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. We 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 twoday period. How is Fig 15.2 different from Fig 15.1? Discuss with your friends. Introduction to Graphs CHAPTER 15 201920 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. We 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 twoday period. How is Fig 15.2 different from Fig 15.1? Discuss with your friends. Introduction to Graphs CHAPTER 15 201920 232 MATHEMATICS Fig 15.2 15.1.2 A Pie graph (or a circlegraph) A piegraph is used to compare parts of a whole. The circle represents the whole. Fig 15.3 is a piegraph. 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 201920 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. We 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 twoday period. How is Fig 15.2 different from Fig 15.1? Discuss with your friends. Introduction to Graphs CHAPTER 15 201920 232 MATHEMATICS Fig 15.2 15.1.2 A Pie graph (or a circlegraph) A piegraph is used to compare parts of a whole. The circle represents the whole. Fig 15.3 is a piegraph. 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 201920 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) 4045 4550 5055 5560 6065 No. of persons 4 12 13 6 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 “timetemperature 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 xaxis) shows the timings at which the temperatures were recorded. What are labelled on the vertical line (usually called the yaxis)? 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. 201920 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. We 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 twoday period. How is Fig 15.2 different from Fig 15.1? Discuss with your friends. Introduction to Graphs CHAPTER 15 201920 232 MATHEMATICS Fig 15.2 15.1.2 A Pie graph (or a circlegraph) A piegraph is used to compare parts of a whole. The circle represents the whole. Fig 15.3 is a piegraph. 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 201920 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) 4045 4550 5055 5560 6065 No. of persons 4 12 13 6 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 “timetemperature 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 xaxis) shows the timings at which the temperatures were recorded. What are labelled on the vertical line (usually called the yaxis)? 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. 201920 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 xaxis) indicates the matches played during the year 2007. The vertical axis (or the yaxis) 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). 201920 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. We 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 twoday period. How is Fig 15.2 different from Fig 15.1? Discuss with your friends. Introduction to Graphs CHAPTER 15 201920 232 MATHEMATICS Fig 15.2 15.1.2 A Pie graph (or a circlegraph) A piegraph is used to compare parts of a whole. The circle represents the whole. Fig 15.3 is a piegraph. 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 201920 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) 4045 4550 5055 5560 6065 No. of persons 4 12 13 6 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 “timetemperature 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 xaxis) shows the timings at which the temperatures were recorded. What are labelled on the vertical line (usually called the yaxis)? 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. 201920 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 xaxis) indicates the matches played during the year 2007. The vertical axis (or the yaxis) 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). 201920 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) Was 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 201920Read More
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