Presentation of data

There are generally three forms of presentation of data:

       ¨            Textual or Descriptive presentation

       ¨            Tabular presentation

       ¨            Diagrammatic presentation

TEXTUAL PRESENTATIONOF DATA

In textual presentation, data are described within the text. When the quantity of data is not too large this from of presentation is more suitable.

TABULAR PRESENTATION OF DATA

In a tabular presentation, data are presented in rows(read horizontally) and columns(read vartically). Or present the data with the help of a table is called tabular representation.

The most important advantage of tabulation is that it organizes data for further statistical treatment and decision making. Classification used in tabulation is four kinds:

       ¨            Qualitative

       ¨            Quantitave

       ¨            Tempornal and

Qualitative classification

When classification is done according to Qualitative characteristics like social status, physical status, nationality, ect., it is called qualitative classification.

Quantitative classification

In quantitative classification, the data are classified on the basis of charateristics which are quantitative in nature. In other words these characteristics can be measured quantitatively.

TABULATION OF DATA AND PARTS OF A TABLE

To construct a table it is important to learn first what are the parts of a good statistical table. When put together in systematically ordered manner these parts form a table. The simplest way of conceptualizing a table may be data presented in rows and columns along with some explanatory notes. Tabuation can be done using one-way, two-way or three-way classification depending upon the number of characteristics involved. A good table should essentitally have the following:

(1)   Table Number

          Table number is assigned to a table for identification purpose or  for easy reference . If more than one table is presented, it is the table number that distinguishes one table from another. It is given at the top or at the beginning of the title of the table.

(2)   Title

             The title of table narrates about the contents of the table. It has to be very clear, brief and carefully worded so that the interpretations  made from any ambiguity.

(3)   Captions or Column Hedings

              .captions refers column headding of the table. At the top of each column in a table a column designation is given to explain figures of the column. This is called caption or column heading 

(4)   Stubs or Row Headings

Like a caption or column heading each row of the table has to be given a heading. The designation of the rows are also called studs or stub items, and the complete left column is known as column.

(5)   Body of the Table

Body of a table is the main part and it contains the actual data. Location of any one figure/date in the table is fixed and determined by the row and column of the table.or the numerical description of atable is called  body or field.

(6)   Unit of Meassurement

The  unit of meassurment of the figures in the table (actual data) should always be stated along with the title if the unit doses not change throughout the table.

(7)   Source Note

It a brief statement or phrase indicating the source of data presented in the table. If more than one source is ther, all the sources are to be written in the source note. Source note is generally written at thebottom of the table.

 8 Unit of measurement.

Rules for constructing tables:

1. Title of the table should be simple, concise and unambiguous. As a rule, it should appear on the table.

2. The table should be suitably divided into columns and rows according to the nature of data and purpose. These columns and rows should be arranged in a logical order to facilitate comparison.

3. The heading of each columns or row should be as brief as possible. Two or more columns or rows with similar headings may be grouped under a common heading to avoid repetition and we may have subheadings or captions.

4. Sub total for each separate classification and a general total for all combined classes are to be given. These totals should be given at the bottom or right of the concerned items.

5. The units in which the data are given must invariably be mentioned.

6. Necessary footnotes should be providing essential explanation of the points to ambiguous representation of the tabulated data must be given at the bottom of the table.

7. The sources from where the data have been received should be given at the end of the table.

8. In tabulating long columns of figures, space should be left after every five or ten rows.

9. If the numbers tabulated have more than three significant figure, the digit should be grouped in threes. For ex.- 4394756 as 4 394 756.

10. For all purposes and by all means, the table should be as simple as possible so that it may be studied by the readers with minimum possible strain and create a clear picture and interpretations of the data.

 DIAGRAMMATIC PRESENTATION OF DATA

 This is the third method of presenting data. This method provides the quickest understanding of the actual situation to be explained by data in comparison to tabular or textual presentations. Diagrammatic presentation of data translates quite effectively the highly abstract ideas containd in numbers into more concrete and easily comprehensible form.

Diagrams may be less accurate but are much more effective then tables in presenting the data.

There are various kinds of diagrams in common use.

Amongst them the impotant ones are the following:

a)      Geometric diagram

b)      Frequency diagram

c)      Arithmetic diagram

 Geometric Diagram

 Bar diagram and pia diagram come in the category of geometric diagram for presentation of data. The bar diagram for presentation of data. The bar diagrams are of three types- simple, multiple and component bar diagrams.

 i) Bar Diagram

 Simple  Bar Diagram

Bar diagram comprises a group of Equi- spaced and equi-width rectangular bars for each class or categore of data. Height or length of the bar reads the magnitude of data.

Multiple Bar Diagram

Multiple bar diagrams are used for comparing two or more sets of data, for example import and export for different years, marks obtained indifferent subjects in different classes, etc.

ii)   Pie Diagram 

A pie diagram is also a component diagram, but unlike a component bar diagram, a circle whose area is proportionally divided among the components it represents.  a pie diagram, the data is represented by a circle of 360degrees into parts, each representing the amount of data converted into angles. The total frequency value is equated to 360 degrees and then the angle corresponding to component parts are calculated. It is also called a pie chart. The circle is divided into as many parts as there are components by drawing straight lines from the centre to the circumference. Pie charts usually are not drawn with absolute values of a category. The values of each category are first expressed as percentage of the total value of all the categories.

It may be interesting to note that data represented by a component bar diagram can also be represented equally well by a pia chart, the only requirement being that absolute values of the components have to be converted into prcentages before they can be used for a pie diagram.

Frequency Diagram

Data in the form of grouped frequency distributions are generally represented by frequency diagrama like histogram, frequency polygon, frequency curve and ogive.

a)Histogram

A histogram is two dimensional diagram. It is a set of rectangles with bases as the intervals between class boundaries(along X-axis) and with areas proportional to the class frequency. If the class intervals are of equal width, which they generally are, the area of the rectangles are proportional to their respective frequencies. However ,in some type of data, it is convenient, at times necessary, to use varying width of intervals.

The width in a histogram is as important as its height. We can have a bar diagram both for discrete and continuous variables, but histogram is drawn only for a continous variable.

Histogram also gives value of mode of the frequency distribution graphically.

b) Frequency Polygon

A frequency polygon is a plane bounded by straight lines, usually four or more lines. Frequency polygon is an alternative to histogram and is also derived from histogram itself. A frequency polygon can be fitted to histogram for studying the shape of the curve. The simplest method of drawing a frequency polygon is to join the midpoints of the topside of the conssecutive rectangles of the histogra

c) Frequency Curve

The frequency curve is obtained by drawing a smooth freehand curve passing through the points of the frquency polygon as closely as possible. It may not necessarily pass through all the points of the frequency polygon but it passes through them as closely aspossible.

d) Ogive

Ogives are the gphical repersentation of  cummulative  frequency .

cummulative Ogive is also called cumulative frequency curve. As there are two types of cumulative freqencies, for examlple less than type and more than type, accordingly there are two ogives for any grouped freqency distribution data. Here in place of simple frequencies  as in the case of frequency polygon, cumulative frequncies are plotted along y-axis against class limits of the freuency distribution. For less than give the cusmulative frequencies are plotted against the respective upper limits of the class interval. An interesting feature of the two ogives together is that their intersection point gives the median

METHOD FOR CONSTRUTING

A CUMULATIVE FREQUENCY GRAPH

1. First of all we calculate the actual upper and lower limits of the class intervals i.e. if the class interval is 20-24 then upper limit is 24.5 and the lower limit is 19.5.

2. We must know select a suitable scale as per the range of the class interval and plot the actual upper limits on the x axis and the respective cumulative frequency on y axis.

3. All the plotted points are then joined by successive straight lines resulting a line graph.

4. To plot the origin of the x axis an extra class interval is taken with cumulative frequency zero is taken.

Arithmetic Line Graph

An arithmetic line graph is also called series graph and is a method of diagrammattic presentation of data. In it, time is plotted along x-axis and the value of the variable along y-axis. A line graph by joining these plotted points, thus, obtained is called arithmetic line graph or time series graph. It helps in understsnding the trend, periodicity, etc. In a long term time series data.