NCERT Textbook: Data Handling

 Page 1


????? ???????? ? ? ? ?
4.1  Looking for Information
In your day-to-day life, you might have come across information, such as:
(a) Runs made by a batsman in the last 10 test matches.
(b) Number of wickets taken by a bowler in the last 10 ODIs.
(c) Marks scored by the students of your class in the Mathematics unit test.
(d) Number of story books read by each of your friends etc.
The information collected in all such cases is called data. Data is usually collected in
the context of a situation that we want to study . For example, a teacher may like to know
the average height of students in her class. To find this, she will write the heights of all the
students in her class, organise the data in a systematic manner and then interpret it
accordingly.
Sometimes, data is represented graphically to give a clear idea of what it represents.
Do you remember the different types of graphs which we have learnt in earlier classes?
1. A Pictograph: Pictorial representation of data using symbols.
? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
?
 = 100 cars ?  One symbol stands for 100 cars
July = 250            denotes 
1
2
of 100
August = 300
September = ?
(i) How many cars were produced in the month of July?
(ii) In which month were maximum number of cars produced?
2. A bar graph: A display of information using bars of uniform width, their heights being proportional to
the respective values.
Reprint 2024-25
Page 2


????? ???????? ? ? ? ?
4.1  Looking for Information
In your day-to-day life, you might have come across information, such as:
(a) Runs made by a batsman in the last 10 test matches.
(b) Number of wickets taken by a bowler in the last 10 ODIs.
(c) Marks scored by the students of your class in the Mathematics unit test.
(d) Number of story books read by each of your friends etc.
The information collected in all such cases is called data. Data is usually collected in
the context of a situation that we want to study . For example, a teacher may like to know
the average height of students in her class. To find this, she will write the heights of all the
students in her class, organise the data in a systematic manner and then interpret it
accordingly.
Sometimes, data is represented graphically to give a clear idea of what it represents.
Do you remember the different types of graphs which we have learnt in earlier classes?
1. A Pictograph: Pictorial representation of data using symbols.
? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
?
 = 100 cars ?  One symbol stands for 100 cars
July = 250            denotes 
1
2
of 100
August = 300
September = ?
(i) How many cars were produced in the month of July?
(ii) In which month were maximum number of cars produced?
2. A bar graph: A display of information using bars of uniform width, their heights being proportional to
the respective values.
Reprint 2024-25
??? ? ? ? ????? ????
(i) What is the information given by the bar graph?
(ii) In which year is the increase in the number of students maximum?
(iii) In which year is the number of students maximum?
(iv) State whether true or false:
‘The number of students during 2005-06 is twice that of 2003-04.’
3. Double Bar Graph: A bar graph showing two sets of data simultaneously . It is
useful for the comparison of the data.
(i) What is the information given by the double bar graph?
(ii) In which subject has the performance improved the most?
(iii) In which subject has the performance deteriorated?
(iv) In which subject is the performance at par?
Bar heights give the
quantity for each
category.
Bars are of equal width
with equal gaps in
between.
THINK, DISCUSS AND WRITE
If we change the position of any of the bars of a bar graph, would it change the
information being conveyed? Why?
Reprint 2024-25
Page 3


????? ???????? ? ? ? ?
4.1  Looking for Information
In your day-to-day life, you might have come across information, such as:
(a) Runs made by a batsman in the last 10 test matches.
(b) Number of wickets taken by a bowler in the last 10 ODIs.
(c) Marks scored by the students of your class in the Mathematics unit test.
(d) Number of story books read by each of your friends etc.
The information collected in all such cases is called data. Data is usually collected in
the context of a situation that we want to study . For example, a teacher may like to know
the average height of students in her class. To find this, she will write the heights of all the
students in her class, organise the data in a systematic manner and then interpret it
accordingly.
Sometimes, data is represented graphically to give a clear idea of what it represents.
Do you remember the different types of graphs which we have learnt in earlier classes?
1. A Pictograph: Pictorial representation of data using symbols.
? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
?
 = 100 cars ?  One symbol stands for 100 cars
July = 250            denotes 
1
2
of 100
August = 300
September = ?
(i) How many cars were produced in the month of July?
(ii) In which month were maximum number of cars produced?
2. A bar graph: A display of information using bars of uniform width, their heights being proportional to
the respective values.
Reprint 2024-25
??? ? ? ? ????? ????
(i) What is the information given by the bar graph?
(ii) In which year is the increase in the number of students maximum?
(iii) In which year is the number of students maximum?
(iv) State whether true or false:
‘The number of students during 2005-06 is twice that of 2003-04.’
3. Double Bar Graph: A bar graph showing two sets of data simultaneously . It is
useful for the comparison of the data.
(i) What is the information given by the double bar graph?
(ii) In which subject has the performance improved the most?
(iii) In which subject has the performance deteriorated?
(iv) In which subject is the performance at par?
Bar heights give the
quantity for each
category.
Bars are of equal width
with equal gaps in
between.
THINK, DISCUSS AND WRITE
If we change the position of any of the bars of a bar graph, would it change the
information being conveyed? Why?
Reprint 2024-25
????? ???????? ? ? ? ?
1. Month July August September October November December
Number of 1000 1500 1500 2000 2500 1500
watches sold
2. Children who prefer School  A School B School C
Walking 40 55 15
Cycling 45 25 35
3. Percentage wins in ODI by 8 top cricket teams.
Teams From Champions Last 10
Trophy to World Cup-06 ODI in 07
South Africa 75% 78%
Australia 61% 40%
Sri Lanka 54% 38%
New Zealand 47% 50%
England 46% 50%
Pakistan 45% 44%
West Indies 44% 30%
               India 43% 56%
TRY THESE
Draw an appropriate graph to represent the given information.
4.2  Circle Graph or Pie Chart
Have you ever come across data represented in circular form as shown (Fig 4.1)?
The time spent by a child during a day Age groups of people in a town
Fig 4.1 (i) (ii)
These are called circle graphs. A circle graph shows the relationship between a
whole and its parts. Here, the whole circle is divided into sectors. The size of each sector
is proportional to the activity or information it represents.
Reprint 2024-25
Page 4


????? ???????? ? ? ? ?
4.1  Looking for Information
In your day-to-day life, you might have come across information, such as:
(a) Runs made by a batsman in the last 10 test matches.
(b) Number of wickets taken by a bowler in the last 10 ODIs.
(c) Marks scored by the students of your class in the Mathematics unit test.
(d) Number of story books read by each of your friends etc.
The information collected in all such cases is called data. Data is usually collected in
the context of a situation that we want to study . For example, a teacher may like to know
the average height of students in her class. To find this, she will write the heights of all the
students in her class, organise the data in a systematic manner and then interpret it
accordingly.
Sometimes, data is represented graphically to give a clear idea of what it represents.
Do you remember the different types of graphs which we have learnt in earlier classes?
1. A Pictograph: Pictorial representation of data using symbols.
? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
?
 = 100 cars ?  One symbol stands for 100 cars
July = 250            denotes 
1
2
of 100
August = 300
September = ?
(i) How many cars were produced in the month of July?
(ii) In which month were maximum number of cars produced?
2. A bar graph: A display of information using bars of uniform width, their heights being proportional to
the respective values.
Reprint 2024-25
??? ? ? ? ????? ????
(i) What is the information given by the bar graph?
(ii) In which year is the increase in the number of students maximum?
(iii) In which year is the number of students maximum?
(iv) State whether true or false:
‘The number of students during 2005-06 is twice that of 2003-04.’
3. Double Bar Graph: A bar graph showing two sets of data simultaneously . It is
useful for the comparison of the data.
(i) What is the information given by the double bar graph?
(ii) In which subject has the performance improved the most?
(iii) In which subject has the performance deteriorated?
(iv) In which subject is the performance at par?
Bar heights give the
quantity for each
category.
Bars are of equal width
with equal gaps in
between.
THINK, DISCUSS AND WRITE
If we change the position of any of the bars of a bar graph, would it change the
information being conveyed? Why?
Reprint 2024-25
????? ???????? ? ? ? ?
1. Month July August September October November December
Number of 1000 1500 1500 2000 2500 1500
watches sold
2. Children who prefer School  A School B School C
Walking 40 55 15
Cycling 45 25 35
3. Percentage wins in ODI by 8 top cricket teams.
Teams From Champions Last 10
Trophy to World Cup-06 ODI in 07
South Africa 75% 78%
Australia 61% 40%
Sri Lanka 54% 38%
New Zealand 47% 50%
England 46% 50%
Pakistan 45% 44%
West Indies 44% 30%
               India 43% 56%
TRY THESE
Draw an appropriate graph to represent the given information.
4.2  Circle Graph or Pie Chart
Have you ever come across data represented in circular form as shown (Fig 4.1)?
The time spent by a child during a day Age groups of people in a town
Fig 4.1 (i) (ii)
These are called circle graphs. A circle graph shows the relationship between a
whole and its parts. Here, the whole circle is divided into sectors. The size of each sector
is proportional to the activity or information it represents.
Reprint 2024-25
??? ? ? ? ????? ????
For example, in the above graph, the proportion of the sector for hours spent in sleeping
= 
number of sleeping hours
whole day
 = 
8 hours 1
24 hours 3
=
So, this sector is drawn as 
1
rd
3
 part of the circle. Similarly, the proportion of the sector
for hours  spent in school = 
number of school hours
whole day
 = 
6 hours 1
24 hours 4
=
So this sector is drawn 
1
th
4
of  the circle. Similarly , the size of other sectors can be found .
Add up the fractions for all the activities . Do you get the total as one?
A circle graph is also called a pie chart.
TRY THESE
Fig 4.2
1. Each of the following pie charts (Fig 4.2) gives you a different piece of information about your class.
Find the fraction of the circle representing each of these information.
(i) (ii) (iii)
2. Answer the following questions based on the pie chart
given (Fig 4.3 ).
(i) Which type of programmes are viewed the most?
(ii) Which two types of programmes have number of
viewers equal to those watching sports channels?
Viewers watching different types
of channels on T.V .
4.2.1  Drawing pie charts
The favourite flavours of ice-creams for
students of a school is given in percentages
as follows.
Flavours Percentage of students
Preferring the flavours
Chocolate 50%
V anilla 25%
Other flavours 25%
Fig 4.3
Reprint 2024-25
Page 5


????? ???????? ? ? ? ?
4.1  Looking for Information
In your day-to-day life, you might have come across information, such as:
(a) Runs made by a batsman in the last 10 test matches.
(b) Number of wickets taken by a bowler in the last 10 ODIs.
(c) Marks scored by the students of your class in the Mathematics unit test.
(d) Number of story books read by each of your friends etc.
The information collected in all such cases is called data. Data is usually collected in
the context of a situation that we want to study . For example, a teacher may like to know
the average height of students in her class. To find this, she will write the heights of all the
students in her class, organise the data in a systematic manner and then interpret it
accordingly.
Sometimes, data is represented graphically to give a clear idea of what it represents.
Do you remember the different types of graphs which we have learnt in earlier classes?
1. A Pictograph: Pictorial representation of data using symbols.
? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ?
?
 = 100 cars ?  One symbol stands for 100 cars
July = 250            denotes 
1
2
of 100
August = 300
September = ?
(i) How many cars were produced in the month of July?
(ii) In which month were maximum number of cars produced?
2. A bar graph: A display of information using bars of uniform width, their heights being proportional to
the respective values.
Reprint 2024-25
??? ? ? ? ????? ????
(i) What is the information given by the bar graph?
(ii) In which year is the increase in the number of students maximum?
(iii) In which year is the number of students maximum?
(iv) State whether true or false:
‘The number of students during 2005-06 is twice that of 2003-04.’
3. Double Bar Graph: A bar graph showing two sets of data simultaneously . It is
useful for the comparison of the data.
(i) What is the information given by the double bar graph?
(ii) In which subject has the performance improved the most?
(iii) In which subject has the performance deteriorated?
(iv) In which subject is the performance at par?
Bar heights give the
quantity for each
category.
Bars are of equal width
with equal gaps in
between.
THINK, DISCUSS AND WRITE
If we change the position of any of the bars of a bar graph, would it change the
information being conveyed? Why?
Reprint 2024-25
????? ???????? ? ? ? ?
1. Month July August September October November December
Number of 1000 1500 1500 2000 2500 1500
watches sold
2. Children who prefer School  A School B School C
Walking 40 55 15
Cycling 45 25 35
3. Percentage wins in ODI by 8 top cricket teams.
Teams From Champions Last 10
Trophy to World Cup-06 ODI in 07
South Africa 75% 78%
Australia 61% 40%
Sri Lanka 54% 38%
New Zealand 47% 50%
England 46% 50%
Pakistan 45% 44%
West Indies 44% 30%
               India 43% 56%
TRY THESE
Draw an appropriate graph to represent the given information.
4.2  Circle Graph or Pie Chart
Have you ever come across data represented in circular form as shown (Fig 4.1)?
The time spent by a child during a day Age groups of people in a town
Fig 4.1 (i) (ii)
These are called circle graphs. A circle graph shows the relationship between a
whole and its parts. Here, the whole circle is divided into sectors. The size of each sector
is proportional to the activity or information it represents.
Reprint 2024-25
??? ? ? ? ????? ????
For example, in the above graph, the proportion of the sector for hours spent in sleeping
= 
number of sleeping hours
whole day
 = 
8 hours 1
24 hours 3
=
So, this sector is drawn as 
1
rd
3
 part of the circle. Similarly, the proportion of the sector
for hours  spent in school = 
number of school hours
whole day
 = 
6 hours 1
24 hours 4
=
So this sector is drawn 
1
th
4
of  the circle. Similarly , the size of other sectors can be found .
Add up the fractions for all the activities . Do you get the total as one?
A circle graph is also called a pie chart.
TRY THESE
Fig 4.2
1. Each of the following pie charts (Fig 4.2) gives you a different piece of information about your class.
Find the fraction of the circle representing each of these information.
(i) (ii) (iii)
2. Answer the following questions based on the pie chart
given (Fig 4.3 ).
(i) Which type of programmes are viewed the most?
(ii) Which two types of programmes have number of
viewers equal to those watching sports channels?
Viewers watching different types
of channels on T.V .
4.2.1  Drawing pie charts
The favourite flavours of ice-creams for
students of a school is given in percentages
as follows.
Flavours Percentage of students
Preferring the flavours
Chocolate 50%
V anilla 25%
Other flavours 25%
Fig 4.3
Reprint 2024-25
????? ???????? ? ? ? ?
Let us represent this data in a pie chart.
The total angle at the centre of a circle is 360°. The central angle of the sectors will be
a fraction of  360°. We make a table to find the central angle of the sectors (T able 4.1).
Table 4.1
Flavours Students in per cent In fractions Fraction of 360°
preferring the flavours
Chocolate 50%
50 1
100 2
=
1
2
 of 360° = 180°
V anilla 25%
25 1
100 4
=
1
4
 of  360° = 90°
Other flavours 25%
25 1
100 4
=
1
4
 of  360° = 90°
Fig 4.4
1. Draw a circle with any convenient radius.
Mark its centre (O) and a radius (OA).
2. The angle of the sector for chocolate is 180°.
Use the protractor to draw ?AOB = 180°.
3. Continue marking the remaining sectors.
Example 1: Adjoining pie chart (Fig 4.4) gives the expenditure (in percentage)
on various items and savings of a family during a month.
(i) On which item, the expenditure was maximum?
(ii) Expenditure on which item is equal to the total
savings of the family?
(iii) If the monthly savings of the family is ? 3000, what
is the monthly expenditure on clothes?
Solution:
(i) Expenditure is maximum on food.
(ii) Expenditure on Education of children is the same
(i.e., 15%) as the savings of the family .
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