 # Graphical Representation  View Notes

## What is a Graph?

In mathematics, a graph is a diagrammatic illustration that is used to represent data values in a systematic, organized and understandable manner.  It is indeed a very tedious task to analyze lots of data. However, when the same numerical data is represented in a pictorial form, it becomes easy to understand the relationship between the provided data objects and the concepts represented. It is often said that a picture is worth a thousand words. Therefore, graphs are particularly useful when it comes to displaying and analyzing data.

The data shown on the graph usually represents a relationship between various things for comparison among them. It could also help us to understand the changing trends over a period of time. With the help of graphs, it becomes easier to comprehend information.

## Types of Graphical Representation

In order to represent various kinds of data, different kinds of graphs are used. Some of the commonly used graphs are as follows:

• ### Line Graph

In a line graph, a line shows trends in data. It can also be used to predict the changing trends of the displayed data objects in the future.

• ### Bar Graph

A bar graph is used when data has been categorized or sorted. It is the best kind of graph for comparing data. In this, solid bars are used to represent different categories or data values.

• ### Histograms

A histogram is similar to a bar graph. However, instead of making comparisons, it groups the numerical data into ranges. It is most commonly used to show frequency distributions.

• ### Pie or Circle Graph

In a pie chart, a circle represents statistical graphics. It is divided into a number of slices or pies to represent the proportion of numbers. The length of the arc of each pipe corresponds to the quantity represented by it.

• ### Stem and Leaf Graph

Stem and leaf plot is a special type of table in which the data values are divided into a stem, which represents the initial digit or digits, and a leaf, which usually represents the last digit.

## How to Plot the Data Accurately on Graphs?

It is of utmost importance that the information which is being represented graphically should be accurate and easy to understand. The various points that should be kept in mind are:

• ### Scale

The scale chosen to plot the graph should be according to the data values that have to be represented.

• ### Index

The index makes it easier for the reader to read and interpret the data represented by various colours, patterns, designs, etc.

• ### The Source of Data

As and when necessary, the source of data can be mentioned at the bottom of the graph.

• ### Neatness

The purpose of making the graph is defeated if the representation does not look tidy. Hence, it must be ensured that the data so represented is neat and visually appealing.

• ### Simple

There is no need to unnecessarily complicate the graph. The simpler, the better.

### Basics of Graphical Representation

A graph usually consists of two lines called the coordinate axes. The horizontal line is called the x-axis, and the vertical line is called the y axis. The intersection of the two axes is the point of origin. The values on the x-axis towards the right of the origin are considered positive, and towards the left are negative. Similarly, on the y-axis, the values above the origin will be positive and the values below the origin will be negative.

### Benefits of Using Graphs

• Graphs save time. If the same information is written down, it becomes a tedious and tiresome process to spot the trends and be able to analyze the data properly.

• A graph can be used to represent information neatly and also takes less space.

• It is easy to understand.

Q1. What is a Frequency Polygon Graph?

Ans: A frequency polygon graph can be used to represent the same set of data which is represented by a histogram. In this type of graph, lines are used to connect the midpoints of each interval. The frequencies of the data interval are represented by the height at which the midpoints are plotted in the graph. A frequency polygon can be created using the already drawn histogram, or by calculating the midpoint from the intervals of the frequency distribution table. To calculate the midpoint, we need to find the average of the upper and the lower values of the interval/range.

Frequency polygon gives us an idea regarding the shape of the data and the trends that it follows during a particular duration of time.

Steps to draw a frequency polygon:

• Calculate the classmark for each interval, which is equal to (upper limit + lower limit)/2.

• Represent the class marks on the x-axis and their corresponding frequencies on the y-axis.

• For every class mark on the x-axis, plot the frequencies of the y-axis.

• Join all the obtained points to get a curve.

• The figure so obtained is called a frequency polygon.

Q2. What is the Difference Between a Bar Graph and a Histogram?

Ans: The most commonly visible difference between a bar graph and a histogram is that, in a bar graph, the bars have spaces between them, whereas, in a histogram, the bars are drawn adjacent to each other, without leaving any spaces.

As they both make use of bars to represent the data, it becomes slightly difficult to understand the fundamental difference between the two. A histogram is a graphical representation that uses bars to demonstrate the frequency of numerical data. In a histogram, elements are grouped together, so they can be considered as ranges.

A bar graph is a diagrammatic representation that uses bars for comparison of different categories of data.  The plotted elements are treated as individual entities, and not as a range. The bars can be drawn horizontally or vertically. The height of the bar corresponds to the size of the data object.

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