240 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
14.3 Presentation of Data
As soon as the work related to collection of data is over, the investigator has to find out
ways to present them in a form which is meaningful, easily understood and gives its
main features at a glance. Let us now recall the various ways of presenting the data
through some examples.
Example 1 : Consider the marks obtained by 10 students in a mathematics test as
given below:
55 36 95 73 60 42 25 78 75 62
The data in this form is called raw data.
By looking at it in this form, can you find the highest and the lowest marks?
Did it take you some time to search for the maximum and minimum scores? Wouldn’t
it be less time consuming if these scores were arranged in ascending or descending
order? So let us arrange the marks in ascending order as
25 36 42 55 60 62 73 75 78 95
Now, we can clearly see that the lowest marks are 25 and the highest marks are 95.
The difference of the highest and the lowest values in the data is called the range of the
data. So, the range in this case is 95 – 25 = 70.
Presentation of data in ascending or descending order can be quite time consuming,
particularly when the number of observations in an experiment is large, as in the case
of the next example.
Example 2 : Consider the marks obtained (out of 100 marks) by 30 students of Class
IX of a school:
10 20 36 92 95 40 50 56 60 70
92 88 80 70 72 70 36 40 36 40
92 40 50 50 56 60 70 60 60 88
Recall that the number of students who have obtained a certain number of marks is
called the frequency of those marks. For instance, 4 students got 70 marks. So the
frequency of 70 marks is 4. To make the data more easily understandable, we write it
ST A TISTICS 241
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
in a table, as given below:
Table 14.1
Marks Number of students
(i.e., the frequency)
10 1
20 1
36 3
40 4
50 3
56 2
60 4
70 4
72 1
80 1
88 2
92 3
95 1
Total 30
Table 14.1 is called an ungrouped frequency distribution table, or simply a frequency
distribution table. Note that you can use also tally marks in preparing these tables,
as in the next example.
Example 3 : 100 plants each were planted in 100 schools during Van Mahotsava.
After one month, the number of plants that survived were recorded as :
95 67 28 32 65 65 69 33 98 96
76 42 32 38 42 40 40 69 95 92
75 83 76 83 85 62 37 65 63 42
89 65 73 81 49 52 64 76 83 92
93 68 52 79 81 83 59 82 75 82
86 90 44 62 31 36 38 42 39 83
87 56 58 23 35 76 83 85 30 68
69 83 86 43 45 39 83 75 66 83
92 75 89 66 91 27 88 89 93 42
53 69 90 55 66 49 52 83 34 36
242 MATHEMA TICS
File Name : C:\Computer Station\Maths-IX\Chapter\Chap-14\Chap-14 (02-01-2006).PM65
To present such a large amount of data so that a reader can make sense of it easily,
we condense it into groups like 20-29, 30-39, . . ., 90-99 (since our data is from
23 to 98). These groupings are called ‘classes’ or ‘class-intervals’, and their size is
called the class-size or class width, which is 10 in this case. In each of these classes,
the least number is called the lower class limit and the greatest number is called the
upper class limit, e.g., in 20-29, 20 is the ‘lower class limit’ and 29 is the ‘upper class
limit’.
Also, recall that using tally marks, the data above can be condensed in tabular
form as follows:
Table 14.2
Number of plants Tally Marks Number of schools
survived (frequency)
20 - 29 ||| 3
30 - 39 |||| |||| |||| 14
40 - 49 |||| |||| || 12
50 - 59 |||| ||| 8
60 - 69 |||| |||| |||| ||| 18
70 - 79 |||| |||| 10
80 - 89 |||| |||| |||| |||| ||| 23
90 - 99 |||| |||| || 12
Total 100
Presenting data in this form simplifies and condenses data and enables us to observe
certain important features at a glance. This is called a grouped frequency distribution
table. Here we can easily observe that 50% or more plants survived in 8 + 18 + 10 +
23 + 12 = 71 schools.
We observe that the classes in the table above are non-overlapping. Note that we
could have made more classes of shorter size, or fewer classes of larger size also. For
instance, the intervals could have been 22-26, 27-31, and so on. So, there is no hard
and fast rule about this except that the classes should not overlap.
Example 4 : Let us now consider the following frequency distribution table which
gives the weights of 38 students of a class:
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