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# Graphical Representation |New topic Based on UGC NET Exam

## Graphical representation (Bar-chart, Histograms, Pie-chart, Table-chart and Line-chart) and mapping of Data.

Graphical representation helps in analyzing data. It helps in representing a relation between ideas, data, concepts, and information represented in a diagram. It is easily understandable and is also among the essential learning strategies. Of course, this always depends on the information type in any specific domain.

Graphical representation implies using graphs and charts for visually displaying, clarifying, analyzing, and interpreting numerical data, functions, and other qualitative structures.

#### Unit-VII Data Interpretation

The use of intuitive charts to effectively illustrate and simplify data sets is called graphical representation. Data is absorbed into the data software’s graphical representation. It is then represented using several symbols, such as bars on a bar chart, lines on a line chart, or slices on a pie chart, from which users can understand better than from numerical analysis alone.

Representational graphics can help predict and make better data-driven decisions by immediately illustrating general behavior and highlighting oddities, phenomena, and linkages between data pieces that could otherwise go unnoticed. The kind of representational graphics utilized will be determined by the data type being investigated.

### Graphical representation types:

Data charts come in various formats, including maps, diagrams, and graphs, and generally include written titles and legends to indicate the chart’s purpose, measurement units, and variables. The type of the data, the goal of the chart, and a graphical representation of quantitative data or a graphical representation of qualitative data are being portrayed. There are many different formats for displaying data graphically. The following are some most popular charts:

#### Line graphs:

A line graph is a visual representation of how the value of a variable change over time. The points with different values of the variable are connected to make this graph. It can help assess data trends and forecast future trends.  It is the simplest method for data representation using straight lines. The line height, here, signifies the magnitude of the class and the distance between all of them is kept uniform.

#### Bar graphs:

It is a type of graphical representation of data in which bars of uniform width are drawn on one axis (typically the x-axis) with equal space between them, displaying the variable. The height of the bars represents the values of the variables. It is also called a bar chart and in this, the rectangular bars represent the grouped data. In this, every bar represents a class and their height is proportional to the item’s magnitude in the given class. You can either represent it horizontally or vertically with equal space between each bar. A bar graph has four types as follows:

1. Simple bar graph: In this, every item is compared with respect to a single character and it can be either horizontal or vertical.
2. Multiple bar graph: It has two or more bars represented side-wise to allow comparing multiple sets. Different shades, colors, or patterns are used for distinguishing between the bars.
3. Subdivided bar graph: It is also called a component bar graph where each bar is divided into various compartments. Every compartment’s size is proportional to the variable’s magnitude. In this type too, the distinguishing is done using various colors, shades or designs, and patterns. Here, the distance between each bar and the width of each of them are constant.
4. Percentage bar graph: It is used for representing a simpler analysis of statistical data in the form of percentages. The bar length is kept constant as 100%, and each of them has some compartments shaded for representing a data value.

#### Histograms:

This is similar to bar graphs, except it is based on numerical values’ frequency rather than the actual values. The data is divided into intervals, and the bars represent the frequency of values inside those intervals. That is, it counts how many of the data’s values fall within a given range. In histogram, the columns are exhibited as the classes and they do not have any space in between. In this, the area of each block represents the frequency of every class.

#### Leaf and stem plot:

This is a plot in which each value is divided into a “leaf” (usually the last number) and a “stem” (other remaining digits). For instance, the number 42 is divided into leaf (2) and stem (4). It is just like a histogram, turned towards its side. They are mostly and efficiently used in case of smaller data set and when we have to find the quartiles or medians.

#### Whisker and box plot:

To demonstrate their summary, these graphs divide the data into four pieces. They are more interested in the data’s spread, average, and median. The found median is then used for splitting the data values into halves and then with the median of each halves, the value is further split for forming the quartiles. The set of variables from the median of the lower portion of the values at the bottom of the box to the median of the higher half of the values at the top of the box is shown in each box on the plot. The median of all the data values is represented by a line in the middle of the box. The whiskers then indicate to the data’s highest and lowest values.

### Pie Chart:

A pie chart is a sort of graph displaying data in the form of a circular graph. The circle is divided into portions, each of which represents a percentage of the total. The total area of 3600 gets divided into further component sectors according to the data provided. The data’s arc length is also proportional to the data frequency. Furthermore, arc length is also proportional to the area of sector and the central angle. For calculation, the formula used is as follows:

Sector angle = (Category’s value / Total categories’ value) * 360

### Frequency Polygon:

It is a curve used for representing frequencies and frequency distribution for a given data. The mid value in the polygon is first obtained for every class. Further, we plot the values and frequency of each class on a graph and then the points are joined for forming a curve. The line thus formed can extend in both directions on the x axis. Finally, the first point gets connected to the lower limit of first class and the last point to the upper limit of the first class. Therefore, the frequency polygon forms a closed graph.

### General Guidelines for Data Graphical Representation

To correctly display information in a graphical representation, there are a few guidelines to follow. They are as follows:

• Acceptable Title: Make sure the graph has an appropriate title that identifies the presentation’s topic.
• Measurement Unit: In the graph, mention the measurement unit.
• Correct Scale: Select a proper scale to depict the facts accurately.
• Index: For better understanding, index the right colors, hues, lines, and design in the graphs.
• Sources of Information: At the bottom of the graph, include the source of information if it is necessary.
• Maintain a straightforward approach: Create a graph that is simple to understand for everyone.
• Neat: Use the right size, fonts, colors, and other elements to make the graph visual assistance for information display.

### Mathematical Graphical Representation

A graph is a chart with statistical data represented by lines or curves drawn across the coordinate point shown on its surface in mathematics. It aids in studying a relationship between two variables by allowing one to assess the change in one variable’s amount concerning another variable over some time. In addition, it aids in the analysis of the series and frequency distributions for a specific situation. There are two sorts of graphs that can be used to represent data visually. They are as follows:

• Time series graph: A line graph is an example of a time-series graph.
• Frequency Distribution Graphs: Frequency Polygon Graph is an example of a frequency distribution graph.

### The Benefits and Drawbacks of Graphical Data Representation

The ability to analyze and understand vast amounts of numerical data and the relationships between data points requires the use of tabular and graphical representations of data. One of the most fundamental ways to data analysis is data visualization, which provides a universal and straightforward way to represent, abstract, and discuss complicated data patterns. The following are the key benefits of graphical data representation:

• Enhances and facilitates learning: Graphics help people grasp data and overcome language and literacy challenges.
• Understand content in a better manner: Visuals are more powerful than text in helping people understand what they’re seeing.
• The flexibility of application: graphical representations can be used in almost any data-related sector.
• Increases structured thinking: visual aids allow users to make quick, data-driven decisions at a glance.
• It supports more engaging and exciting visual presentations: by allowing for more creative, tailored reports.
• It improves communication: studying graphics highlighting important topics is much faster than reading a detailed report line by line.
• Displays the entire picture: a real-time, comprehensive view of all variables, time frames, data behavior, and relationships.

• The cost of human work and resources
• The process of selecting the most effective graphical and tabular representation of data
• The increased design complexity of visualizing data
• The possibility for human bias.

### Why is Data Graphical Representation Important?

Understanding and recognizing patterns and trends in the ever-increasing data flow requires a graphic visual representation of data. The use of graphical representations allows for the rapid examination of vast volumes of data at once, which can aid in forming forecasts and informed decisions. Data visualizations also make cooperation far more effective by employing common visual metaphors to demonstrate relationships and highlight meaning, obviating the need for sophisticated, long-winded explanations of what appears to be a chaotic array of statistics.

Data is worth only when its importance has been disclosed and consumed. This is best accomplished through graphical representation tools created with human cognition and perception in mind. Human visual processing is excellent when it comes to identifying relationships and changes in sizes, shapes, colors, and numbers. Attempting to obtain insight solely from numerical data, especially in big data scenarios with billions of rows of data, is hugely time-consuming and wasteful.‍

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1. Gangatharan VT says