Classification and tabulation of data - Statistical Classifications

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Classification and tabulation of data

The collected data is usually contained in schedules and questionnaires. But that is not in an easily assailable form. The answers will require some analysis if their salient points are to be brought out. As a rule, the first step in the analysis is to classify and tabulate the information collected, or, if published statistics have been employed, rearrange these into new groups and tabulate the new rearrangement. In case of some investigations, the classification and tabulation may give such a clear picture of the significance of the material that no further analysis is required. In other cases these processes, though may materially assist the analysis, are not sufficient presentation of the facts. They are however, very important whether they have been very carefully drawn up and the answers may be both complete and accurate, but until these answers are all brought together into the class to which they belong and the whole information displayed in a tabular form, no one will be a great deal wiser as to the contents of the replies.

Although the phase classification and tabulation has been used, classification is, in effect, only the first step in tabulation, for, in general, items having common characteristics must be brought together before the data can be displayed in tabular form.

Some of its main topics are:

1.       chronological classification 

2.       formation of a discrete frequency distribution

3.       parts of a table

4.       Quantitative classification

5.       relative frequency distribution

6.       types of tables

Types of Statistical Classifications

Chronological Classification

When data are observed over a period of time the type of classification is known as chronological classification. For example, we may present the figures of population (or production, sales. etc.) As follows

year

Population (in crores)

year

 Population (in crores)

1951

  36.11

1981

68.33

1961

43.92

1991

84.64

1971

54.82

2001

102.87

Time series are usually listed in chronological order, normally starting with the earliest period. When the major emphasis falls on the most recent events, a reverse time order may be used.

Quantitive classification

Quantitative classification refers to the classification of data according to some characteristics that can be measured, such as height, weight, income, sales, profits, production etc. for example, the students of a college may be classified to weight as follows:

Weight (in lb.)

No. of students

90-100

50

100-110

200

110-120

260

120-130

360

130-140

90

140-150

40

Total

1,000

Such a distribution is known as emperical frequency distribution or simple frequency distribution.

In this type of classification, there are two elements, namely (i) the variable, i.e. the weight in the above example, and (ii) the frequency, i.e. the number of students in each class. There are 50 students having weight ranging from 90 to 100 lb, 200 students having weight ranging from 100 to 110 lb, and so on. Thus we can find out the ways in which the frequencies are distributed.

The following are two examples of discrete and continuous frequency distributions:

DISCRETE

CONTINUOUS

 

No. of children

No. of families

weight (lb.)

no. of persons

0

10

100-110

10

1

40

110-120

15

2

80

120-130

40

3

100

130-140

45

4

250

140-150

20

5

150

150-160

4

6

50

 

 

total

680

 

Total 134

(a)   Discrete frequency distribution

(b)  Continuous frequency distribution

Formation of a discrete frequency distribution

The process of preparing these types of distribution is very simple. We have just to count the number of times a particular value is repeated which is called the frequency of that class. In order to facilitate counting prepare a column of tallies''. In another column, place all possible values of variable from the lowest to the highest. This put a bar (vertical line) opposite the particular value to which it elates. To facilitate counting, blokes of five bars are prepared and some space is left in between each block. We finally count the number of bars and get frequency.

The process shall be clear from the following examples:

Illustration 1.

In a survey of 35 families in a village, the number of children per family was recorded and the following data obtained

        1

      0

        2

       3

        4

        5

        6

        7

      2

        3

       4

        0

        2

        5

        8

      4

        5

      12

        6

        3

        2  

        7

      6

        5

        3

        3

        7

        8

        9

      7

        9

        4

        5

        4

        3

Represent the data in the form of a discrete frequency distribution.

Solution.

Frequency distribution of the number of children*

          No. of children

                tallies

                   frequency

               0

                  ll      

                        2

               1

                  l

                        1

               2

                  llll

                        4

               3

                No  llll  l

                        6

               4

              No    llll

                        5

               5

                  llll

                        5

               6

                  lll

                        3

               7

                  llll

                        4

               8

                   ll

                        2

               9

                   ll 

                        2

              10

                  -

                        0  

              11

                  -

                        0

              12

                  l

                        1  

 

 

             Total     35

It is clear from the table that the number of children varied from 0 to 12. There were 2 families with no child, 5 families with 4 children and only one family with 12 children.

A simple formula to obtain the estimate of appropriate class interval, i.e. i is:

i = L - S/k

Where, L = largest item

S = smallest item

k = the number of classes

For example, if the salary of 100 employees in a commercial undertaking varied between $500 and 45500 and we want to form 10 classes, then the class interval would be:

i = l - S/k

L = 5500, S = 500, k = 10

i = 5500 - 500/10 = 5000/10 = 500

Parts of a Table,

The number of parts of a varies from case to depending upon the given data. However the main parts of a table in general are discussed here.

(1) Table number: - each take should be numbered. There are different practices with regard to the place where this number is to be given. The number may be given either in the centre at the top above the title or inside of the title at the top or in the bottom of the table on the left hand side. However, if space permits the table number should be given in the centre as is shown in the specimen table give on page. When there so that easy reference to it is possible.

(2) Title of the table: - every table must be given suitable title. The title is a description of the contents of the table. A complete title has to answer the question what, where and when in that sequence. In other words:

(a)   What precisely are the data in the table (i.e.) what categories of statistical data are shown0?

(b)  Where the data occurred 9i.e. the precise geographical, political or physical area covered)?

(c)   When the data occurred (i.e. the specific time or period covered by the statistical materials in the table)?

(3) Caption: - caption refers to the column headings. It explains what the column represents it may consist of one or more column headings. Under a column heading there may be sub-heads. The caption should be clearly defined and placed at the middle of the column, if the different columns are expressed in different units. The units should be mentioned with the captions. As compared with the main part of the table the caption should be shown in smaller letters. This helps in saving space.

(4) Stub: - as distinguished from caption, studs are the designations of the rows or row heading. They are at the extreme lift and perform the same function for the horizontal rows of numbers in the table as the column headings do for the vertical columns of numbers. The stubs are usually wide than column headings but should be kept as narrow as possible without sacrificing precision and clarity of statements.

(5) Body: - the body of the table contains the numerical information. This is the most vital art of the. Data presented in the body arranged according to description are classifications of the captions and studs.

(6) Head note: - it is a brief explanatory statement applying to all or a major part of the material in the table, and is placed below the point centered and enclosed in brackets. It is used to explain certain points relating to the whole table that have not been included in the title nor in the cations or studs. For example, the unit of measurement is frequently written as a head note, such as ''in thousands'' or ''in million tonne3s or ''in crores'', etc.

(7) Footnotes: - anything in a table which the reader may find difficult to understand from the title, captions and studs should be explained in footnotes. If footnotes are needed they are placed directly below the body of the table. Footnotes are used for the following main purposes:

(a) To points out any exceptions as to the basis of arriving at the data

(b) Any special circumstances affecting the data, for example, strike, lock-out fire, etc.

(c) To clarify anything in the table

(d) To give the source in case of secondary data.

Format of a table

Title

Head Note

Stub Heading

Caption Heading-Column heading

Stub Entries

Body

Footnotes

Table Number

Quantitative classification

Quantitative classification refers to the classification of data according to some characteristics that can be measured, such as height, weight, income, sales, profits, production, etc. for example. The students of a college may be classified according to weight as follows:

Weight (in ib.)

No. of students

    90-100

      50

   100-120

     200

   110-120

     260

   120-130

     360

   130-140

       90

   140-150

       40

    total

   1,000

Such a distribution is knows as empirical frequency distribution or simple frequency distribution.

In this type of classification, there are two elements, namely (I) the variable. I.e. the weight in the above example, and (ii) the frequency, i.e. the number of students in each class. There were 50 students having weight ranging from 90 to100 ib., 200 students having weight ranging from 100 to 110 ib., and so no. thus we can find out the ways in which the frequencies are distributed.

A frequency distribution refers to data classified on the basis of some variable that can be measured such as prices, wages. Age. Number of units produced of consumed. The term variable refers to the characteristic that varies in amount of magnitude in a frequency distribution. A variable may be either continuous or discrete. A continuous variable also called continuous random variable is capable of manifesting every conceivable fractional value within the weight of a product. In a continuous variable, thus data are obtained by numerical measurements rather than counting. For example, when a student grows, sat, from 90 cm. to 150 cm. his height passes through all values between these limits on the other hand, a discrete variable is that which can vary only by finite jumps and cannot manifest every conceivable fractional value. For instance the number of rooms in a house can only take certain values such as 1, 2, 3, etc. similarly, the number of machines in an establishment are discrete variables. Generally speaking. Continuous data are obtained through measurements, while discontinuous data are derived by counting. Serves which can be represented by a discrete variable are called discrete series. The following are two examples of discrete and continuous frequency distributions:

                           Discrete                                                                 continuous

    No. of children

       No. of families

          Weight (ib.)

        No. of persons

            0

             10

            100-110

           10

            1

             40

            110-120

           15

            2

             80

            120-130

           40

            3

            100

            130-140

           45

            4

            250

            140-150

           20

            5

            150

            150-160

            4

            6

              50

 

 

      total

            680

 

       Total 134

(a) Discrete frequency distribution                 (b) continuous frequency distribution

Although the theoretical distinction between continuous and discrete variations is clear and precise, in practical statistical work it is only an approximation. The reason is that even the most precise instruments of measurement can be used only to a finite number of places. Thus every theoretically continuous series can never be expected to flow continuously with one measurement touching another without any break in actual observations.

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