Graph:
The graphs are the visual representation of the data. They are particularly useful for comparison of data. The purpose of the graph is to show numerical facts in visual form so that they can be understood quickly, easily and clearly.
1. Bar Graph:
In this type of graph, bars of uniform widths are used for representing different quantities, but, the heights of these bars are proportional to the respective values of the quantities. It shows comparison among categories.
Example: The bar graph shown below represents the student’s favorite subjects amongst math, reading, science and writing.
2. Double Bar Graph:
In this type of graph, a bar graph represents two sets of data simultaneously. This type of graph is mainly used for comparing data.
Example: The double graph below shows % of literate (blue bar)
and illiterate (green bar) for five different cities A, B, C, D and E.
3. Pie Graph or Circle Graph:
When the given data are represented in circular form, then such type of graph is known as circular graph or pie chart. It is used to compare parts of a whole. The circle represents the whole.
In this type of graph, as per the proportion of different quantities, the part of the circle as a whole is divided.
Example: Pie-chart below shows distribution of river water into four different regions A, B, C, and D.
4. Histogram:
If a bar graph is plotted for data which has continuous class intervals or grouped frequency distributed type of data, then such a graph is known as histogram. It shows data in intervals.
Example: Consider the table given below:
Class Interval |
Frequency |
0 - 10 |
2 |
10-20 |
10 |
20-30 |
21 |
30-40 |
19 |
40-50 |
7 |
50-60 |
1 |
Total |
60 |
Here, the height of the bars represents the frequency of the class interval.
Note that there is no gap between the bars as the class intervals are continuous.
5. Line Graph:
When data changes continuously over a period of time then we can represent such data using line graph.
Example: The line graph shows the temperature fluctuations of a particular city for one week.
Some Examples
Example 1: The following line graph shows the yearly sales figures for a manufacturing company. (a) What were the sales in (i) 2002 (ii) 2006? (b) What were the sales in (i) 2003 (ii) 2005? (c) Compute the difference between the sales in 2002 and 2006. (d) In which year was there the greatest difference between the sales as compared to its previous year?Solution:
(a) (i) From the graph, it can be observed that sales in 2002 was Rs 4 crores.
(ii) From the graph, it can be observed that sales in 2006 was Rs 8 crores.
(b) (i) From the graph, it can be observed that sales in 2003 was Rs 7 crores.
(ii) From the graph, it can be observed that sales in 2005 was Rs 10 crores.
(c) From the graph, it can be observed that the sales in 2002 was Rs 4 crore and in 2006 it was Rs 8 crore.
Hence, the difference between the sales in 2002 and 2006 will be Rs (8 – 4) crores = Rs 4 crores.
(d) From the graph, the individual difference between the successive years are as follows:
The difference between sales in year 2006 and 2005 is Rs (10 – 8) crores = Rs 2 crores
The difference between sales in year 2005 and 2004 is Rs (10 – 6) crores = Rs 4 crores
The difference between sales in year 2046 and 2003 is Rs (7 – 6) crores = Rs 1 crores
The difference between sales in year 2003 and 2002 is Rs (7 – 4) crores = Rs 3 crores
Hence, the difference was maximum in the year 2005 as compared to its previous year 2004.
Example 2: Draw a linear graph for following data:
Year |
2003 | 2004 | 2005 | 2006 |
Days | 8 | 10 | 5 |
12 |
Solution: For the given data, years will be taken on x-axis and days on y-axis. Here, scale for x-axis is 2 unit = 1 year and for y-axis 1 unit = 2 days. The linear graph is as follows:
6. Linear Graphs:
Basically, a line graph is composed of line segments which are made on joining distinct points. Sometimes the graph may be a whole unbroken line. Such a graph is called a linear graph.
To draw such a line we need to locate some points on the graph sheet
(a) Location of a point:
Cartesian system – It is the system of fixing a point with the help of two measurements which are vertical and horizontal lines.
(b) Co-ordinates of a point:
Consider the figure given below to understand the coordinates of a point.
For the given point A, it is observed that it is obtained after moving 2 units on x-axis and 3 units on y-axis.
Here, 2 is called the x-coordinate and 3 is called the y-coordinate of point A.
Hence, coordinates of point A are (2, 3).
Example: Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.
Solution: Following is the graph drawn for the given data:From the graph, it can be observed that the line joining the given two points (2, 3) and (3, 2) meets the x-axis at the co-ordinate (5,0) and the y-axis at the co-ordinate (0,5).
Applications of Graph:
In everyday life, there are many situations where we can use graph for comparison and analysis.
Example: The electricity bill we pay is directly proportional to the amount of time for which electricity was consumed. The more the electricity is consumed; the bill amount will be high.
Independent variable : The electricity in this case is not dependent on other factors. Hence, such quantities are termed as independent variables.
Dependent variable : The amount of bill in this case is dependent on the time for which the electricity was consumed. Hence, such quantities are as dependent variables.
The relationship between independent and dependent quantities can be shown with the help of a graph.
Example: Draw a graph for the following:
Side of square (in cm) |
2 | 3 | 3.5 | 5 | 6 |
Perimeter (in cm) | 8 | 12 | 14 | 20 |
24 |
Solution: For the given data, side of square will be taken on x-axis and perimeter on y-axis. Here, scale for x-axis is 1 unit = 1 cm and for y-axis 1 unit = 4 cm. The graph is as shown below:
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