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 meant by the graphical representation of data in Maths?
Graphical representation in Mathematics refers to the use of graphs, charts, or plots to visually display numerical and categorical data, making it easier to observe patterns, trends, and comparisons. Common types include bar graphs, line graphs, histograms, and pie charts, each suited for different data types and purposes as per the CBSE 2025-26 syllabus.
2. What are the main types of graphs used to represent data in Class 11 Maths?
The primary types of graphs covered in Class 11 Maths for data representation include:
- Bar Graph: Used for comparing distinct categories.
- Line Graph: Useful for showing trends over time.
- Histogram: Represents frequency distribution of continuous data.
- Pie Chart: Displays proportional data in a circular graph.
- Frequency Polygon: Shows frequency distribution using a continuous line.
3. How does a bar graph differ from a histogram?
The key differences are:
- Bar Graph: Bars are separated by spaces and represent categorical data.
- Histogram: Bars are adjacent (no gaps) and show frequency for continuous data grouped in intervals.
The distinction is important for choosing the right type of graphical representation for your dataset.
4. Why is graphical representation considered essential in presenting mathematical data?
Graphical representation enhances data interpretation by providing a visual overview that helps identify patterns, trends, and outliers quickly. It simplifies complex datasets, enables easy comparison between groups, and supports informed decision-making even for non-experts.
5. What steps should be followed to ensure accuracy while drawing a graph?
To ensure an accurate graph, always:
- Choose a scale that fits your data range.
- Label both axes clearly with measurement units.
- Include a descriptive title and meaningful index/key if colors or patterns are used.
- Plot data points precisely and connect them as per the graph type.
- Maintain neatness and simplicity for clarity and readability.
6. In which situations would a pie chart be preferred for data representation?
A pie chart is ideal when you need to show the proportional relationship of parts to a whole, such as representing the percentage breakdown of categories within a single dataset. CBSE recommends pie charts for comparing fractions or percentages, especially for data that forms a complete set (100%).
7. How can frequency polygons be constructed from a frequency distribution?
To construct a frequency polygon:
- Calculate the class mark for each interval: (Upper Limit + Lower Limit)/2.
- Plot these class marks on the x-axis against their respective frequencies on the y-axis.
- Join consecutive points with straight lines to form the polygon.
- Close the polygon by extending lines to the x-axis at both ends.
8. What mistakes should students avoid while interpreting graphs in board exams?
Common mistakes to avoid:
- Misreading scales on axes, leading to incorrect values.
- Ignoring the unit of measurement or index provided.
- Confusing the type of graph (e.g., using a bar graph for continuous data).
- Overlooking trends or outliers due to lack of attention to detail.
9. How can proper graphical representation support scoring higher in CBSE board exams?
Correct graphical representation demonstrates analytical understanding and precision in Maths. Using clear scales, neat plotting, and correct type selection ensures full marks for such questions. Well-drawn graphs also make your answers stand out and allow examiners to easily assess your grasp of data analysis.
10. What are some real-life applications of graphical representation taught in this chapter?
Real-life uses include:
- Comparing sales or profits across months (bar/line graphs).
- Visualizing population or temperature changes over time (line graphs).
- Displaying survey results, such as favorite sports or foods (pie charts).
- Analysing frequency of marks scored in exams (histograms/frequency polygons).
Such applications help students relate Mathematical concepts to everyday decision-making and analysis.
