what is graphical representation

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Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

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Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

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Graphical Representation

Graphical representation definition.

Graphical representation refers to the use of charts and graphs to visually display, analyze, clarify, and interpret numerical data, functions, and other qualitative structures. ‍

What is Graphical Representation?

Graphical representation refers to the use of intuitive charts to clearly visualize and simplify data sets. Data is ingested into graphical representation of data software and then represented by a variety of symbols, such as lines on a line chart, bars on a bar chart, or slices on a pie chart, from which users can gain greater insight than by numerical analysis alone. 

Representational graphics can quickly illustrate general behavior and highlight phenomenons, anomalies, and relationships between data points that may otherwise be overlooked, and may contribute to predictions and better, data-driven decisions. The types of representational graphics used will depend on the type of data being explored.

Types of Graphical Representation

Data charts are available in a wide variety of maps, diagrams, and graphs that typically include textual titles and legends to denote the purpose, measurement units, and variables of the chart. Choosing the most appropriate chart depends on a variety of different factors -- the nature of the data, the purpose of the chart, and whether a graphical representation of qualitative data or a graphical representation of quantitative data is being depicted. There are dozens of different formats for graphical representation of data. Some of the most popular charts include:

• Bar Graph -- contains a vertical axis and horizontal axis and displays data as rectangular bars with lengths proportional to the values that they represent; a useful visual aid for marketing purposes
• Choropleth -- thematic map in which an aggregate summary of a geographic characteristic within an area is represented by patterns of shading proportionate to a statistical variable
• Flow Chart -- diagram that depicts a workflow graphical representation with the use of arrows and geometric shapes; a useful visual aid for business and finance purposes
• Heatmap -- a colored, two-dimensional matrix of cells in which each cell represents a grouping of data and each cell’s color indicates its relative value
• Histogram – frequency distribution and graphical representation uses adjacent vertical bars erected over discrete intervals to represent the data frequency within a given interval; a useful visual aid for meteorology and environment purposes
• Line Graph – displays continuous data; ideal for predicting future events over time;  a useful visual aid for marketing purposes
• Pie Chart -- shows percentage values as a slice of pie; a useful visual aid for marketing purposes
• Pointmap -- CAD & GIS contract mapping and drafting solution that visualizes the location of data on a map by plotting geographic latitude and longitude data
• Scatter plot -- a diagram that shows the relationship between two sets of data, where each dot represents individual pieces of data and each axis represents a quantitative measure
• Stacked Bar Graph -- a graph in which each bar is segmented into parts, with the entire bar representing the whole, and each segment representing different categories of that whole; a useful visual aid for political science and sociology purposes
• Timeline Chart -- a long bar labelled with dates paralleling it that display a list of events in chronological order, a useful visual aid for history charting purposes
• Tree Diagram -- a hierarchical genealogical tree that illustrates a family structure; a useful visual aid for history charting purposes
• Venn Diagram -- consists of multiple overlapping usually circles, each representing a set; the default inner join graphical representation

Proprietary and open source software for graphical representation of data is available in a wide variety of programming languages. Software packages often provide spreadsheets equipped with built-in charting functions.

Advantages and Disadvantages of Graphical Representation of Data

Tabular and graphical representation of data are a vital component in analyzing and understanding large quantities of numerical data and the relationship between data points. Data visualization is one of the most fundamental approaches to data analysis, providing an intuitive and universal means to visualize, abstract, and share complex data patterns. The primary advantages of graphical representation of data are:

• Facilitates and improves learning: graphics make data easy to understand and eliminate language and literacy barriers
• Understanding content: visuals are more effective than text in human understanding
• Flexibility of use: graphical representation can be leveraged in nearly every field involving data
• Increases structured thinking: users can make quick, data-driven decisions at a glance with visual aids
• Supports creative, personalized reports for more engaging and stimulating visual  presentations 
• Improves communication: analyzing graphs that highlight relevant themes is significantly faster than reading through a descriptive report line by line
• Shows the whole picture: an instantaneous, full view of all variables, time frames, data behavior and relationships

Disadvantages of graphical representation of data typically concern the cost of human effort and resources, the process of selecting the most appropriate graphical and tabular representation of data, greater design complexity of visualizing data, and the potential for human bias.

Why Graphical Representation of Data is Important

Graphic visual representation of information is a crucial component in understanding and identifying patterns and trends in the ever increasing flow of data. Graphical representation enables the quick analysis of large amounts of data at one time and can aid in making predictions and informed decisions. Data visualizations also make collaboration significantly more efficient by using familiar visual metaphors to illustrate relationships and highlight meaning, eliminating complex, long-winded explanations of an otherwise chaotic-looking array of figures. 

Data only has value once its significance has been revealed and consumed, and its consumption is best facilitated with graphical representation tools that are designed with human cognition and perception in mind. Human visual processing is very efficient at detecting relationships and changes between sizes, shapes, colors, and quantities. Attempting to gain insight from numerical data alone, especially in big data instances in which there may be billions of rows of data, is exceedingly cumbersome and inefficient.

Does HEAVY.AI Offer a Graphical Representation Solution?

HEAVY.AI's visual analytics platform is an interactive data visualization client that works seamlessly with server-side technologies HEAVY.AIDB and Render to enable data science analysts to easily visualize and instantly interact with massive datasets. Analysts can interact with conventional charts and data tables, as well as big data graphical representations such as massive-scale scatterplots and geo charts. Data visualization contributes to a broad range of use cases, including performance analysis in business and guiding research in academia.

Introduction to Graphs

Table of Contents

15 December 2020                 

Read time: 6 minutes

Introduction

What are graphs?

What are the different types of data?

What are the different types of graphical representations?

The graph is nothing but an organized representation of data. It helps us to understand the data. Data are the numerical information collected through observation.

The word data came from the Latin word Datum which means “something given”

After a research question is developed, data is being collected continuously through observation. Then it is organized, summarized, classified, and then represented graphically.

Differences between Data and information: Data is the raw fact without any add on but the information is the meaning derived from data.

Introduction to Graphs-PDF

The graph is nothing but an organized representation of data. It helps us to understand the data. Data are the numerical information collected through observation. Here is a downloadable PDF to explore more.

• Line and Bar Graphs Application
• Graphs in Mathematics & Statistics

What are the different Types of Data?

There are two types of Data :

Quantitative

The data which are statistical or numerical are known as Quantitive data. Quantitive data is generated through. Quantitative data is also known as Structured data. Experiments, Tests, Surveys, Market Report.

Quantitive data is again divided into Continuous data and Discrete data.

Continuous Data

Continuous data is the data which can have any value. That means Continuous data can give infinite outcomes so it should be grouped before representing on a graph.

• The speed of a vehicle as it passes a checkpoint
• The mass of a cooking apple
• The time taken by a volunteer to perform a task

Discrete Data

Discrete data can have certain values. That means only a finite number can be categorized as discrete data.

• Numbers of cars sold at a dealership during a given month
• Number of houses in certain block
• Number of fish caught on a fishing trip
• Number of complaints received at the office of airline on a given day
• Number of customers who visit at bank during any given hour
• Number of heads obtained in three tosses of a coin

Differences between Discrete and Continuous data

• Numerical data could be either discrete or continuous
• Continuous data can take any numerical value (within a range); For example, weight, height, etc.
• There can be an infinite number of possible values in continuous data
• Discrete data can take only certain values by finite ‘jumps’, i.e., it ‘jumps’ from one value to another but does not take any intermediate value between them (For example, number of students in the class)

Qualitative

Data that deals with description or quality instead of numbers are known as Quantitative data. Qualitative data is also known as unstructured data. Because this type of data is loosely compact and can’t be analyzed conventionally.

Different Types of Graphical Representations

There are many types of graph we can use to represent data. They are as follows,

A bar graph or chart is a way to represent data by rectangular column or bar. The heights or length of the bar is proportional to the values.

A line graph is a type of graph where the information or data is plotted as some dots which are known as markers and then they are added to each other by a straight line.

The line graph is normally used to represent the data that changes over time.

A histogram graph is a graph where the information is represented along with the height of the rectangular bar. Though it does look like a bar graph, there is a fundamental difference between them. With the histogram, each column represents a range of quantitative data when a bar graph represents categorical variables.

The other name of the pie chart is a circle graph. It is a circular chart where numerical information represents as slices or in fractional form or percentage where the whole circle is 100%.

• Stem and leaf plot

The stem and leaf plot is a way to represents quantitative data according to frequency ranges or frequency distribution.

In the stem and leaf plot, each data is split into stem and leaf, which is 32 will be split into 3 stems and 2 leaves.

Frequency table: Frequency means the number of occurrences of an event. A frequency distribution table is a graph or chart which shows the frequency of events. It is denoted as ‘f’ .

Pictograph or Pictogram is the earliest way to represents data in a pictorial form or by using symbols or images. And each image represents a particular number of things.

According to the above-mentioned Pictograph, the number of Appels sold on Monday is 6x2=12.

• Scatter diagrams

Scatter diagram or scatter plot is a way of graphical representation by using cartesian coordinates of two variables. The plot shows the relationship between two variables. Below there is a data table as well as a Scattergram as per the given data.

What is the meaning of Graphical representation?

Graphical representation is a way to represent and analyze quantitive data. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables.

Principles of graphical representation

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin.

On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value.

When X-axis and y-axis intersected each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV.

The location on the coordinate plane is known as the ordered pair and it is written as (x,y). That means the first value will be on the x-axis and the second one is on the y-axis. When we will plot any coordinate, we always have to start counting from the origin and have to move along the x-axis, if it is positive then to the right side, and if it is negative then to the left side. Then from the x-axis, we have to plot the y’s value, which means we have to move up for positive value or down if the value is negative along with the y-axis.

In the following graph, 1st ordered pair (2,3) where both the values of x and y are positive and it is on quadrant I. 2nd ordered pair (-3,1), here the value of x is negative and value of y is positive and it is in quadrant II. 3rd ordered pair (-1.5, -2.5), here the value of x as well as y both are Negative and in quadrant III.

Methods of representing a frequency distribution

There are four methods to represent a frequency distribution graphically. These are,

• Smoothed Frequency graph
• Cumulative frequency graph or Ogive.
• Pie diagram.

Advantages and Disadvantages of Graphical representation of data

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represents it graphically.

You may also like:

• Graphing a Quadratic Function
• Empirical Relationship Between Mean, Median, and Mode

Not only in mathematics but almost in every field the graph is a very important way to store, analyze, and represents information. After any research work or after any survey the next step is to organize the observation or information and plotting them on a graph paper or plane. The visual representation of information makes the understanding of crucial components or trends easier.

A huge amount of data can be store or analyze in a small space.

The graphical representation of data helps to decide by following the trend.

A complete Idea: Graphical representation constitutes a clear and comprehensive idea in the minds of the audience. Reading a large number (say hundreds) of pages may not help to make a decision. Anyone can get a clear idea just by looking into the graph or design.

Graphs are a very conceptual topic, so it is essential to get a complete understanding of the concept. Graphs are great visual aids and help explain numerous things better, they are important in everyday life. Get better at graphs with us, sign up for a free trial . 

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Frequently Asked Questions (FAQs)

What is data.

Data are characteristics or information, usually numerical, that are collected through observation.

How do you differentiate between data and information?

Data is the raw fact without any add on but the information is the meaning derived from data.

What are the types of data?

There are two types of Data:

What are the ways to represent data?

Tables, charts and graphs are all ways of representing data , and they can be used for two broad purposes. The first is to support the collection, organisation and analysis of data as part of the process of a scientific study.

- Tables, charts and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organisation and analysis of data as part of the process of a scientific study.

What are the different types of graphs?

Different types of graphs include:

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Graphical Representation

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Graphical representations encompass a wide variety of techniques that are used to clarify, interpret and analyze data by plotting points and drawing line segments, surfaces and other geometric forms or symbols.

The purpose of a graph is a rapid visualization of a data set. For instance, it should clearly illustrate the general behavior of the phenomenon investigated and highlight any important factors. It can be used, for example, as a means to translate or to complete a  frequency table .

Therefore, graphical representation is a form of data representation.

The concept of plotting a point in coordinate space dates back to at least the ancient Greeks, but we had to wait until the work of Descartes, René for mathematicians to investigate this concept.

According to Royston, E. (1970), a German mathematician named Crome, A.W. was among the first to use graphical representation in statistics . He initially used it as a teaching tool.

In his works Geographisch-statistische Darstellung...

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Crome, A.F.W.: Ueber die Grösse und Bevölkerung der sämtlichen Europäischen Staaten. Weygand, Leipzig (1785)

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(2008). Graphical Representation. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_174

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