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 have 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 some time. With the help of graphs, it becomes easier to comprehend information.
Types of Graphical Representation
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 many 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
A 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 period 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.
Analysing a graphical representation of data does not take much and helps in making quick decisions.
Graphs give you a summarized version of a long report that contains a large amount of data.
Graphs and tables are less likely to have any errors and mistakes.
Graphical representation of two or more data sets will allow you to compare the information and take preventive measures to avoid mistakes in the future.
By making the data easy to understand, graphs eliminate the literacy barriers so that anyone can analyse and interpret the presented data.
With just a glance at the graphical representation, a person can make quick and informed decisions.
Some Rules for Graphical Representation of Data
Like any other mathematical concept, graphical representation also has some rules you must follow. These rules will help you present the information on a graph effectively. Below are the rules for graphical representation of data:
When you are making a graph, you should give it an appropriate title that highlights the subject of the given data.
While making a graph, do not forget to mention the measurement unit.
Make an index using colours, designs, shades, lines, etc. to make the graphical representation easier to understand.
You have to choose an appropriate scale to represent the given set of data.
Construct the graph as simple as possible so that everyone can easily understand the presented data.
Whether you are making a pie chart or a bar graph, it should look neat and clean so that the teacher can easily read the figures.
Importance of Graphical Representation
Graphical representation gives you a visual presentation of the given data to make it easier to understand. Graphs help you identify different patterns over a short and long period. It assists you in the interpretation of data and comparison of two or more data sets. Here are reasons why graphical representation is important:
Graphs are widely accepted in the corporate world as it summarises the data into an understandable format and avoids wastage of time.
When you want to compare two or more different data sets, graphs are your best choice. A graphical representation of all the data sets will allow you to quickly analyze the information and help you in making quick decisions.
Through descriptive reports and information, it becomes difficult to make decisions. However, with graphs, the management can analyse the situation more clearly and make the right decisions.
With tables and graphs, the information can be presented in an organised and logical manner, making it easier to understand for anyone.
Graphical representation of data does not demand much of your time, improving the overall efficiency. You can quickly make the graphs within minutes and focus on other important work.
Qualitative representation might include many grammatical errors and other mistakes that can mislead the person reading it. Since graphs involve numerical representation of data, there are fewer chances of errors and mistakes.
Graphs give you the entire summary of a large amount of data.
FAQs on Graphical Representation
1. What is a frequency polygon graph?
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 obtained is called a frequency polygon.
2. What is the difference between a Bar Graph and a Histogram?
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, so they can be considered as ranges.
A bar graph is a diagrammatic representation that uses bars for the 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.
3. From which platform can I learn Graphical Representation?
Vedantu is the best e-learning platform from where you can learn Graphical Representation. To start studying the concept of graphical representations, you can visit our official website or download our mobile app from the app store or play store. Our learning platform is available to all students across the globe for absolutely free. Apart from the Graphical Representation, you will find plenty of study material for different topics of Maths. From the website, you can learn concepts, such as Number System, Area of Triangle, Factorisation, and much more.
4. What are the advantages of a Bar Graph?
A bar graph is the most widely used method of graphical representation. Below are some of the advantages of a bar graph:
A bar graph shows every category from the given frequency distribution.
Bar graphs summarize a large chunk of data into a simple, understandable, and interpretable form.
With a bar graph, you can easily compare two or more different data sets.
You can study the varying patterns in a bar graph over a long period.
A bar graph makes the trends easier to highlight than other types of graphical representation.
5. How to decide which graph is suitable for a situation?
Sometimes, the question does not specify which type of graph you have to use. In these cases, you will have to analyze the given data and decide which graph will be more suitable. When you have to compare two different categories of data sets, you should use a bar graph as it makes the data easy to interpret. If you have to find the trends and progress over a short period, you can use line graphs. Moreover, when you have to represent a whole graphically, a pie chart is the best option.