Statistics

Statistics this part is the basic chapter for class 11 in Economics and covers the complete syllabus of the class 11 with definition, classification and organization of data .

STATISTICS FOR ECONOMICS

Economics by Alfred Marshall, “The study of man in the ordinary business of life”.

Consumer

“A consumer is one who consumes goods and services for the satisfaction of his wants”.

Consumption

“Consumption is the process of using up utility value of goods and services for the direct satisfaction of our wants”.

Producer

“A producer is one who produces/or sells goods and services for the generation of income”.

Production

“Production is the process of converting raw material into useful thing”.

Saving

It is the part of income which is not consumed. It is an art of abstinence from consumption.

Investment

It is expenditure by the producers on the purchase of such assets which help to generate income.

Economic Activity

It is an activity which is related to the use of scarce means. Means are always scarce in relation to our wants.

Economic Problem

It is the problem of choice arising on account of the facts that resources are scarce and these have alternative uses.

Components of Economics There are three components of economics

Consumption
Production
Distribution

Statistics –

A Plural Sense Statistics refers to information in terms of numbers or numerical data, such as population statistics, employment statistics etc.

According to Bowley, “Statistics are numerical statements of facts in any department of enquiry placed in relation to each other.”

Features of Statistics in the Plural Sense

Aggregate of facts
Numerically expressed
Affected by multiplicity of causes
Reasonable accuracy
Placed in relation to each other
Predetermined purpose
Estimated

Statistics –

A Singular Sense It refers to techniques or methods relating to collection, classification, presentation analysis and interpretation of quantitative data.

According to Seligman, “Statistics is the science which deals with the methods of collecting, classifying, presenting, comparing and interpreting numerical data collected to throw some light on any sphere of enquiry”.

Importance of Statistics in Economics:

Quantitative expression of economic problem
Inter-sectoral and inter-temporal comparisons
Working out cause and effect relationship
Construction of economic theories or economic models
Economic forecasting
Formulation of policies

Limitations of Statistics:

Study of numerical facts only
Study of aggregates only
Results are true only on an average
Without reference, results may prove to be wrong
Can be used only by the experts
Prone to misuse

Collection of Data

Sources of Data There are two sources of data

(i )Primary Source of Data It implies collection of data from its source of origin.

ii)Secondary Source of Data It implies collection of data from some agency or institution which already happens to have collected the data through statistical survey.

Types of Data There are two types of data

i) Primary Data Data collected by the investigator for his own purpose for the first time, from beginning to end are called primary data.

ii)Secondary Data These data have already been collected by somebody else, these are available in the form of published or unpublished report.

Principal Differences between Primary and Secondary Data

a)Primary data are original and secondary data are already in existence and therefore, are not original. b)Primary data do not need any adjustment, secondary data need to be adjustment to suit the objective of study in hand. c)Primary data are expensive and secondary data are less expensive.

Statistical Methods of Data Collection
(i) Direct Personal Investigation
It is the method by which data are personally collected by the investigator from the information. Merits and demerits of this method are follows.
Merits: It consists of Originality, reliability, accuracy , uniformity along with accuracy .The personal investigation are flexibility with detailed insight , enhanced the credibility , it uncovers the hidden information , It also build rapport and real time updates.

Demerit; It is difficult to cover wide areas It is Costly and time consuming . It is not suitable for wide aeras . Lack of trained personal and personal prejudice

(ii) Indirect Oral Investigation
It is the method by which information is obtained not from the persons regarding whom the information is needed. It is collected orally from other persons who are expected to possess the necessary information. Merits and demerits of this method are given below
Merits:

It is time consuming but affordable , It helps in collecting the secrets values , acquiring the correct information which is confidential ,It is simple with wide coverage with expert opinion and they are free from the bias

Demerits:

It gives indirect information with partiality of witness with lack of accurate and lack of uniformity and lack of interest of informants and biased with doubtful conclusions

(iii) Information from Local Sources or Correspondents
Under this method, the investigator appoints local persons or correspondents at different places. Merits and demerits of this method are given below
Merits

It is very Economical with Wide coverage full of Continuity ,Suitable for special purpose

Demerits

There is Loss of originality with Lack of uniformity It also have Personal bias ,Less accurate It create Delay in collection

(iv) Information Through Questionnaires and Schedules
There are two ways of collecting information on the basis of questionnaire

Mailing Method

Under this method questionnaires are mailed to the informants. The method is most suited when The area of the study is very wide. and The informants are educated.

(b) Enumerator’s Methods

Under this Method enumerator himself fills the schedules after seeking information from the informants. This method is mostly used.

when their field of investigation is large ,the investigation need specialised and skilled investigation. and the investigators are well versed in the local language and cultural norms of the informants.

Collection of Secondary Data

There are two main sources of secondary data Published sources/Unpublished sources

Published Sources Some of the published source of secondary data are

i)Government publication

ii) Semi-government publication

iii)Reports of committees and commissions

iv)Publications of trade associations

v)Publication of research institutions

vi )Journals and papers

vii)Publication of research scholars and International publication

Unpublished Sources These data are collected by the government organization’s and others, generally for their self use or office record.

For the reliability, suitability and adequacy of the data we should have Ability of the collecting organization must Objective and scope with proper method of collection keeping in mind Time and condition of organization and Accuracy

(v) Census ‘Method
Census method is that method in which data are collected covering every item of the universe or population relating to the problem under investigation.
Merits

This method is most Reliable and accurate, Less biased with Extensive information along Study of diverse characteristic and complex investigation withIndirect investigation

Demerits

It is Costly and time consuming which needs Large manpower but not suitable for large investigation

(vi) Sample Method
It is that method in which data is collected about the sample on a group of items taken from the populations for examination and conclusions are drawn on their basis.
Merits

This method is more Economical, Time saving in which Identification of error can be made easily , suitable for Large investigating conclusions

Difficulty in selecting representative sample Difficulty in framing a sample Specialized knowledge

Methods of Sampling
Random Sampling Random sampling is that method of sampling in which each and every item of the universe has equal chance of being selected in the sample.
Random sampling may be done in any of the following ways a)Lottery method

b)Tables of random number

Deliberate Sampling is that method in which the investigator himself makes the choice of the samples items which in his opinion are the best representative of the universe.
Stratified / Mixed Sampling in which sampling population is divided into different strata having different characteristics and some of the items are selected from each strata, so the entire population gets represented.
Systematic Sampling

According to this methods, units of the population are numerically, geographically and alphabetically arranged. Every nth item of the numbered is selected as a sample item.
Quota Sampling

In this method, the population is divided into different groups or classes according to different characteristics of the population.

Convenience Sampling In this method, sampling is done by the investigator in such a manner that suits his convenience.

Reliability of Sampling Data depends upon

i)Size of the sample

ii)Method of sampling

iii)Bias of correspondents and enumerators

iv)Training of enumerators

Important agencies at the national level which collect process and tabulate the statistical data. NSSO (National Sample Survey Organisation), RGI (Registrar General of India), DGCIS (Directorate General of Commercial Intelligence and Statistics) and Labour Bureaus

Organization of Data
Organization of data is the arrangement of figures in such a form that comparison of the similar data and further analysis as much as possible.

Classification
Classification is the process of arranging things in groups or classes according to their resemblances and affinities and gives expression similar attributes that may exist amongst a diversity of individuals.

Objectives of Classification :

There are five objectives of classification of data

It gives the idea of Simplification and Briefness with complete distinctiveness . It also help to comparability between the data .This should be given with Scientific arrangement which is attractive and effective . It will completely produce utility.

Characteristic of a Good Classification

The classification should be absolutely clear, completely Homogeneity :

The items within a specific group or class should be similar to each other

Comprehensiveness :

It should cover all the items of data It should be so comprehensive that classify all items in some group or class

Clarity:

There should be no confusion of the placement of any data items in the group /class so the classification should be absolutely clear.

Suitability:

The attribute or characteristics according to which classification is done should agree with classification

Stability :

There should be stability in the basis of the classification of data It means that the basis of the classification of data should not change with every investigation In the other words a specific kind of investigation should be performed on the basis of the same set of classifications

Elastic:

Good classification of data are elastic because of variable in nature

Classification basis

Geographical Classification This classification of data is based on the geographical or locational differences of the data. The geographical limits or the boundaries like cities , village , districts , state country are considered .

Classify data geographically for example as calculating the number of senior citizens in all the states of India above the age of 60 years such as population of literate persons in different states UP –48665 cr ,MP 27136 cr Rajasthan 86623 lakhs etc

Chronological Classification When data are classified on the basis of time, it is known as chronological classification. For example the number of the students in last five successive years can be presented on the basis of time

1951 —1744 , 1961 — 2659 , 1971–4060 , 1981–9400,

1991 –12351

Qualitative Classification

This classification is according to qualities or attributes of the data.

i)Simple classification :

When the classification is based on only one attributes , the given data is classified in two class which is called a simple classification for example dividing the population of Bihar among literate and illiterate

ii)Manifold classification when the classification is made consisting of two or more attributes for when the population of the place is divided into literate and illiterate ,than sub divided into male and female and further sub divided into married and unmarried are the example of manifold classification

Quantitative or Numerical Classification Data are classified in to classes or groups on the basis of their numerical values.

age (years) | 10- 12 | 12- 14 | 14-16|

No. students| 140 | 135 | 100| total = 375

Quantitative classification is also called classification by variables.

Concept of Variable

A characteristic or a phenomenon which is capable of being measured and changes its value overtime is called a variable.
The variable may be either discrete or continuous

Discrete Variable These are those variables that increase in jumps or in compete numbers of particular values / set of all whole numbers is discrete variable because it only includes the whole number such as 1,2,3,4 —- but no 1/2

Continuous Variable:

Variable that assume a range of values or increase not in jumps but continuously or in fractions are called continuous variables.

weight of students in kg | 40-50 | 50-60| 60-70 |

Number of students | 25 | 15 | 10 | Total = 50

Raw Data A mass of data in its crude form is called raw data. Frequency is the number of times value appears in the distribution as given above number of students having weights varies 40 -50 kg is 25 and so on .

Types of Statistical Series Statistical series are of two type the frequencies

Individual Series:

These are those series in which the items are listed singly. These series may be presented in two ways

According to serial numbers such as

s.no 1 ———-2——–3——-4

no of Boys 35 40 34 46 —––

Ascending or descending order of data

ascending order such as 17 , 18 , 43, 54 —–

descending order such as 54,43, 18, 17 —–

Frequency Series :

Frequency series may be of two types

Discrete Series or Frequency Array It is that series in which data are presented in way that exact measurement of items are clearly shown. In this series there are no class intervals and a particular item in the series.

example ; 20, 15, 15 ,10 ,15 ,20 ,15 ,10 ,20 , 15 ,10,25,20 ,25

we can have frequency distribution as

Marks 10———15 ———20 ——25

Tally ||| ||||| |||| ||

frequency 3 5 4 2

Frequency Distribution

It that series in which items cannot be exactly measured. The items assume a range of values and are placed within the limits is called class interval.

Frequency distribution is also known as continuous series or series with class-intervals, or series of grouped data.

Types of Frequency Distribution

Exclusive Series

It is that series in which every class-interval excludes items corresponding to its upper limit it is included in the upcoming class It isa type of continuous series . The upper limit of the class is included in the next interval.

example such as 0-10, 10-20, 20-30,——

Inclusive Series :

An inclusive series is that series which includes all items up to its upper limit. It means that it includes both the lower as well as upper limit items such as

0-9,10-19, 20-29, 30-39 —–

Open End Series:

An open end series is that series in which lower limit of the first class-interval and the upper limit of last class- interval is missing like as below – 5, 20 and above

marks | less than 10 , 10 -20 ,20 -30 , 30 and above

frequency| 10 15 5 20 total = 50

Cumulative Frequency Series

It is that series in which the frequencies are continuously added corresponding to each class-interval in the series.
There are two ways of converting this series into cumulative frequency series

Cumulative frequencies may be expressed on the basis of upper class limits of the class-intervals.

marks | less than 10 less than 20 less than 30 less than 40

students — 2 ————-7—————-17————–30

Cumulative frequencies may b expressed on the basis of lower class limits of the class-intervals.

students —50 ———–40——————20————–5—-

Mid Values Frequency Series Mid value frequency series are those series in which we have only mid values of the class intervals and the corresponding frequencies.

Mid value (x) —5——-15——–25——-35—–

frequency (f) — 4——–8———-10——–6—-

Univariate Distribution The frequency distribution of a single variable is called a univariate distribution.

Bivariate Distribution A bivariate distribution is the frequency distribution of two variables

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