NCERT Textbook- Introduction to Graphs Class 8 Notes | EduRev

Mathematics (Maths) Class 8

Created by: Indu Gupta

Class 8 : NCERT Textbook- Introduction to Graphs Class 8 Notes | EduRev

 Page 1


 INTRODUCTION TO GRAPHS  231
15.1  Introduction
Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose
of the graph is to show numerical facts in visual form so that they can be understood
quickly , easily and clearly . Thus graphs are visual representations of data collected. Data
can also be presented in the form of a table; however a graphical presentation is easier to
understand. This is true in particular when there is a trend or comparison to be shown.
W e have already seen some types of graphs. Let us quickly recall them here.
15.1.1  A Bar graph
A bar graph is used to show comparison among categories. It may consist of two or more
parallel vertical (or horizontal) bars (rectangles).
The bar graph in Fig 15.1 shows Anu’s mathematics marks in the three terminal
examinations. It helps you to compare her performance easily . She has shown good progress.
Fig 15.1
Bar graphs can also have double bars as in Fig 15.2. This graph gives a comparative
account of sales (in `) of various fruits over a two-day period. How is Fig 15.2 different
from Fig 15.1? Discuss with your friends.
Introduction to Graphs
CHAPTER
15
Page 2


 INTRODUCTION TO GRAPHS  231
15.1  Introduction
Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose
of the graph is to show numerical facts in visual form so that they can be understood
quickly , easily and clearly . Thus graphs are visual representations of data collected. Data
can also be presented in the form of a table; however a graphical presentation is easier to
understand. This is true in particular when there is a trend or comparison to be shown.
W e have already seen some types of graphs. Let us quickly recall them here.
15.1.1  A Bar graph
A bar graph is used to show comparison among categories. It may consist of two or more
parallel vertical (or horizontal) bars (rectangles).
The bar graph in Fig 15.1 shows Anu’s mathematics marks in the three terminal
examinations. It helps you to compare her performance easily . She has shown good progress.
Fig 15.1
Bar graphs can also have double bars as in Fig 15.2. This graph gives a comparative
account of sales (in `) of various fruits over a two-day period. How is Fig 15.2 different
from Fig 15.1? Discuss with your friends.
Introduction to Graphs
CHAPTER
15
232  MATHEMATICS
Fig 15.2
15.1.2  A Pie graph (or a circle-graph)
A pie-graph is used to compare parts of a whole. The circle represents the whole. Fig 15.3
is a pie-graph. It shows the percentage of viewers watching different types of TV channels.
15.1.3  A histogram
A Histogram is a bar graph that shows data in intervals. It has adjacent bars over
the intervals.
Fig 15.3
Page 3


 INTRODUCTION TO GRAPHS  231
15.1  Introduction
Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose
of the graph is to show numerical facts in visual form so that they can be understood
quickly , easily and clearly . Thus graphs are visual representations of data collected. Data
can also be presented in the form of a table; however a graphical presentation is easier to
understand. This is true in particular when there is a trend or comparison to be shown.
W e have already seen some types of graphs. Let us quickly recall them here.
15.1.1  A Bar graph
A bar graph is used to show comparison among categories. It may consist of two or more
parallel vertical (or horizontal) bars (rectangles).
The bar graph in Fig 15.1 shows Anu’s mathematics marks in the three terminal
examinations. It helps you to compare her performance easily . She has shown good progress.
Fig 15.1
Bar graphs can also have double bars as in Fig 15.2. This graph gives a comparative
account of sales (in `) of various fruits over a two-day period. How is Fig 15.2 different
from Fig 15.1? Discuss with your friends.
Introduction to Graphs
CHAPTER
15
232  MATHEMATICS
Fig 15.2
15.1.2  A Pie graph (or a circle-graph)
A pie-graph is used to compare parts of a whole. The circle represents the whole. Fig 15.3
is a pie-graph. It shows the percentage of viewers watching different types of TV channels.
15.1.3  A histogram
A Histogram is a bar graph that shows data in intervals. It has adjacent bars over
the intervals.
Fig 15.3
 INTRODUCTION TO GRAPHS  233
The histogram in Fig 15.4 illustrates the distribution of weights (in kg) of 40 persons of
a locality .
Weights (kg) 40-45 45-50 50-55 55-60 60-65
No. of persons 412 136 5
Fig 15.4
There are no gaps between bars, because there are no gaps between the intervals.
What is the information that you gather from this histogram? Try to list them out.
15.1.4  A line graph
A line graph displays data that changes continuously over periods of time.
When Renu fell sick, her doctor maintained a record of her body temperature, taken
every four hours. It was in the form of a graph (shown in Fig 15.5 and Fig 15.6).
W e may call this a “time-temperature graph”.
It is a pictorial representation of the following data, given in tabular form.
Time 6 a.m. 10 a.m. 2 p.m. 6 p.m.
Temperature(°C) 37 40 38 35
The horizontal line (usually called the x-axis) shows the timings at which the temperatures
were recorded. What are labelled on the vertical line (usually called the y-axis)?
In Fig 15.4 a jagged line
( ) has been  used along
horizontal line to indicate
that we are not showing
numbers between 0 and 40.
Page 4


 INTRODUCTION TO GRAPHS  231
15.1  Introduction
Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose
of the graph is to show numerical facts in visual form so that they can be understood
quickly , easily and clearly . Thus graphs are visual representations of data collected. Data
can also be presented in the form of a table; however a graphical presentation is easier to
understand. This is true in particular when there is a trend or comparison to be shown.
W e have already seen some types of graphs. Let us quickly recall them here.
15.1.1  A Bar graph
A bar graph is used to show comparison among categories. It may consist of two or more
parallel vertical (or horizontal) bars (rectangles).
The bar graph in Fig 15.1 shows Anu’s mathematics marks in the three terminal
examinations. It helps you to compare her performance easily . She has shown good progress.
Fig 15.1
Bar graphs can also have double bars as in Fig 15.2. This graph gives a comparative
account of sales (in `) of various fruits over a two-day period. How is Fig 15.2 different
from Fig 15.1? Discuss with your friends.
Introduction to Graphs
CHAPTER
15
232  MATHEMATICS
Fig 15.2
15.1.2  A Pie graph (or a circle-graph)
A pie-graph is used to compare parts of a whole. The circle represents the whole. Fig 15.3
is a pie-graph. It shows the percentage of viewers watching different types of TV channels.
15.1.3  A histogram
A Histogram is a bar graph that shows data in intervals. It has adjacent bars over
the intervals.
Fig 15.3
 INTRODUCTION TO GRAPHS  233
The histogram in Fig 15.4 illustrates the distribution of weights (in kg) of 40 persons of
a locality .
Weights (kg) 40-45 45-50 50-55 55-60 60-65
No. of persons 412 136 5
Fig 15.4
There are no gaps between bars, because there are no gaps between the intervals.
What is the information that you gather from this histogram? Try to list them out.
15.1.4  A line graph
A line graph displays data that changes continuously over periods of time.
When Renu fell sick, her doctor maintained a record of her body temperature, taken
every four hours. It was in the form of a graph (shown in Fig 15.5 and Fig 15.6).
W e may call this a “time-temperature graph”.
It is a pictorial representation of the following data, given in tabular form.
Time 6 a.m. 10 a.m. 2 p.m. 6 p.m.
Temperature(°C) 37 40 38 35
The horizontal line (usually called the x-axis) shows the timings at which the temperatures
were recorded. What are labelled on the vertical line (usually called the y-axis)?
In Fig 15.4 a jagged line
( ) has been  used along
horizontal line to indicate
that we are not showing
numbers between 0 and 40.
234  MATHEMATICS
Fig 15.5 Fig 15.6
Each piece of data is shown The points are then connected by line
by a point on the square grid. segments. The result is the line graph.
What all does this graph tell you? For example you can see the pattern of temperature;
more at 10 a.m. (see Fig 15.5) and then decreasing till 6 p.m. Notice that the temperature
increased by 3° C(= 40° C – 37° C) during the period 6 a.m. to 10 a.m.
There was no recording of temperature at 8 a.m., however the graph suggests that it
was more than 37 °C (How?).
Example 1: (A graph on “performance”)
The given graph (Fig 15.7) represents the total runs scored by two batsmen A and B,
during each of the ten different matches in the year 2007. Study the graph and answer the
following questions.
(i) What information is given on the two axes?
(ii) Which line shows the runs scored by batsman A?
(iii) Were the run scored by them same in any match in 2007? If so, in which match?
(iii) Among the two batsmen, who is steadier? How do you judge it?
Solution:
(i) The horizontal axis (or the x-axis) indicates the matches played during the year
2007. The vertical axis (or the y-axis) shows the total runs scored in each match.
(ii) The dotted line shows the runs scored by Batsman A. (This is already indicated at
the top of the graph).
Page 5


 INTRODUCTION TO GRAPHS  231
15.1  Introduction
Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose
of the graph is to show numerical facts in visual form so that they can be understood
quickly , easily and clearly . Thus graphs are visual representations of data collected. Data
can also be presented in the form of a table; however a graphical presentation is easier to
understand. This is true in particular when there is a trend or comparison to be shown.
W e have already seen some types of graphs. Let us quickly recall them here.
15.1.1  A Bar graph
A bar graph is used to show comparison among categories. It may consist of two or more
parallel vertical (or horizontal) bars (rectangles).
The bar graph in Fig 15.1 shows Anu’s mathematics marks in the three terminal
examinations. It helps you to compare her performance easily . She has shown good progress.
Fig 15.1
Bar graphs can also have double bars as in Fig 15.2. This graph gives a comparative
account of sales (in `) of various fruits over a two-day period. How is Fig 15.2 different
from Fig 15.1? Discuss with your friends.
Introduction to Graphs
CHAPTER
15
232  MATHEMATICS
Fig 15.2
15.1.2  A Pie graph (or a circle-graph)
A pie-graph is used to compare parts of a whole. The circle represents the whole. Fig 15.3
is a pie-graph. It shows the percentage of viewers watching different types of TV channels.
15.1.3  A histogram
A Histogram is a bar graph that shows data in intervals. It has adjacent bars over
the intervals.
Fig 15.3
 INTRODUCTION TO GRAPHS  233
The histogram in Fig 15.4 illustrates the distribution of weights (in kg) of 40 persons of
a locality .
Weights (kg) 40-45 45-50 50-55 55-60 60-65
No. of persons 412 136 5
Fig 15.4
There are no gaps between bars, because there are no gaps between the intervals.
What is the information that you gather from this histogram? Try to list them out.
15.1.4  A line graph
A line graph displays data that changes continuously over periods of time.
When Renu fell sick, her doctor maintained a record of her body temperature, taken
every four hours. It was in the form of a graph (shown in Fig 15.5 and Fig 15.6).
W e may call this a “time-temperature graph”.
It is a pictorial representation of the following data, given in tabular form.
Time 6 a.m. 10 a.m. 2 p.m. 6 p.m.
Temperature(°C) 37 40 38 35
The horizontal line (usually called the x-axis) shows the timings at which the temperatures
were recorded. What are labelled on the vertical line (usually called the y-axis)?
In Fig 15.4 a jagged line
( ) has been  used along
horizontal line to indicate
that we are not showing
numbers between 0 and 40.
234  MATHEMATICS
Fig 15.5 Fig 15.6
Each piece of data is shown The points are then connected by line
by a point on the square grid. segments. The result is the line graph.
What all does this graph tell you? For example you can see the pattern of temperature;
more at 10 a.m. (see Fig 15.5) and then decreasing till 6 p.m. Notice that the temperature
increased by 3° C(= 40° C – 37° C) during the period 6 a.m. to 10 a.m.
There was no recording of temperature at 8 a.m., however the graph suggests that it
was more than 37 °C (How?).
Example 1: (A graph on “performance”)
The given graph (Fig 15.7) represents the total runs scored by two batsmen A and B,
during each of the ten different matches in the year 2007. Study the graph and answer the
following questions.
(i) What information is given on the two axes?
(ii) Which line shows the runs scored by batsman A?
(iii) Were the run scored by them same in any match in 2007? If so, in which match?
(iii) Among the two batsmen, who is steadier? How do you judge it?
Solution:
(i) The horizontal axis (or the x-axis) indicates the matches played during the year
2007. The vertical axis (or the y-axis) shows the total runs scored in each match.
(ii) The dotted line shows the runs scored by Batsman A. (This is already indicated at
the top of the graph).
 INTRODUCTION TO GRAPHS  235
(iii) During the 4th match, both have scored the same
number of 60 runs. (This is indicated by the point
at which both graphs meet).
(iv) Batsman A has one great “peak” but many deep
“valleys”. He does not appear to be  consistent.
B, on the other hand has never scored below a
total of 40 runs, even though his highest score is
only 100 in comparison to 115 of A. Also A has
scored a zero in two matches and in a total of 5
matches he has scored less than 40 runs. Since A
has a lot of ups and downs, B is a more consistent
and reliable batsman.
Example 2:  The given graph (Fig 15.8) describes
the distances of a car from a city P at different times
when it is travelling from City P to City Q, which are
350 km apart. Study the graph and answer the following:
(i) What information is given on the two axes?
(ii) From where and when did the car begin its
journey?
(iii) How far did the car go in the first hour?
(iv) How far did the car go during (i) the 2nd hour? (ii) the 3rd hour?
(v) W as the speed same during the first three hours? How do you know it?
(vi) Did the car stop for some duration at any place? Justify your answer.
(vii) When did the car reach City Q?
Fig 15.7
Fig 15.8
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