Class 8 Maths Chapter 15 Notes - Introduction to Graphs

Introduction to Graphs

A graph is a pictorial representation or a diagram that represents the data in an organised manner. The purpose of graphs is to represent numerical data in a graphical form. Data can also be represented in a tabular form. However, when data is represented in graphical form, it becomes much easier to understand. There are many types of graphs and each serves specific purposes in different fields.

Bar Graphs

In a bar graph, the information is represented by bars of the same width with equal gaps in-between, the height of the bars represents the respective values. Between each pair of bars, there is an equal gap.

Double Bar Graph

To compare the data, we use a double bar graph as it shows the information of quantities for two different periods simultaneously.

Pie Chart

When the data is represented in a circular form, it is said to be a pie chart. It shows the data of a quantity as the part of a whole.

Histogram

The bar graph of a grouped frequency distribution or continuous class interval is called a histogram. The class intervals are shown on the horizontal line and the frequency of the class intervals is shown as the height of the bars. This is also like a bar graph, but there is no gap between each bar.

Line graph

When we want to see the changes in the data continuously over a period of time, a line graph is used.

Let us understand line graphs with the help of an example.

Interpreting Line Graphs

The given graph shows the number of people in a store at different times in a day. At what time, were the number of people maximum and minimum in the store.



Maximum number of people = 22
Minimum number of people = 2

Time at which there were maximum people in the store = 1 PM
Time at which there were minimum people in the store = 10 AM

Now, let us read about linear graphs.

NCERT Solutions for Class 8 Maths Chapter 15
NCERT Solutions Class 8 Maths Chapter 15
NCERT Solutions Class 8 Maths Exercise 15.1
NCERT Solutions Class 8 Maths Exercise 15.2
NCERT Solutions Class 8 Maths Exercise 15.3

Linear Graph

A graph in which all the data points gives a single straight line is called a linear graph. Let’s see how do we plot the data of a linear graph.

Location of a Point

To plot a linear graph, a Cartesian plane is used. It is the system in which we mark the points with the help of vertical (y-axis) and horizontal lines (x-axis). For locating a point on the graph, we need its x-coordinate and y-coordinate.

The x-coordinate of a point reveals how much we have to move from origin (O) towards the right or the left along the x-axis. It is also called abscissa. The y-coordinate of a point reveals how much we have to move above or below the origin (O) along the y-axis. It is also called ordinate.

While writing the coordinates of a point, the x-coordinate is written first and then the y-coordinate is written. The coordinates are placed inside a bracket. The point is written as (x, y). The coordinate where the x-axis and the y-axis meet is called the origin and is marked as (0, 0).

If we have to locate the point (1, 3) on the coordinate axis, it will be done as shown in the image.



Let us read about quadrants.

Quadrants

In a two-dimensional plane, there are 4 quadrants. The quadrants are numbered as I, II, III, and IV in the counter-clockwise direction. A point can be located in any of these quadrants.

• In the first quadrant, the points are of the form (x, y), which means both the x and y coordinate are positive. For example: (1, 9) and (2, 8).
• In the second quadrant, the points are of the form (–x, y), which means the x coordinate is negative and y coordinate is positive. For example: (–2, 5) and (–6, 2).
• In the third quadrant, the points are of the form (–x, –y), which means both the x and y coordinate are negative. For example: (–4, –1) and (–5, –19).
• In the fourth quadrant, the points are of the form (x, – y), which means the x coordinate is positive and y coordinate is negative. For example: (3, –9) and (6, –5).

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Types of Variables

Variables are divided into two types on the basis of how the value of the variable change with the increase or decrease of the other variables.

Independent Variable

Variable that is independent and whose value doesn’t depend on other variables.

Dependent Variable

Variable whose value increases or decreases with the changes in any other factor or it is dependent on any other variable.

Let's have a look at an example.

The table given below shows the savings for Priya for different number of years (in lakhs). Draw a graph for the same.


Here, number of years is the independent variable and the savings is the dependent variable.
We will take the number of years on the x-axis and the savings on the y-axis.

Scale:

On x-axis: 1 interval = 1 year
On y-axis: 1 interval = ₹5 lakhs
On plotting the points, we get the graph as shown in the image.

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