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Descriptive Statistics

Graphic Presentation of Data

Apart from diagrams, Graphic presentation is another way of the presentation of data and information. Usually, graphs are used to present time series and frequency distributions. In this article, we will look at the graphic presentation of data and information along with its merits, limitations, and types.

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Construction of a Graph

The graphic presentation of data and information offers a quick and simple way of understanding the features and drawing comparisons. Further, it is an effective analytical tool and a graph can help us in finding the mode, median, etc.

We can locate a point in a plane using two mutually perpendicular lines – the X-axis (the horizontal line) and the Y-axis (the vertical line). Their point of intersection is the Origin.

We can locate the position of a point in terms of its distance from both these axes. For example, if a point P is 3 units away from the Y-axis and 5 units away from the X-axis, then its location is as follows:

presentation of data and information

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Some points to remember:

  • We measure the distance of the point from the Y-axis along the X-axis. Similarly, we measure the distance of the point from the X-axis along the Y-axis. Therefore, to measure 3 units from the Y-axis, we move 3 units along the X-axis and likewise for the other coordinate.
  • We then draw perpendicular lines from these two points.
  • The point where the perpendiculars intersect is the position of the point P.
  • We denote it as follows (3,5) or (abscissa, ordinate). Together, they are the coordinates of the point P.
  • The four parts of the plane are Quadrants.
  • Also, we can plot different points for a different pair of values.

General Rules for Graphic Presentation of Data and Information

There are certain guidelines for an attractive and effective graphic presentation of data and information. These are as follows:

  1. Suitable Title – Ensure that you give a suitable title to the graph which clearly indicates the subject for which you are presenting it.
  2. Unit of Measurement – Clearly state the unit of measurement below the title.
  3. Suitable Scale – Choose a suitable scale so that you can represent the entire data in an accurate manner.
  4. Index – Include a brief index which explains the different colors and shades, lines and designs that you have used in the graph. Also, include a scale of interpretation for better understanding.
  5. Data Sources – Wherever possible, include the sources of information at the bottom of the graph.
  6. Keep it Simple – You should construct a graph which even a layman (without any exposure in the areas of statistics or mathematics) can understand.
  7. Neat – A graph is a visual aid for the presentation of data and information. Therefore, you must keep it neat and attractive. Choose the right size, right lettering, and appropriate lines, colors, dashes, etc.

Merits of a Graph

  • The graph presents data in a manner which is easier to understand.
  • It allows us to present statistical data in an attractive manner as compared to tables. Users can understand the main features, trends, and fluctuations of the data at a glance.
  • A graph saves time.
  • It allows the viewer to compare data relating to two different time-periods or regions.
  • The viewer does not require prior knowledge of mathematics or statistics to understand a graph.
  • We can use a graph to locate the mode, median, and mean values of the data.
  • It is useful in forecasting, interpolation, and extrapolation of data.

Limitations of a Graph

  • A graph lacks complete accuracy of facts.
  • It depicts only a few selected characteristics of the data.
  • We cannot use a graph in support of a statement.
  • A graph is not a substitute for tables.
  • Usually, laymen find it difficult to understand and interpret a graph.
  • Typically, a graph shows the unreasonable tendency of the data and the actual values are not clear.

Types of Graphs

Graphs are of two types:

  1. Time Series graphs
  2. Frequency Distribution graphs

Time Series Graphs

A time series graph or a “histogram” is a graph which depicts the value of a variable over a different point of time. In a time series graph, time is the most important factor and the variable is related to time. It helps in the understanding and analysis of the changes in the variable at a different point of time. Many statisticians and businessmen use these graphs because they are easy to understand and also because they offer complex information in a simple manner.

Further, constructing a time series graph does not require a user with technical skills. Here are some major steps in the construction of a time series graph:

  • Represent time on the X-axis and the value of the variable on the Y-axis.
  • Start the Y-value with zero and devise a suitable scale which helps you present the whole data in the given space.
  • Plot the values of the variable and join different point with a straight line.
  • You can plot multiple variables through different lines.

Line Graph

You can use a line graph to summarize how two pieces of information are related and how they vary with each other.

Advantages

  • You can compare multiple continuous data-sets easily
  • You can infer the interim data from the graph line

Disadvantages

  • It is only used with continuous data.

Use of a false Base Line

Usually, in a graph, the vertical line starts from the Origin. However, in some cases, a false Base Line is used for a better representation of the data. There are two scenarios where you should use a false Base Line:

  1. To magnify the minor fluctuation in the time series data
  2. To economize the space

Net Balance Graph

If you have to show the net balance of income and expenditure or revenue and costs or imports and exports, etc., then you must use a net balance graph. You can use different colors or shades for positive and negative differences.

Frequency Distribution Graphs

Let’s look at the different types of frequency distribution graphs.

Histogram

A histogram is a graph of a grouped frequency distribution. In a histogram, we plot the class intervals on the X-axis and their respective frequencies on the Y-axis. Further, we create a rectangle on each class interval with its height proportional to the frequency density of the class.

presentation of data and information

 

Frequency Polygon or Histograph

A frequency polygon or a Histograph is another way of representing a frequency distribution on a graph. You draw a frequency polygon by joining the midpoints of the upper widths of the adjacent rectangles of the histogram with straight lines.

presentation of data and information

Frequency Curve

When you join the verticals of a polygon using a smooth curve, then the resulting figure is a Frequency Curve. As the number of observations increase, we need to accommodate more classes. Therefore, the width of each class reduces. In such a scenario, the variable tends to become continuous and the frequency polygon starts taking the shape of a frequency curve.

Cumulative Frequency Curve or Ogive

A cumulative frequency curve or Ogive is the graphical representation of a cumulative frequency distribution. Since a cumulative frequency is either of a ‘less than’ or a ‘more than’ type, Ogives are of two types too – ‘less than ogive’ and ‘more than ogive’.

presentation of data and information

Scatter Diagram

A scatter diagram or a dot chart enables us to find the nature of the relationship between the variables. If the plotted points are scattered a lot, then the relationship between the two variables is lesser.

presentation of data and information

Solved Question

Q1. What are the general rules for the graphic presentation of data and information?

Answer: The general rules for the graphic presentation of data are:

  • Use a suitable title
  • Clearly specify the unit of measurement
  • Ensure that you choose a suitable scale
  • Provide an index specifying the colors, lines, and designs used in the graph
  • If possible, provide the sources of information at the bottom of the graph
  • Keep the graph simple and neat.
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