# NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.2

NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.2 (Ex. 15.2) Introduction to Graphs in PDF file format free to download for academic session 2021-2022. Practice here with the given questions and their solutions available in PDF and videos.

Class 8 mathematics exercise 15.2 is based on the concept coordinate geometry. This topic is one of the important topic not only in class 8 but in further classes.

## Class 8 Maths Chapter 15 Exercise 15.2 Solution

 Class: 8 Mathematics Chapter: 15 Introduction to Graphs Exercise: 15.2 Hindi and English Medium Solution

### Class 8 Maths Chapter 15 Exercise 15.2 Solution in Videos

Class 8 Maths Chapter 15 Exercise 15.2 Solution
Class 8 Maths Chapter 15 Exercise 15.2 Explanation

#### Bar Graph (or Column Graph)

A bar graph is a pictorial representation of numerical data in the form of rectangles (or bars) of equal width and varying heights.
These rectangles are drawn either vertically or horizontally, keeping equal space between them. The height (or length) of a rectangle depends upon the numerical value it represents.

##### Method to Draw a Bar Graph

Suppose some numerical data is given to us, and we have to represent it by a bar graph on a graph paper.
We can draw the graph by following the steps given below:
Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY. These lines are called the x-axis and the y-axis respectively.
Step 2: Mark points at equal intervals along the x-axis. Below these points write the names of the data items whose values are to be plotted.
Step 3: Choose a suitable scale. On that scale determine the heights of the bars for the given numerical values.
Step 4: Mark off these heights parallel to the y-axis from the points taken in Step 2.
Step 5: On the x- axis, draw bars of equal width for the heights marked in Step 4. The bars Should be centred on the points marked on the x-axis. These bars represent the given numerical data.

##### The marks obtained by Tanvy in her annual examination are shown below: Subjects: English, Mathematics, Hindi, Social, studies Science Marks obtained: 54, 82, 63, 38, 70

For drawing the given bar graph, we proceed as under:
Step 1: On a graph paper, draw a horizontal line OX and a vertical line OY, representing the x-axis and the y-axis respectively.
Step 2: Along OX, write the names of the subjects at points taken at uniform gaps.
Step 3: Choose the scale: 1 small division @ 1 mark.
Step 4. The heights of the various bars are:
English = 54 small divisions
Mathematics = 82 small divisions
Hindi= 63 small divisions
Social studies = 38 small divisions
Science = 70 small divisions
Step 5. On the x-axis, draw bars of equal width having heights obtained in Step 4 at the points marked in Step 2.

#### Line Graph

A line graph displays data that changes continuously over periods of time. To draw a line graph, XOX’ and YOY’ are drawn perpendicular to each other. Independent variable is taken on x-axis whereas dependent variable on the y-axis. We plot the points and join these points in pairs to get the line graph.

Note: The variable whose value does not depend upon the value of the other is called independent variable and the variable whose value depends upon the other is called dependent variable.

If we are to plot a graph of the relation between length of a side of square and its perimeter, the length of the square is independent variable and the perimeter dependent variable.

#### Pie Charts

In a pie chart, the various observations or components are represented by the sectors of a circle and the whole circle represents the sum of the values of all components.
The central angle for a component is given by:
Central angle for a component = {(Value of the component /Sum of the values of all components) x 360}0

##### Steps of construction

1. Calculate the central angle for each component, given by
Central angle for a component = {(Value of the component /Total value) x 360}0
2. Draw a circle of convenient radius.
3. Within this circle, draw a horizontal radius.
4. Starting with the horizontal radius, draw radii making central angles corresponding to the values of the respective components, till all the components are exhausted. These radii divide the whole circle into various sectors.
5. Shade each sector with different design. This will be the required pie chart for the given data.

##### What does every good graph need?

The essential graph elements that should be included in almost every graph are… Clearly visible data points. Appropriate labels on each axis that include units. A trend line showing the mathematical model of the fit of your data, when appropriate.

##### What information does the bar graph give?

Bar graphs are ideal for comparing two or more values, or values over time. Data is displayed either horizontally or vertically. Single bar graphs are used to convey discrete values of an item within a category. For instance, a bar graph could display the number of males with a certain trait for specific ages.

##### How can bar graphs be useful?

Bar graphs are used to compare things between different groups or to track changes over time. However, when trying to measure change over time, bar graphs are best when the changes are larger.

##### What do you have to remember when drawing bar charts?

Drawing a bar chart
Take care to ensure an appropriate scale, to number the axes uniformly, and give the appropriate label on the axes. Finally remember to give the graph a suitable title.

##### What is the difference between a histogram and bar graph?

Histograms are used to show distributions of variables while bar charts are used to compare variables. Histograms plot quantitative data with ranges of the data grouped into bins or intervals while bar charts plot categorical data.  