In the previous section we completed the discussion on 'how data is represented by tables'. In this section, we will see how data can be represented by graphs. It is said that one picture is better than a thousand words. This is very true when data is represented by pictorial representations like graphs and pie charts. The main features of the data will easily become clear when using graphs. We will now see various types of graphs.
• All bars have the same width
• The spacing between all bars are the same
• The base of each bar rests on the horizontal axis. That is., the ‘x-axis’
• Variables (eg: expenses, sales, profits etc.,) are marked on the x-axis
• The values of the variables are marked on the vertical axis. That is., the ‘y-axis’
• The heights of the bars depend upon the values taken by the variables
Let us see an example:
In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared from the data so obtained:
Observe the bar graph given above and answer the following questions:
(i) How many students were born in the month of November?
(ii) In which month were the maximum number of students born?
Solution:
The variable in this problem is ‘Month of Birth’. For getting the value of the variable at a particular point (here, point is the name of the month), we look at the corresponding point on the y-axis. The white horizontal dotted lines will help us to find this value from the y-axis.
Part (i)
1. First we take the point ‘November’ on the x-axis.
2. The height of the bar at November is 4. So the value of the variable is 4
3. Thus we get the answer: 4 students were born in the month of november
Part (ii)
1. Here we have to find the maximum y value first. Looking at the y-axis, we find that, the maximum y value is 6.
2. The x value corresponding to it is August
3. Thus we get the answer: The Maximum number of students were born in the month of August.
Now we will see an example which demonstrates the construction of a bar graph:
A family with a monthly income of Rs 20,000 had planned the following expenditures per month under various heads:
Draw a bar graph for the data above.
Solution:
We can construct the bar graph by the following steps:
• There must be one bar for each item
• Width of all bars must be the same
• Spacing between all bars must be the same
• Height of each bar will be equal to the corresponding value in the ‘Expenditure’ column of the given data table
• Each unit on the y-axis represents Rs. 1000
♦ Example: The height of education column is 5 units. That means, the actual expenditure is Rs. 5000
• The completed graph is shown below:
So we have completed the discussion on bar graphs. We can write this:
• First we obtain the raw data from the field
• Next we form the ‘frequency distribution table’
• Finally, based on the frequency distribution table, we construct the bar graph
■ So we can say: Bar graph correspond to ‘frequency distribution table’
• For example, in the first section of this chapter, we saw a frequency distribution table related to the marks scored by students in a class. See it here. And just below that, the corresponding bar graph was given.
Now we will see some solved examples
Solved example 25.10
A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):
(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women’s ill health and death worldwide?
Solution:
Part (i)
The given data can be represented graphically using a 'Bar graph' as shown in fig.25.2 below.
Each item should be given a bar.
A sample bar:
• Consider item no.2: Neuropsychiatric conditions. It's frequency in the given data table is 25.4.
• In the bar graph, we see that the bar of this item has a height just above the horizontal line through 25. The excess above the horizontal line is '0.4'.
• The reader is advised to draw the whole graph himself/herself on a fresh graph paper.
• When a suitable scale is fixed, the thin subdivision lines in the graph paper will enable us to mark the correct heights of the bars
Part (ii)
The tallest bar is that of item 1. So we can write this:
Reproductive health conditions is the major cause of women’s ill health and death worldwide
Solved example 25.11
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below:
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.
Solution:
The required bar graph is shown in fig.25.3 below:
A sample bar:
• Consider item no.5: Non-backward districts. It's frequency in the given data table is 920.
• In the bar graph, we see that the bar of this item has a height exactly same as the horizontal line through 920.
• The reader is advised to draw the whole graph himself/herself on a fresh graph paper.
• When a suitable scale is fixed, the thin subdivision lines in the graph paper will enable us to mark the correct heights of the bars
• But in this case, we will not need to consider the subdivision lines. If the scale chosen is “10 no. of girls = 1 cm”, the top edge of all the bars will fall on main lines of the graph paper
Part (ii)
We can arrive at many conclusions from the above bar graph:
• Surveys were conducted separately on different sections of the society
• Number of girls and number of boys were obtained from each section
• Based on those numbers, the following result was obtained for each section:
♦ The number of girls per 1000 boys
• According to World health organisation (WHO) guide lines, If there are 1000 boys, the number of girls should be greater than 1000
♦ But the above survey results show that this is not achieved
• In some sections, the number of girls is far less than 1000. Example: Non SC/ST and Non-backward districts. There are only 920 girls per 1000 boys.
• The condition is even worse in urban section. The number is only 910. It has the shortest bar.
• In Scheduled tribe section, there are 970 girls per 1000 boys. So it is a more desirable result obtained so far. It has the tallest bar.
Solved example 25.12
Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?
Solution:
The required bar graph is shown in fig.25.4 below:
A sample bar:
• Consider 'C': It's frequency in the given data table is 37.
• In the bar graph, we see that the bar of this item has a height between 30 and 40. It is nearly 40. That is., it is above the 'midpoint 35' between 30 and 40.
• The reader is advised to draw the whole graph himself/herself on a fresh graph paper.
• When a suitable scale is fixed, the thin subdivision lines in the graph paper will enable us to mark the correct heights of the bars
• If the scale chosen is “10 seats = 1 cm”, the top edge of bar of C will be 7 subdivisions above 30.
Part (ii)
The tallest bar is that of Party A. So it has won the election. The number of seats is 75
In the next section we will see histograms.
Bar Graphs
We have already learned about bar graphs in our earlier classes. Details here. Let us look at their main features:• All bars have the same width
• The spacing between all bars are the same
• The base of each bar rests on the horizontal axis. That is., the ‘x-axis’
• Variables (eg: expenses, sales, profits etc.,) are marked on the x-axis
• The values of the variables are marked on the vertical axis. That is., the ‘y-axis’
• The heights of the bars depend upon the values taken by the variables
Let us see an example:
In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared from the data so obtained:
(i) How many students were born in the month of November?
(ii) In which month were the maximum number of students born?
Solution:
The variable in this problem is ‘Month of Birth’. For getting the value of the variable at a particular point (here, point is the name of the month), we look at the corresponding point on the y-axis. The white horizontal dotted lines will help us to find this value from the y-axis.
Part (i)
1. First we take the point ‘November’ on the x-axis.
2. The height of the bar at November is 4. So the value of the variable is 4
3. Thus we get the answer: 4 students were born in the month of november
Part (ii)
1. Here we have to find the maximum y value first. Looking at the y-axis, we find that, the maximum y value is 6.
2. The x value corresponding to it is August
3. Thus we get the answer: The Maximum number of students were born in the month of August.
A family with a monthly income of Rs 20,000 had planned the following expenditures per month under various heads:
Solution:
We can construct the bar graph by the following steps:
• There must be one bar for each item
• Width of all bars must be the same
• Spacing between all bars must be the same
• Height of each bar will be equal to the corresponding value in the ‘Expenditure’ column of the given data table
• Each unit on the y-axis represents Rs. 1000
♦ Example: The height of education column is 5 units. That means, the actual expenditure is Rs. 5000
• The completed graph is shown below:
• First we obtain the raw data from the field
• Next we form the ‘frequency distribution table’
• Finally, based on the frequency distribution table, we construct the bar graph
■ So we can say: Bar graph correspond to ‘frequency distribution table’
• For example, in the first section of this chapter, we saw a frequency distribution table related to the marks scored by students in a class. See it here. And just below that, the corresponding bar graph was given.
Solved example 25.10
A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):
(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women’s ill health and death worldwide?
Solution:
Part (i)
The given data can be represented graphically using a 'Bar graph' as shown in fig.25.2 below.
 |
| Fig.25.2 |
Each item should be given a bar.
A sample bar:
• Consider item no.2: Neuropsychiatric conditions. It's frequency in the given data table is 25.4.
• In the bar graph, we see that the bar of this item has a height just above the horizontal line through 25. The excess above the horizontal line is '0.4'.
• The reader is advised to draw the whole graph himself/herself on a fresh graph paper.
• When a suitable scale is fixed, the thin subdivision lines in the graph paper will enable us to mark the correct heights of the bars
Part (ii)
The tallest bar is that of item 1. So we can write this:
Reproductive health conditions is the major cause of women’s ill health and death worldwide
Solved example 25.11
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below:
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.
Solution:
The required bar graph is shown in fig.25.3 below:
 |
| Fig.25.3 |
• Consider item no.5: Non-backward districts. It's frequency in the given data table is 920.
• In the bar graph, we see that the bar of this item has a height exactly same as the horizontal line through 920.
• The reader is advised to draw the whole graph himself/herself on a fresh graph paper.
• When a suitable scale is fixed, the thin subdivision lines in the graph paper will enable us to mark the correct heights of the bars
• But in this case, we will not need to consider the subdivision lines. If the scale chosen is “10 no. of girls = 1 cm”, the top edge of all the bars will fall on main lines of the graph paper
Part (ii)
We can arrive at many conclusions from the above bar graph:
• Surveys were conducted separately on different sections of the society
• Number of girls and number of boys were obtained from each section
• Based on those numbers, the following result was obtained for each section:
♦ The number of girls per 1000 boys
• According to World health organisation (WHO) guide lines, If there are 1000 boys, the number of girls should be greater than 1000
♦ But the above survey results show that this is not achieved
• In some sections, the number of girls is far less than 1000. Example: Non SC/ST and Non-backward districts. There are only 920 girls per 1000 boys.
• The condition is even worse in urban section. The number is only 910. It has the shortest bar.
• In Scheduled tribe section, there are 970 girls per 1000 boys. So it is a more desirable result obtained so far. It has the tallest bar.
Solved example 25.12
Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?
Solution:
The required bar graph is shown in fig.25.4 below:
 |
| Fig.25.4 |
• Consider 'C': It's frequency in the given data table is 37.
• In the bar graph, we see that the bar of this item has a height between 30 and 40. It is nearly 40. That is., it is above the 'midpoint 35' between 30 and 40.
• The reader is advised to draw the whole graph himself/herself on a fresh graph paper.
• When a suitable scale is fixed, the thin subdivision lines in the graph paper will enable us to mark the correct heights of the bars
• If the scale chosen is “10 seats = 1 cm”, the top edge of bar of C will be 7 subdivisions above 30.
Part (ii)
The tallest bar is that of Party A. So it has won the election. The number of seats is 75
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