Diagrammatic and Graphic Presentation of Data in Statistics

Diagrammatic and Graphic Presentation

 

What precisely is Diagrammatic Representation? Explain the significance of diagrams.

 

Diagrammatic presentation is the representation of statistical data in the form of appealing forms such as bars, circles, and rectangles. A diagram is a visual representation of statistical data that highlights key facts and relationships. Geometrical figures include lines, bars, squares, rectangles, circles, curves, and so on.

Diagrams are very useful in the display of various forms of facts. When properly created, they clearly display information that may otherwise be lost in the complexities of numerical tabulation.

 

Importance of Diagrams: - A correctly produced diagram appeals to both the eye and the mind since it is practical, straightforward, and easily intelligible even by people unfamiliar with presenting methods.

 

The following principles will help you understand the use or significance of diagrams:

 

                 i.  Attractive and Effective Presentation Methods: Beautiful lines full of diverse colours and indications captivate human sight and do not strain the observer's thinking. A well-prepared graphic can convey a message to a layperson who does not desire to engage with figures.

                   ii.  Make Data Simple and Understandable: A large amount of complicated data may be readily comprehended when presented in the form of a diagram. "Diagrams let us comprehend the whole meaning of a complex numerical issue at a single glance," says Shri Morane.

           iii. Facilitate Comparison: Diagrams allow for comparison of two sets of data from various times, areas, or facts by presenting them side by side in a diagrammatic format.

            iv.  Save Time and Energy: Data that would take hours to grasp becomes evident by simply looking at whole facts represented by diagrams.

          v. Universal Utility: Because of their advantages, the diagrams are employed to convey statistical data in a variety of contexts. It is a popular strategy in economics, business, administration, social work, and other fields.

                 vi. Useful in Information Communication: A diagram depicts more information than a table does. Data information is made more accessible to the general public through diagrams, and it enters the mind of a person with ordinary understanding.

 

What are the different sorts of diagrams?

 

The many forms of diagrams may be classified under the following headings —

(1)  Two-dimensional diagrams,

(2)  One-dimensional diagrams

(3)  Three dimensions diagrams

(4)  Pictograms

(5)  Cartograms

 

     1.  One Dimensional Diagrams (also known as Bar Diagrams): - The most popular sort of diagram is a bar diagram. A bar is a thick line whose breadth is only presented to draw attention to it. They are dubbed one-dimensional because the length of the bar is all that matters, not the breadth.

 

Types of Bar Diagrams:

                      i. Line Graphs: Lines can be drawn to save space when the number of items is vast but the percentage between the maximum and minimum is small. These graphics only depict individuals or time series.

                 ii. Simple bar diagrams: They are used to depict only one variable. For example, a basic bar diagram can be used to display sales, production, and other numbers from various years. The width of the bars is the same, but the length varies.

These diagrams are useful for individual series, discrete series, and temporal series.

                   ii Multiple Bar Diagrams: A multiple bar diagram depicts two or more sets of connected data. To differentiate the bars, different hues, colours, or dots are employed. These are used to compare two or more time and place related variables.

               iv. Sub-divided Bar Diagrams: A sub-divided bar diagram is one in which a bar is divided into many pieces. Each component takes up a section of the bar in proportion to its percentage of the total. A subdivided bar diagram, for example, can indicate a family's total expenditure on numerous commodities such as food, clothes, education, housing rent, and so on.

               v. Percentage Sub-Divided Bar Diagrams: Percentage sub-divided bars are very useful for measuring relative data changes. When creating such diagrams, the length of the bar is kept constant at 100, and segments are cut in these bars to represent the components of an aggregate.

                 vi. Profit – Loss Diagrams: If the relative change in cost and sales, or profit or loss, is to be depicted using bars, a profit – loss diagram is created. These diagrams are created in the same manner as percentage subdivided bars.

        vii. Duo-Directional Bar Diagrams: A duo-directional bar diagram is a comparative assessment of two primary components of data in a single bar. These pair directional diagrams are shown on both sides of the horizontal axis, above and below the base line.

     viii. Paired Bars: Paired bar diagrams are employed when two separate pieces of information in different units need to be shown. These bars are horizontal rather than vertical, with the first scale in the first half and the second scale in the second half.

                   ix.  Deviation Bar Diagram: Deviation bars are commonly used to indicate net amounts, such as net profit, net loss, net exports, net imports, and so on. Positive and negative values can be assigned to such bars. Positive values are displayed above the base line, while negative values are displayed below it.

           x.  Progress Chart or Gant Chart: These charts are commonly used in factories to compare actual production to planned production. It can be seen how much output has been achieved and how much is still lagging behind capacity.

                  xi. Pyramid Bar Diagram: This type of diagram is used to depict population distribution. This graphic depicts the population distribution based on gender, age, education, and so on. The base line is in the centre of this diagram, and it has the shape of a pyramid.

              xii. Sliding Bar Diagrams: These bars are similar to deo-directional bars, but instead of absolute values, they indicate percentages of two variables. One is featured on the right side of the base, while the other is presented on the left.

     2. Two Dimensional Diagrams: The height and breadth of the bars will be evaluated in two dimensional diagrams. The magnitude of data is represented by the area of the bars. These diagrams are frequently referred to as area diagrams or surface diagrams.

 

The most important kinds are as follows:

                  i.  A rectangle diagram.

                 ii.  A square diagram; and

                 iii. A circle or pie diagram.

               \      i.  Rectangle Diagram: Rectangles are frequently used to show the magnitude of two or more values. Rectangles' areas are retained in proportion to their values. They are set side by side like bars, with regular space between each rectangle.

There are three sorts of rectangles:

a)     Simple rectangles,

b)     Sub-divided rectangles, and

c)     Percentage sub-divided rectangles.

               ii. Square Diagrams: A square diagram is more suited when there is a considerable difference between the extreme values (for example, the lowest value is 4 and the largest value is 800). First, the square roots of the provided values are computed, then the sides are determined in proportion to the square roots. To create a beautiful and appealing look, the squares are drawn serially on the common base line, either in rising or decreasing heights.

For computing the scale, the area is computed by squaring its side, and a value of 1 sq.cm. is calculated on that basis.

                  iii.   Circle or Pie Diagram: Because these diagrams are more appealing, pie diagrams are chosen over square diagrams. These diagrams are used to show facts such as population, international commerce, and production, among other things. To obtain the radii for the circles, the square roots of the provided numbers are computed and then divided by a common factor.

The formula is used to compute the area of a circle. The sides of squares are used to calculate the radii of various circles. A circle can also be subdivided based on the angles that must be computed for each component.

There is a 360-degree circle in the middle of the circle, and proportional sectors are chopped to make the total data equal 360 degrees.

    3. Three Dimensional Diagrams: Three-dimensional diagrams take length, breadth, and height (depth) into account. If the gap between the minimum and maximum value is too large to be represented by a square or circle diagram, a three-dimensional graphic is employed. The cubic roots of the provided integers are computed for this purpose.

Cubes, blocks, spheres, and cylinders are examples of three-dimensional diagrams.

  4. Pictograms: Government and non-government organisations utilise pictograms for marketing and publicity by using relevant images.

  5. Cartograms: Cartograms, also known as statistical maps, are used to depict data. Cartograms are a simple and basic style of visual display that is very simple to grasp. Mapographs or cartograms are commonly used to emphasise regional or geographical similarities.

What exactly is Graphic Presentation?

According to M.M. Blair, "the graph is the most simple to grasp, the easiest to construct, the most changeable, and the most extensively used sort of chart." A graphic presentation is a visually appealing way of presenting statistical data. The graph serves as an analytical tool, simplifying and making complicated data understandable.

Graphs are preferable in the following situations:

a) If it is more necessary to measure trend than actual measurement.

b) When a comparative evaluation of many data series on a single graph is necessary.

c) If estimate and interpolation are to be graphed.

d) If the frequency distribution is shown by two or more curves.

 

What exactly is a False Base Line?

 

When creating the graph, the vertical scale (y-axis) must begin at zero. However, because the numbers are large in some circumstances, adjusting the scale on the (y-axis) beginning with zero is not feasible. If the vertical scale starts at 0, the curve will be largely focused on the top of the graph paper.

In such circumstances, the scale part from zero to the minimum value of the objects to be displayed is ignored. This is expressed on the graph paper by drawing a double saw tooth line in the empty area or by cutting the y-axis. This is referred to as utilising a fake base line.

It's designed this way to emphasise that the Y axis is missing in the middle.

 

What exactly is a histogram? Explain the distinction between the Absolute Histogram and the Index Histogram.

 

The curve produced on graph paper by displaying variables of a time series is known as a 'Histogram,' since it exposes the data's prior history. A time series is a collection of statistical data arranged in chronological order with regard to the passage of time. A year, quarter, month, week, days, hours, and so on are all examples of time periods.

These graphs can be made on either a natural scale or a ratio scale. Absolute histograms are created when the actual values of a variable are drawn on graph paper.

 

Absolute histograms can be composed of:

                                  i.            One variable or

                                ii.            Two or more variables.

 

Plotting index numbers of real values on graph paper yields index histograms.

 

What are the many forms of frequency distribution graphs?

 

Graphs may also be used to depict frequency distribution. Such graphs make it possible to compare the form and pattern of two or more frequency distributions.

 

The following are the most commonly used graphs:

                    i. Frequency diagram on a line

                  ii. The histogram

                  iii.  Frequency polygon

                  iv.   Frequency curves or Ogive curves

                  v.   Cumulative frequency curves or Ogive curves

                   i. Line Frequency Diagram: This diagram is commonly used to graph discrete series. The values are displayed on the X-axis, while the frequencies are displayed on the Y axis. Vertical lines are drawn on the X-axis against the relevant values, with the height corresponding to the respective frequencies.

             ii. Histogram: A histogram is a type of graph that is commonly used to display a continuous series. The class intervals are presented on the X-axis, while the frequencies are shown on the Y-axis. The data is represented as a sequence of rectangles stacked on top of each other.

The frequency of the group is represented by the height of the rectangle. Each rectangle is connected to the next to form a continuous image. A histogram is a graphical approach for determining mode in a continuous series.

The rectangle with the greatest frequency is considered to be the rectangle in which mode exists. This rectangle's top corner, as well as the surrounding rectangles on all sides, are linked diagonally. A perpendicular line is drawn on the OX-axis where two lines interact with one other.

The value of mode is the place where the perpendicular line intersects the OX-axis.

                  iii.  Frequency polygon: It’s a graphical representation of both discrete and continuous series. The frequency polygon for a discrete frequency distribution is obtained by plotting frequencies on the Y-axis against the corresponding size of the variables on the X-axis and then joining all the points with a straight line. A straight line connects the mid-points of the top of each rectangle of the histogram in a continuous series.

To make the area of the frequency polygon equal to the histogram, the line is stretched on both sides to reach the base line (X-axis). 

           iv. Frequency Curve: The frequency curve is the curve formed by creating a smooth frequency polygon. It is made by smoothing the lines of a frequency polygon. This curve is made freehand such that the angularity vanishes, and the area of the frequency curve stays equal to the area of the frequency polygon.

Cumulative Frequency Curve, often known as the Ogive Curve, is a graphical representation of the cumulative frequency distribution of a continuous series.

 

It may be classified into two types:

(a)  Less than Ogive and

(b) More than Ogive.

 

Less than Ogive: This curve is generated by graphing less than cumulative frequencies against the corresponding upper-class limitations. A straight line connects the obtained locations. It is a sloping uphill curve sloping from left to right.

More than Ogive: It is calculated by graphing the cumulative frequency of ‘more than' against the lower-class boundaries of the individual classes. The collected points are linked by a straight line to yield ‘more than ogive'.