46 Presentation of data II – Graphical representation

Pa . Raajeswari

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DEFINITION

 

 

Graphical representation is the visual display of data using plots and charts. It is used in many academic and professional disciplines but most widely so in the fields of mathematics, medicine and sciences. Graphical representation helps to quantify, sort and present data in a method that is understandable to a large variety of audiences. A graph is the representation of data by using graphical symbols such as lines, bars, pie slices, dots etc. A graph does represent a numerical data in the form of a qualitative structure and provides important information.

 

Statistical surveys and experiments provides valuable information about numerical scores. For better understanding and making conclusions and interpretations, the data should be managed and organized in a systematic form.

 

Graphs also enable in studying both time series and frequency distribution as they give clear account and precise picture of problem. Above all graphs are also easy to understand and eye catching and can create a storing impact on memory.

 

General Principles of Graphic Representation:

 

There are some algebraic principles which apply to all types of graphic representation of data. In a graph there are two lines called coordinate axes. One is vertical known as Y axis and the other is horizontal called X axis. These two lines are perpendicular to each other. Where these two lines intersect each other is called ‘0’ or the Origin. On the X axis the distances right to the origin have positive value and distances left to the origin have negative value. On the Y axis distances above the origin have a positive value and below the origin have a negative value.

TYPES OF GRAPHICAL REPRESENTATON:

 

The various types of graphical representations of the data are

  • Dot Plots
  • Bar Graph
  • Line Graph
  • Circle Graph
  • Histogram and Frequency Polygon

1.Dot Plots

 

The dot plot is one of the most simplest ways of graphical representation of the statistical data. As the name itself suggests, a dot plot uses the dots. It is a graphic display which usually compares frequency within different categories. The dot plot is composed of dots that are to be plotted on a graph paper.

In the dot plot, every dot denotes a specific number of observations belonging to a data set. One dot usually represents one observation. These dots are to be marked in the form of a column for each category. In this way, the height of each column shows the corresponding frequency of some category. The dot plots are quite useful when there are small amount of data is given within the small number of categories.

 

2.Bar Graph

 

A bar graph is a very frequently used graph in statistics as well as in media. A bar graph is a type of graph which contains rectangles or rectangular bars. The lengths of these bars should be proportional to the numerical values represented by them. In bar graph, the bars may be plotted either horizontally or vertically. But a vertical bar graph (also known as column bar graph) is used more than a horizontal one.

 

A vertical bar graph is shown below:

 

Number of students went to different countries for study:

The rectangular bars are separated by some distance in order to distinguish them from one another. The bar graph shows comparison among the given categories.

 

Mostly, horizontal axis of the graph represents specific categories and vertical axis shows the discrete numerical values.

 

3.Line Graph

 

A line graph is a kind of graph which represents data in a way that a series of points are to be connected by segments of straight lines. In a line graph, the data points are plotted on a graph and they are joined together with straight line.

 

A sample line graph is  illustrated  in  the following diagram:

The line graphs are used in the science, statistics and media. Line graphs are very easy to create. These are quite popular in comparison with other graphs since they visualize characteristics revealing data trends very clearly. A line graph gives a clear visual comparison between two variables which are represented on X-axis and Y-axis.

 

4.Circle Graph

 

A circle graph is also known as a pie graph or pie chart. It is called so since it is similar to slice of a “pie”. A pie graph is defined as a graph which contains a circle which is divided into sectors. These sectors illustrate the numerical proportion of the data.

 

A pie chart are shown in the following diagram:

The arc lengths of the sectors, in pie chart, are proportional to the numerical value they represent.Circle graphs are quite commonly seen in mass media as well as in business world.

 

5.Histogram and Frequency Polygon

 

The histograms and frequency polygons are very common graphs in statistics. A histogram is defined as a graphical representation of the mutually exclusive events. A histogram is quite similar to the bar graph. Both are made up of rectangular bars. The difference is that there is no gap between any two bars in the histogram. The histogram is used to represent the continuous data.

A histogram may look like the following graph:

The frequency polygon is a type of graphical representation which gives us better understanding of the shape of given distribution. Frequency polygons serve almost the similar purpose as histograms do. But the frequency polygon is quite helpful for the purpose of comparing two or more sets of data. The frequency polygons are said to be the extension of the histogram. When the midpoints of tops of the rectangular bars are joined together, the frequency polygon is made.

Examples

 

Few   examples    of    graphical    representation    of    statistical    data    are    given    below:

 

Example 1: Draw a dot plot for the following data.

Solution: The pie graph of the above data is:

Methods to Represent a Frequency Distribution:

 

Generally four methods are used to represent a frequency distribution graphically. These are Histogram, Smoothed frequency graph and Ogive or Cumulative frequency graph and pie diagram.

 

1. Histogram:

 

Histogram is a non-cumulative frequency graph, it is drawn on a natural scale in which the representative frequencies of the different class of values are represented through vertical rectangles drawn closed to each other. Measure of central tendency, mode can be easily determined with the help of this graph.

 

How to draw a Histogram:

 

Step—1:

 

Represent the class intervals of the variables along the X axis and their frequencies along the Y-axis on natural scale.

 

Step—2:

 

Start X axis with the lower limit of the lowest class interval. When the lower limit happens to be a distant score from the origin give a break in the X-axis n to indicate that the vertical axis has been moved in for convenience.

 

Step—3:

 

Now draw rectangular bars in parallel to Y axis above each of the class intervals with class units as base: The areas of rectangles must be proportional to the frequencies of the corresponding classes.

Solution:

In this graph we shall take class intervals in the X axis and frequencies in the Y axis. Before plotting the graph we have to convert the class into their exact limits.

Advantages of histogram:

 

1.  It is easy to draw and simple to understand.

2.  It helps us to understand the distribution easily and quickly.

3.  It is more precise than the polygene.

 

Limitations of histogram:

 

1.  It is not possible to plot more than one distribution on same axes as histogram.

2.  Comparison of more than one frequency distribution on the same axes is not possible.

3.  It is not possible to make it smooth.

 

Uses of histogram:

 

1.Represents the data in graphic form.

2.Provides the knowledge of how the scores in the group are distributed. Whether the scores are piled up at the lower or higher end of the distribution or are evenly and regularly distributed throughout the scale.

3.Frequency Polygon. The frequency polygon is a frequency graph which is drawn by joining the coordinating points of the mid-values of the class intervals and their corresponding fre-quencies.

 

How to draw a frequency polygon:

Step-1:

 

Draw a horizontal line at the bottom of graph paper named ‘OX’ axis. Mark off the exact limits of the class intervals along this axis. It is better to start with i. of lowest value. When the lowest score in the distribution is a large number we cannot show it graphically if we start with the origin. Therefore put a break in the X axis to indicate that the vertical axis has been moved in for convenience. Two additional points may be added to the two extreme ends.

 

Step-2:

 

Draw a vertical line through the extreme end of the horizontal axis known as OY axis. Along this line mark off the units to represent the frequencies of the class intervals. The scale should be chosen in such a way that it will make the largest frequency (height) of the polygon approximately 75 percent of the width of the figure.

 

Step-3:

 

Plot the points at a height proportional to the frequencies directly above the point on the horizontal axis representing the mid-point of each class interval.

 

Step-4:

 

After plotting all the points on the graph join these points by a series of short straight lines to form the frequency polygon. In order to complete the figure two additional intervals at the high end and low end of the distribution should be included. The frequency of these two intervals will be zero.

 

Illustration: No. 7.3:

 

Draw a frequency polygon from the following data:

Advantages of frequency polygon:

 

1.  It is easy to draw and simple to understand.

2.  It is possible to plot two distributions at a time on same axes.

3.  Comparison of two distributions can be made through frequency polygon.

4.  It is possible to make it smooth.

 

Limitations of frequency polygon:

 

1.  It is less precise.

2.  It is not accurate in terms of area the frequency upon each interval.

 

Uses of frequency polygon:

 

1. When two or more distributions are to be compared the frequency polygon is used.

2. It represents the data in graphic form.

3. It provides knowledge of how the scores in one or more group are distributed. Whether the scores are piled up at the lower or higher end of the distribution or are evenly and regularly distributed throughout the scale.

 

2. Smoothed Frequency Polygon:

 

When the sample is very small and the frequency distribution is irregular the polygon is very jig-jag. In order to wipe out the irregularities and “also get a better notion of how the figure might look if the data were more numerous, the frequency polygon may be smoothed.”

 

In this process to adjust the frequencies we take a series of ‘moving’ or ‘running’ averages. To get an adjusted or smoothed frequency we add the frequency of a class interval with the two adjacent intervals, just below and above the class interval. Then the sum is divided by 3. When these adjusted frequencies are plotted against the class intervals on a graph we get a smoothed frequency polygon.

 

Illustration 7.4:

 

Draw a smoothed frequency polygon, of the data given in the illustration No. 7.3:

 

Solution:

 

Here we have to first convert the class intervals into their exact limits. Then we have to determine the adjusted or smoothed frequencies.

3. Ogive or Cumulative Frequency Polygon:

 

Ogive is a cumulative frequency graphs drawn on natural scale to determine the values of certain factors like median, Quartile, Percentile etc. In these graphs the exact limits of the class intervals are shown along the X-axis and the cumulative frequencies are shown along the Y-axis. Below are given the steps to draw an ogive.

 

Step—1:

 

Get the cumulative frequency by adding the frequencies cumulatively, from the lower end (to get a less than ogive) or from the upper end (to get a more than ogive).

 

Step—2:

 

Mark off the class intervals in the X-axis.

 

Step—3:

 

Represent the cumulative frequencies along the Y-axis beginning with zero at the base.

 

Step—4:

 

Put dots at each of the coordinating points of the upper limit and the corresponding frequencies.

 

Step—5:

 

Join all the dots with a line drawing smoothly. This will result in curve called ogive.

 

Illustration No. 7.5:

 

Draw an ogive from the data given below:

Solution:

To plot this graph first we have to convert, the class intervals into their exact limits. Then we have to calculate the cumulative frequencies of the distribution.

Uses of Ogive:

1.  Ogive is useful to determine the number of students below and above a particular score.

2.  When the median as a measure of central tendency is wanted.

3.  When the quartiles, deciles and percentiles are wanted.

4.  By plotting the scores of two groups on a same scale we can compare both the groups.

 

4. The Pie Diagram:

 

Figure given below shows the distribution of elementary pupils by their academic achievement in a school. Of the total, 60% are high achievers, 25% middle achievers and 15% low achievers. The construction of this pie diagram is quite simple. There are 360 degree in the circle. Hence, 60% of 360′ or 216° are counted off as shown in the diagram; this sector represents the proportion of high achievers students.

 

Ninety degrees counted off for the middle achiever students (25%) and 54 degrees for low achiever students (15%). The pie-diagram is useful when one wishes to picture proportions of the total in a striking way. Numbers of degrees may be measured off “by eye” or more accurately with a protractor.

Uses of Pie diagram:

 

1.  Pie diagram is useful when one wants to picture proportions of the total in a striking way.

2.  When a population is stratified and each strata is to be presented as a percentage at that time pie diagram is used.

 

PURPOSE OF GRAPHICAL REPRESENTATION:

 

The purpose of graphical presentation of data is to provide a quick and easy-to-read picture of information that clearly shows what otherwise takes a great deal of explanation.The impact of graphical data is typically more pointed and memorable than paragraphs of written information

 

For example, a person making a presentation regarding sales in various states across the country establishes the point of the presentation to the audience more quickly by using a color-coded map rather than merely stating the sales figures for each state. Observers quickly determine which states are ahead and which are behind in sales, and they know where emphasis needs to be placed. Alternatively, when making a presentation on sales by age groups using a pie chart that divides the pie into various ages, the audience quickly sees the results of sales by age. This means that the audience is more likely to retain that information than if the presenter simply reads the results aloud or puts it into writing.

 

GENERAL RULES DISPLAYING DATA

  • Simpler is Better
  • Graphs, Tables and charts can be used together
  • Use clear Description, title and labels
  • Provide a narrative Description of the highlights
  • Don’t compare variables with different scales of magnitude.
  • A Diagram must be attractive, well proportioned,neat and pleasing to the eyes.
  • They should be geometrically Accurate
  • Size of the diagram should be proportional to paper should not be too big or too small
  • Different colors should be used to classify data’s.

ADVANTAGES:

 

  1. Acceptability: graphical report is acceptable to the busy persons because it easily highlights about the theme of the report. This helps to avoid wastage of time.
  2. Comparative Analysis: Information can be compared in terms of graphical representation. Â Such comparative analysis helps for quick understanding and attention.
  3. Less cost: Information if descriptive involves huge time to present properly. It involves more money to print the information but graphical presentation can be made in short but catchy view to make the report understandable. It obviously involves less cost.
  4. Decision Making: Business executives can view the graphs at a glance and can make decision very quickly which is hardly possible through descriptive report.
  5. Logical Ideas: If tables, design and graphs are used to represent information then a logical sequence is created to clear the idea of the audience.
  6. Helpful for less literate Audience: Less literate or illiterate people can understand graphical representation easily because it does not involve going through line by line of any descriptive report.
  7. Less Effort and Time: To present any table, design, image or graphs require less effort and time. Furthermore, such presentation makes quick understanding of the information.
  8. Less Error and Mistakes: Qualitative or informative or descriptive reports involve errors or mistakes. As graphical representations are exhibited through numerical figures, tables or graphs, it usually involves less error and mistake.
  9. A complete Idea: Such representation creates clear and complete idea in the mind of audience. Reading hundred pages may not give any scope to make decision. But an instant view or looking at a glance obviously makes an impression in  the mind of audience regarding the topic or subject.
  10. Use in the Notice Board: Such representation can be hanged in the notice board to quickly raise the attention of employees in any organization.

 

DISADVANTAGES:

 

Graphical representation of reports is not free from limitations. The following are the problems of graphical representation of data or reports:

  • Costly: Graphical representation pf reports are costly because it involves images, colors and paints. Combination of material with human efforts makes the graphical presentation expensive.
  • More time: Normal report involves less time to represent but graphical representation involves more time as it requires graphs and figures which are dependent to more time.
  • Errors and Mistakes: Since graphical representations are complex, there is- each and every chance of errors and mistake. This causes problems for better understanding to general people.
  • Lack of Secrecy: Graphical representation makes full presentation of information which may hamper the objective to keep something secret.
  • Problems to select the suitable method: Information can be presented through various graphical methods and ways. Which should be the suitable method is very hard to select.
  • Problem of Understanding: All may not be able to get the meaning of graphical representation because it involves various technical matters which are complex to general people.

Last of all it can be said that graphical representation does not provide proper information to general people.

 

CONCLUSION:

 

Graphical representation makes the datamore possible to easily draw; visual impression of data. Graphical representation of data enhances the understandings of the observer. It makes comparisons easy. This kind of method creates an imprint on mind for a long period of time. Well in this chapter we have discussed about the definition ,types ,advantages and disadvantages in detail with relevant examples which will have an impact in the power of understanding. I request you all to go through the various types of graphs commonly used in research studies in with reference to home science research studies to explore new ideas in the field of research.

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Web links

 

  • http://shodhganga.inflibnet.ac.in/bitstream/10603/143688/2/file%202%20chapter%201 %20data%20representation%20techniques.pdf
  • http://www.mas.ncl.ac.uk/~ndah6/teaching/MAS1403/notes_chapter2.pdf https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5453888/
  • http://cec.nic.in/wpresources/module/Anthropology/PaperIX/9/content/downloads/file1. pdf
  • https://www.kluniversity.in/arp/uploads/2096.pdf