Graphical Representation: A graph is a categorised representation of data. It helps us understand the data easily. Data is a collection of numerical figures collected through surveying. The word data came from the Latin word ‘Datum’, which means ‘something given’. After developing a research question, data is being collected constantly through observation. Then the data collected is arranged, summarised, classified, and finally represented graphically. This is the concept of graphical representation of data.

Let’s study different kinds of graphical representations with examples, the types of graphical representation, and graphical representation of data in statistics, in this article.

What Are Graphical Representations?

Graphical representation refers to the use of intuitive charts to visualise clearly and simplify data sets. Data obtained from surveying is ingested into a graphical representation of data software. Then it is represented by some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. In this way, users can achieve much more clarity and understanding than by numerical study alone. 

Advantages of Graphical Representation

Some of the advantages of using graphs are listed below:

1. The graph helps us understand the data or information even when we have no idea about it.
2. It saves time.
3. It makes it easier for us to compare the data for different time periods or different kinds.
4. It is mainly used in statistics to determine the mean, median and mode for different data and interpolation and extrapolation of data.

Use of Graphical Representations

The main agenda of presenting scientific data into graphs is to provide information efficiently to utilise the power of visual display while avoiding confusion or deception. This is important in communicating our findings to others and our understanding and analysis of the data.

Graphical data representation is crucial in understanding and identifying trends and patterns in the ever-increasing data flow. Graphical representation helps in quick analysis of large quantities and can support making predictions and informed decisions.

General Rules for Graphical Representation of Data

The following are a few rules to present the information in the graphical representation:

1. Suitable title: The title of the graph should be appropriate that indicates the subject of the presentation.
2. Measurement unit: The measurement unit in the graph should be mentioned.
3. Proper scale:  Choose a proper scale to represent the data accurately.
4. Index: For better understanding, index the appropriate colours, shades, lines, and designs in the graphs. 
5. Data sources: Data should be included wherever it is necessary at the bottom of the graph.
6. Keep it simple: The construction of a graph should be such a way that it is effortlessly understood.
7. Neat: The correct size, fonts, colours etc., should be chosen so that the graph should be a visual aid for presenting the information.

Types of Graphical Representation

1. Line graph
2. Histogram
3. Bar graph
4. Pie chart
5. Frequency polygon
6. Ogives or Cumulative frequency graphs

1. Line Graph

A line graph is a chart used to show information that changes over time. We plot line graphs by connecting several points with straight lines.  Another name is a line chart. The line graph contains two axes: \(x-\)axis and \(y-\)axis.

1. The horizontal axis is the \(x-\)axis.
2. The vertical axis is the \(y-\)axis.

Example: The following graph shows the number of motorbikes sold on different days of the week.

2. Histogram

Continuous data represented on the two-dimensional graph is called a histogram. In the histogram, the bars are placed continuously side by side without a gap between consecutive bars. In other words, rectangles are erected on the class intervals of the distribution. The areas of the rectangles formed by bars are proportional to the frequencies.

Example: Following is an example of a histogram showing the average pass percentage of students.

3. Bar Graph

Bar graphs can be of two types – horizontal bar graphs and vertical bar graphs. While a horizontal bar graph is applied for qualitative data or data varying over space, the vertical bar graph is associated with quantitative data or time-series data.

Bars are rectangles of varying lengths and of equal width usually are drawn either horizontally or vertically. We consider multiple or grouped bar graphs to compare related series. Component or sub-divided bar diagrams are applied for representing data divided into several components. 

Example: The following graph is an example of a bar graph representing the money spent month-wise

4. Pie Chart

The sector of a circle represents various observations or components, and the whole circle represents the sum of the value of all the components. The total central angle of a circle is \({360^{\rm{o}}}\) and is divided according to the values of the components.

The central angle of a component\( = \frac{{{\rm{ value}}\,{\rm{of}}\,{\rm{the}}\,{\rm{component }}}}{{{\rm{total}}\,{\rm{value}}}} \times {360^{\rm{o}}}\)

Sometimes, the value of the components is expressed in percentages. In such cases,
The central angle of a component\( = \frac{{{\rm{ percentage}}\,{\rm{value}}\,{\rm{of}}\,{\rm{the}}\,{\rm{component }}}}{{100}} \times {360^{\rm{o}}}\)

Example: The following figure represents a pie-chart

5. Frequency Polygon

A frequency polygon is another way of representing frequency distribution graphically. Follow the steps below to make a frequency polygon:

(i) Calculate and obtain the frequency distribution and the mid-points of each class interval.
(ii) Represent the mid-points along the \(x-\)axis and the frequencies along the \(y-\)axis.
(iii) Mark the points corresponding to the frequency at each midpoint.
(iv) Now join these points in straight lines.
(v) To finish the frequency polygon, join the consecutive points at each end (as the case may be at zero frequency) on the \(x-\)axis.

Example: The following graph is the frequency polygon showing the road race results.

6. Ogives or Cumulative Frequency Graphs

By plotting cumulative frequency against the respective class intervals, we obtain ogives.
There are two ogives – less than type ogives and more than type.

Less than type ogives is obtained by taking less than cumulative frequency on the vertical axis. We can obtain more than type ogives by plotting more than type cumulative frequency on the vertical axis and joining the plotted points successively by line segments.

Example: The below graph represents the less than and more than ogives for the entrance examination scores of \(60\) students.

Solved Examples – Basic Graphical Representation

Q.1. The wildlife population in the following years, \(2013, 2014, 2015, 2016, 2017, 2018,\) and \(2019\) were \(300, 200, 400, 600, 500, 400\) and \(500,\) respectively. Represent these data using a line graph.
Ans: We can represent the population for seven consecutive years by drawing a line diagram as given below. Let us consider years on the horizontal axis and population on the vertical axis.

For the year \(2013,\) the population was \(300.\) It can be written as a point \((2013, 300)\)
Similarly, we can write the points for the succeeding years as follows:
\((2014, 200), (2015, 400), (2016, 600), (2017, 500), (2018, 400)\) and \((2019, 500)\)

We can obtain the line graph by plotting all these points and joining them using a ruler.
The following line diagram shows the population of wildlife from \(2013\) to \(2019.\)

Q.2. Draw a histogram for the following data that represents the marks scored by \(120\) students in an examination:

Score	\(0-20\)	\(20-40\)	\(40-60\)	\(60-80\)	\(80-100\)
Number of students	\(5\)	\(10\)	\(40\)	\(45\)	\(20\)

Ans: The class intervals are of an equal length of \(20\) marks. Let us indicate the class intervals along the \(x-\)axis and the number of students along the \(y-\)axis, with the appropriate scale. The histogram is given below.

Q.3. The total number of scoops of vanilla ice cream in the different months of a year is given below:

Month	Mar	Apr	May	Jun	Jul
Number of scoops sold	\(240\)	\(400\)	\(440\)	\(320\)	\(200\)

For the above data, draw a bar graph.
Ans: The following graph represents the number of vanilla ice cream scoops sold from March to July. The month is indicated along the \(x-\)axis, and the number of scoops sold is represented along the \(y-\)axis.

Q.4. The number of hours spent by a working woman on various activities on a working day is given below. Using the angle measurement, draw a pie chart.

Activity	Household	Sleep	Cooking	Office	TV	Other
Number of hours	\(3\)	\(7\)	\(2\)	\(9\)	\(1\)	\(2\)

Ans: The central angle of a component\( = \frac{{{\rm{ value}}\,{\rm{of}}\,{\rm{the}}\,{\rm{component }}}}{{{\rm{total}}\,{\rm{value}}}} \times {360^{\rm{o}}}\). We may calculate the central angles for various components as follow:

Activity	Duration in hours	Central angle
Household	\(3\)	\(\frac{3}{{24}} \times {360^{\rm{o}}} = {45^{\rm{o}}}\)
Sleep	\(7\)	\(\frac{7}{{24}} \times {360^{\rm{o}}} = {105^{\rm{o}}}\)
Cooking	\(2\)	\(\frac{2}{{24}} \times {360^{\rm{o}}} = {30^{\rm{o}}}\)
Office	\(9\)	\(\frac{9}{{24}} \times {360^{\rm{o}}} = {135^{\rm{o}}}\)
TV	\(1\)	\(\frac{1}{{24}} \times {360^{\rm{o}}} = {15^{\rm{o}}}\)
Other	\(2\)	\(\frac{2}{{24}} \times {360^{\rm{o}}} = {30^{\rm{o}}}\)
Total	\(24\)	\({360^{\rm{o}}}\)

By knowing the central angle, a pie chart is drawn,

Q.5. Draw a frequency polygon for the following data using a histogram.

Height of students	\(140-145\)	\(145-150\)	\(150-155\)	\(155-160\)	\(160-165\)	\(165-170\)	\(170-175\)
Number of students	\(35\)	\(40\)	\(55\)	\(50\)	\(40\)	\(35\)	\(20\)

Ans: To draw a frequency polygon, we take the imagined classes \(135-140\) at the beginning and \(175-180\) at the end, each with frequency zero. The following is the frequency table tabulated for the given data

Class interval	Midpoint	Frequency
\(140-145\)	\(142.5\)	\(35\)
\(145-150\)	\(147.5\)	\(40\)
\(150-155\)	\(152.5\)	\(55\)
\(155-160\)	\(157.5\)	\(50\)
\(160-165\)	\(162.5\)	\(40\)
\(165-170\)	\(167.5\)	\(35\)
\(170-175\)	\(172.5\)	\(20\)

Let’s mark the class intervals along the \(x-\)axis and the frequency along the \(y-\)axis.

Using the above table, plot the points on the histogram: \((137.5, 0), (142.5, 35), (147.5, 40), (152.5, 55), (157.5, 50), (162.5, 40),\)
\((167.5, 35), (172.5, 20)\) and \((177.5, 0).\)

We join these points one after the other to obtain the required frequency polygon.

Summary

In this article, we have studied the details of the graphical representation of data. We learnt the meaning, uses, and advantages of using graphs. Then we studied the different types of graphs with examples. Lastly, we solved examples to help students understand the concept in a better way.

Frequently Asked Questions (FAQs) on Basic Graphical Representation

Q.1: What are graphical representations?
Ans: Graphical representations represent given data using charts or graphs numerically and then visually analyse and interpret the information.

Q.2: What are the 6 types of graphs used?
Ans: The following are the types of graphs we use commonly:
1. Line graph
2. Histogram
3. Bar graph
4. Pie chart
5. Frequency polygon
6. Ogives or cumulative frequency graphs

Q.3: What are the advantages of the graphical method?
Ans: The advantages of using a graphical method are:
1. Facilitates improved learning
2. Knowing the content
3. Usage of flexibility
4. Increases thinking
5. Supports creative, personalised reports for more engaging and stimulating visual presentations
6. Better communication
7. It shows the whole picture

Q.4: What is the graphical representation of an idea?
Ans: The graphical representations exhibit relationships between ideas, data, information and concepts in a visual graph or map. Graphical representations are effortless to acknowledge.

Q.5: How do you do frequency polygon?
Ans: Frequency distribution is first obtained, and the midpoints of each class interval are found. Mark the midpoints along the \(x-\)axis and frequencies along the \(y-\)axis. Plot the points corresponding to the frequency. Join the points, using line segments in order.