3. Private Documents

These include unpublished reports and records of companies, trade unions, different political and apolitical organisations and residents’ welfare associations.

Tabulation and Classification of Data

The data collected from primary or secondary sources initially appear as a big jumble of information with the least of comprehension. This is known as raw data. To draw meaningful inferences and to make them usable the raw data requires tabulation and classification.

One of the simplest devices to summarise and present the data is the Statistical Table. It is a systematic arrangement of data in columns and rows. The purpose of table is to simplify the presentation and to facilitate comparisons. This table enables the reader to locate the desired information quickly. Thus, the tables make it possible for the analyst to present a huge mass of data in an orderly manner within a minimum of space.

Data Compilation and Presentation

Data are collected, tabulated and presented in a tabular form either in absolute terms, percentages or indices.

Absolute Data

When data are presented in their original form as integers, they are called absolute data or raw data. For example, the total population of a country or a state, the total production of a crop or a manufacturing industry, etc. Table 1.1  shows the absolute data of population of India and some of the selected states.

table 1.1 :  Population of India and Selected States/Union Territories, 2011

1 inclusive of all territorial boundary of India 

2 excluding PoK 

3 Union Territory  

Source : Census, 2011

Percentage/Ratio

Some time data are tabulated in a ratio or percentage form that are computed from a common parameter, such as literacy rate or growth rate of population, percentage of agricultural products or industrial products, etc. literacy rates of India over the decades Table 1.2  presents

Table 1.2 :  Literacy Rate : 1951 – 2011 in a percentage form.

Year	Person	Male	Female
1951	18.33	27.16	8.86
1961	28.3	40.4	15.35
1971	34.45	45.96	21.97
1981	43.57	56.38	29.76
1991	52.21	64.13	39.29
2001	64.84	75.85	54.16
2011	73.0	80.9	64.6

Source: Census, 2011  

Literacy rate is calculated as : 

Total Literates / TotalPopulation X 100 

Index Number

An index number is a statistical measure designed to show changes in variable or a group of related variables Source: Census, 2011

with respect to time, geographic

location or other characteristics. It is to be noted that index numbers not only measure changes over a period of time but also compare economic conditions of different locations, industries, cities or countries. Index number is widely used in economics and business to see changes in price and quantity. There are various methods for the calculation of index number. However, the simple aggregate method is most commonly used. It is obtained using the following formula:

 Σq1/Σq0 x 100

∑ q 1 = Total of the current year production

∑ q 0 = Total of the base year production

Generally, base year values are taken as 100 and index number is calculated thereupon. For example, Table 1.3  shows the production of iron ore in India and the changes in index number from 1970–71 to 2000–01 taking 1970–71 as the base year. 

Table 1.3 :  Production of Iron Ore in India

	Production (in million tonnes)	Calculation	Index Number
1970-71	32.5	32 5. / 32 5.  x 100	100
1980-81	42.2	42.2/ 32.5 x 100	130
1990-91	53.7	53.7/32.5 x 100	165
2000-01	67.4	67.4/32.5 x 100	207

Source – India: Economic Year Book, 2005

Processing of Data

The processing of raw data requires their tabulation and classification in selected classes. For example, the data given in Table 1.4  can be used to understand how they are processed.

We can see that the given data are ungrouped. Hence, the first step is to group data in order to reduce its volume and make it easy to understand.

Table 1.4 :  Score of 60 Students in Geography Paper

47	02	39	64	22	46	28	02	09	10
89	96	74	06	26	15	92	84	84	90
32	22	53	62	73	57	37	44	67	50
18	51	36	58	28	65	63	59	75	70
56	58	43	74	64	12	35	42	68	80
64	37	17	31	41	71	56	83	59	90

Grouping of Data

The grouping of the raw data requires determining of the number of classes in which the raw data are to be grouped and what will be the class intervals. The selection of the class interval and the number of classes, however, depends upon the range of raw data. The raw data given in Table 1.4 ranges from 02 to 96.  We can, therefore, conveniently choose to group the data into ten classes with an interval of ten units in each group, e.g. 0–10, 10–20, 20–30, etc. ( Table 1.5 ).

 Table 1.5 :  Making Tally Marks to Obtain Frequency

Group	Numerical of Raw Data	Tally Marks	Number of Individual
0-10	02,02,09,06	||||	4
10-20	10,15,18,12,17	llll	5
20-30	22,28,26,22,28	llll	5
30-40	39,32,37,36,35,37,31	llll ||	7
40-50	47,46,44,43,42,41	llll |	6
50-60	53,57,50,51,58, 59,56,58,56,59	llll |||	10
60-70	64,62,67,65, 63,64,68,64	llll  llll	8
70-80	74,73,75,70,74,71	llll |||	6
80-90	89,84,84,80,83	llll |	5
90-100	96,92,90,90	llll	4
			Σƒ=N=60

Process of Classification

Once the number of groups and the class interval of each group are determined, the raw data are classified as shown in Table 1.5 . It is done by a method popularly known as Four and Cross Method   or tally marks.

First of all, one tally mark is assigned to each individual in the group in which it is falling. For example, the first numerical in the raw data is 47. Since, it falls in the group of 40–50, one tally mark is recorded in the column 3 of Table 1.5 .

Frequency Distribution

In Table 1.5  we have classified the raw data of a quantitative variable and  have grouped them class-wise. The number of individuals (places in the fourth column of Table 1.5 ) is known as frequency and the column represents the frequency distribution. It illustrates how the different values of a variable are distributed in different classes. Frequencies are classified as Simple and Cumulative frequencies.

Simple Frequencies

It is expressed by ‘f’ and represent the number of individuals falling in each group (Table 1.6). The sum of all the frequencies, assigned to all classes, represents the total number of individual observations in the given series. In statistics, it is expressed by the symbol N that is equal to ∑ f . It is expressed as ∑ f = N = 60 (Table 1.5 and 1.6).  

Cumulative Frequencies

Table 1.6 :  Frequency Distribution

Advantage of cumulative frequency is that one can easily make out that there are 27 individuals scoring less than 50 or that 45 out of 60 individuals lie below the score of 70.

Each simple frequency is associated with its group or class. The exclusive or inclusive   methods are used for forming the groups or classes.

Exclusive Method

As shown in Table 1.6 , two numbers are shown in its first column . Notice that the upper limit of one group is the same as the lower limit of the next group. For example, the upper limit of the one group (20 – 30) is 30, which is the lower limit of the next group (30 – 40), making 30 to appear in both groups. But any observation having the value of 30 is included in the group where it is at its lower limit and it is excluded from the group where it is the upper limit as (in 20-30 groups). That is why the method is known as exclusive method, i.e. a group is excluded of its upper limits. You may now make out where all the marginal values of Table 1.4  will go.

The groups in Table 1.6 , are interpreted in the following manner –

         0 and under 10        10 and under 20

         20 and under 30        30 and under 40

         40 and under 50        50 and under 60

         60 and under 70        70 and under 80

         80 and under 90        90 and under100

Hence, in this type of grouping the class extends over ten units. For example, 20, 21, 22, 23, 24, 25, 26, 27, 28 and 29 are included in the third group.

Inclusive Method

In this method, a value equal to the upper limit of a group is included in the same group. Therefore, it is known as inclusive method. Classes are mentioned in a different form in this method, as shown in the first column of Table 1.7 . Normally, the upper limit of a group differs by 1 with the lower limits of the next group. It is important to note that each group spreads over ten units in this method also. For example, the group of 50–59 includes the ten values i.e. 50, 51, 52, 53, 54, 55, 56, 57, 58 and 59 ( Table 1.7 ). In this method, both the upper and and lower limit are included to find the frequency distribution.

Table 1.7 :  Frequency Distribution

Group	ƒ	cƒ
0-9	4	4
10-19	5	6
20-29	5	14
30-39	7	21
40-49	6	27
50-59	10	37
60-69	8	45
70-79	6	51
80-89	5	56
90-99	4	60
	Σƒ=N=60

Frequency Polygon  

Fig. 1.5 : Frequency Distribution Polygon  

Ogive  

Table 1.8 : Frequency Distribution less than Method  

---

Less than Method	Cƒ
Less than 10	4
Less than 20	9
Less than 30	14
Less than 40	21
Less than 50	27
Less than 60	37
Less than 70	45
Less than 80	51
Less than 90	56
Less than 100	60

Fig. 1.6 : Less than Ogive

Table 1.9 : Frequency Distribution more than Method  

Less than Method	Cƒ
More than 0	60
More than 10	56
More than 20	51
More than 30	44
More than 40	38
More than 50	28
More than 60	20
More than 70	14
More than 80	9
More than 90	4

Fig. 1.7 : More than Ogive  

Table 1.10 : Less than and more than Ogive 

Marks obtained	Less than	More than
0-10	4	60
10-20	9	56
20-30	14	51
30-40	21	44
40-50	27	38
50-60	37	28
60-70	45	21
70-80	51	14
80-90	56	9
90-100	60	4

Fig. 1.8 : Less than and more than Ogive  

Excercises

1. Choose the right answer from the four alternatives given below:

(i)  A number or character which represents measurement is called

(a) Digit        

(b) Data        

(c) Number        

(d) Character

(ii) A single datum is a single measurement from the

(a) Table        

(b) Frequency        

(c) Real world       

(d) Information

(iii) In a tally mark grouping by four and crossing fifth is called

  (a) Four and Cross Method        

(b) Tally Marking Method

(c) Frequency plotting Method        

(d) Inclusive Method
(iv) An Ogive is a method in which

(a) Simple frequency is measured
(b) Cumulative frequency is measured
(c) Simple frequency is plotted
(d) Cumulative frequency is plotted

(v) If both ends of a group are taken in frequency grouping, it is called

(a) Exclusive Method        

(b) Inclusive Method 

(c)Marking Method        

(d)Statistical Method

2. Answer the following questions in about 30 words:

(i) Differentiate between data and information.
(ii) What do you mean by data processing?
(iii) What is the advantage of foot note in a table?
(iv) What do you mean by primary sources of data?
(v) Enumerate five sources of secondary data.

3. Answer the following questions in about 125 words:

(i) Discuss the national and international agencies where from secondary data may be collected.
(ii) What is the importance of an index number? Taking an example examine the process of calculating an index number and show the changes.

Activity

1. In a class of 35 students of Geography, following marks were obtained out of 10 marks in unit test – 1, 0, 2, 3, 4, 5, 6, 7, 2, 3, 4, 0, 2, 5, 8, 4, 5, 3, 6, 3, 2, 7, 6, 5, 4, 3, 7, 8, 9, 7, 9, 4, 5, 4, 3. Represent the data in the form of a group frequency distribution.
2. Collect the last test result of Geography of your class and represent the marks in the form of a group frequency distribution