Part – B

Answer The Following Questions In One or Two Sentences.

Question 21.
What is Statistics?
Answer:

  1. The term‘Statistics’is used in two senses: as singular and plural.
  2. In singular form it simply means statistical methods.
  3. Statistics when used in singular form helps in the collection, presentation, classification and interpretation of data to make it easily comprehensible.
  4. In its plural form it denotes collection of numerical figures and facts.
  5. In the narrow sense it has been defined as the science of counting and science of averages.


Question 22.
What are the kinds of Statistics?
Answer:
Types of Statistics:
1. There are two major types of statistics named as Descriptive Statistics and Inferential Statistics.

2. Descriptive Statistics:
The branch of statistics devoted to the summarization and description of data is called Descriptive Statistics.

3. Inferential Statistics:
The branch of statistics concerned with using sample data to make an inference about a population of data is called Inferential Statistics.

Question 23.
What do you mean by Inferential Statistics?
Answer:
Inferential Statistics:

  1. The branch of statistics concerned with using sample data to make an inference about a population of data is called Inferential Statistics.
  2. It draws conclusion for the population based on the sample result.
  3. It uses hypotheses, testing and predicting on the basis of the outcome.
  4. It tries to understand the population beyond the sample.


Question 24.
What are the kinds of data?
Answer:


Question 25.
Define Correlation?
Answer:
Correlation is a statistical device that helps to analyse the covariation of two or more variables. Sir Francis Galton, is responsible for the calculation of correlation coefficient.


Question 26.
Define Regression?
Answer:

  1. The term ‘Regression’ was first coined and used in 1877 by Francis Galton while studying the relationship between the height of fathers and sons.
  2. The average height of children bom of parents of a given height tended to move or “regress” toward the average height in the population as a whole.
  3. Gabon’s law of universal regression was confirmed by his friend Karl Pearson, who collected more than a thousand records of heights of members of family groups.
  4. The literal meaning of the word “regression” is “Stepping back towards the average”.

Question 27.
What is Econometrics?
Answer:
Origin Of Econometrics:

  1. Economists tried to support their ideas with facts and figures in ancient times.
  2. Irving Fisher is the first person, developed mathematical equation in the quantity theory of money with help of data.
  3. Ragnar Frisch, a Norwegian economist and statistician named the integration of three subjects such that mathematics, statistical methods and economics as Econometrics” in 1926.

Part – C
Answer The Following Questions In One Paragraph.

Question 28.
What are the functions of Statistics?
Answer:
Functions of Statistics:

  1. Statistics presents facts in a definite form.
  2. It simplifies mass of figures.
  3. It facilitates comparison.
  4. It helps in formulating and testing.
  5. It helps in prediction.
  6. It helps in the formulation of suitable policies.

(I) Statistics are an aggregate of facts:
For example, numbers in a calendar pertaining to a year will not be called statistics, but to be included in statistics it should contain a series of figures with relationships for a prolonged period.

(II) Statistics are numerically enumerated, estimated and expressed.

(III) Statistical collection should be systematic with a predetermined purpose:
The purpose of collection of statistics should be determined beforehand in order to get accurate information.

(IV) Should be capable of being used as a technique for drawing comparison:
It should be capable of drawing comparison between two different sets of data by tools such as averages, ratios, rates, coefficients etc.


Question 29.
Find the Standard Deviation of the following data:
14, 22, 9, 15, 20, 17, 12, 11

Question 30.
State and explain the different kinds of Correlation?
Answer:

Type I:
Based on the direction of change of variables:
Correlation is classified into two types as Positive correlation and Negative Correlation based on the direction of change of the variables.

Positive Correlation:
The correlation is said to be positive if the values of two variables move in the same direction.

Ex 1:
If income and Expenditure of a Household may be increasing or decreasing simultaneously. If so, there is positive correlation. Ex. Y = a + bx

Negative Correlation:
The Correlation is said to be negative when the values of variables move in the opposite directions. Ex. Y = a – bx

Ex 1:
Price and demand for a commodity move in the opposite direction.

Type II:
Based upon the number of variables studied
There are three types based upon the number of variables studied as

  1. Simple Correlation
  2. Multiple Correlation
  3. Partial Correlation

Simple Correlation:
If only two variables are taken for study then it is said to be simple correlation. Ex. Y = a + bx

Multiple Correlations:
If three or more than three variables are studied simultaneously, then it is termed as multiple correlation.

Ex: Determinants of Quantity demanded
Qd = f (P, Pc, Ps, t, y)
Where Qd stands for Quantity demanded, f stands for function.
P is the price of the goods,
Pc is the price of competitive goods
Ps is the price of substituting goods
t is the taste and preference
y is the income.

Partial Correlation:
If there are more than two variables but only two variables are considered keeping the other variables constant, then the correlation is said to be Partial Correlation.

Type III: Based upon the constancy of the ratio of change between the variables

Correlation is divided into two types as linear correlation and Non – Linear correlation based upon the Constancy of the ratio of change between the variables.

Linear Correlation:
Correlation is said to be linear when the amount of change in one variable tends to bear a constant ratio to the amount of change in the other.
Ex. Y = a + bx

Non Linear:
The correlation would be non-linear if the amount of change in one variable does not bear a constant ratio to the amount of change in the other variables.
Ex. Y = a + bx2


Question 31.
Mention the uses of Regression Analysis?
Answer:
Use of Regression Analysis:

  1. Regression means going back and it is a mathematical measure showing the average relationship between two variables.
  2. Both the variables may be random variables.
  3. It indicates the cause and effect relationship between the variables and establishes functional relationship.
  4. Besides verification it is used for the prediction of one value, in relation to the other given value.
  5. Regression coefficient is an absolute figure. If we know the value of the independent variable, we can find the value of the dependent variable.
  6. In regression there is no such spurious regression.
  7. It has wider application, as it studies linear and nonlinear relationship between the variables.
  8. It is widely used for further mathematical treatment.


Question 32.
Specify the objectives of econometrics?
Answer:
Objectives of Econometrics:
The general objective of Econometrics is to give empirical content to economic theory. The specific objectives are as follows:

  1. It helps to explain the behaviour of a forthcoming period that is forecasting economic phenomena.
  2. It helps to prove the old and established relationships among the variables or between the variables
  3. It helps to establish new theories and new relationships.
  4. It helps to test the hypotheses and estimation of the parameter.

Question 33.
Differentiate the economic model with econometric model?
Answer:
Economic Model:

  1. Economic model is the theoretical construct that represents the complex economic process.
  2. Economic model is based on mathematical modeling.
  3. Economic model is focused on establishing the logical relationships between the variables in the model.
  4. Economic model is applied in stating the theoretical relationship into mathematical equations.
  5. Economic model believes that outcome is certain and exact. So disturbance term is not required.
  6. Economic model is deterministic in nature.
  7. The Keynesian consumption function: C = a + by is the economic model

Econometric Model:

  1. Econometric model is the statistical concept that represents the numerical estimate of the variables involved in economic process.
  2. Econometric model is based on statistical modeling.
  3. Econometric model is focused on estimating the magnitude and direction of relationship between the variables.
  4. Econometric model is applied in stating the empirical extent of the economic model.
  5. Econometric model believes that outcome is certain but not exact. So disturbance term plays the vital role.
  6. Econometric model is stochastic in nature.
  7. The Keynesian consumption function: C = a + by + µ is the econometric model


Question 34.
Discuss the important statistical organizations (offices) in India?
Answer:

  1. Official Statistics are statistics published by government agencies or other public bodies such as international organizations.
  2. They provide quantitative or qualitative information on all major areas of citizens’ lives.
  3. Official Statistics make information on economic and social development accessible to the public, allowing the impact of government policies to be assessed, thus improving accountability.
  4. The Ministry of Statistics and Programme Implementation (MOSPI) came into existence as an Independent Ministry in 1999 after the merging of the Department of Statistics and the Department of Programme Implementation.
  5. The Ministry has two wings, Statistics and Programme Implementation.

National Sample Survey Organisation (NSSO):

  1. The National Sample Survey Organisation, now known as National Sample Survey Office, is an organization under the Ministry of Statistic of the Government of India.
  2. It is the largest organisation in India, conducting regular socio-economic surveys.
  3. It was established in 1950. NSSO has four divisions:
    1. Survey Design and Research Division (SDRD)
    2. Field Operations Division (FOD)
    3. Data Processing Division (DPD)
    4. Co-ordination and Publication Division (CPD)

The Programme Implementation Wing has three Divisions, namely,

  1. Twenty Point Programme
  2. Infrastructure Monitoring and Project Monitoring
  3. Member of Parliament Local Area Development Scheme.

Besides these three wings, there is National Statistical Commission created through a Resolution of Government of India (MOSPI) and one autonomous Institute, viz., Indian Statistical Institute declared as an institute of National importance by an Act of Parliament.

Part – D
Answer The Following Questions.

Question 35.
Elucidate the nature and scope of Statistics?
Nature of Statistics:

  1. Different Statisticians and Economists differ in views about the nature of statistics, some call it a science and some say it is an art.
  2. Tipett on the other hand considers Statistics both as a science as well as an art.

Scope of Statistics:
Statistics is applied in every sphere of human activity – social as well as physical – like Biology, Commerce, Education, Planning, Business Management, Information Technology, etc.

Statistics and Economics:

  1. Statistical data and techniques are immensely useful in solving many economic problems
  2. Such as fluctuation in wages, prices, production, distribution of income and wealth and so on.

Statistics and Firms:
Statistics is widely used in many firms to find whether the product is conforming to specifications or not.

Statistics and Commerce:

  1. Statistics are life blood of successful commerce.
  2. Market survey plays an important role to exhibit the present conditions and to forecast the likely changes in future.

Statistics and Education:

  1. Statistics is necessary for the formulation of policies to start new course, according to the changing environment.
  2. There are many educational institutions owned by public and private engaged in research and development work to test the past knowledge and evolve new knowledge.
  3. These are possible only through statistics.

Statistics and Planning:
1. Statistics is indispensable in planning. In the modem world, which can be termed as the “world of planning”, almost all the organisations in the government are seeking the help of planning for efficient working, for the formulation of policy decisions and execution of the same.

2. In order to achieve the above goals, various advanced statistical techniques are used for processing, analyzing and interpreting data.

3. In India, statistics play an important role in planning, both at the central and state government levels, but the quality of data highly unscientific.

Statistics and Medicine:

  1. In Medical sciences, statistical tools are widely used. In order to test the efficiency of a new drug or to compare the efficiency of two drugs or two medicines, t – test for the two samples is used.
  2. More and more applications of statistics are at present used in clinical investigation.

Statistics and Modern applications:

  1. Recent developments in the fields of computer and information technology have enabled statistics to integrate their models and thus make statistics a part of decision making procedures of many organisations.
  2. There are many software packages available for solving simulation problems.


Question 36.
Calculate the Karl Pearson Correlation Co-efficient for the following data?
Answer:

Question 38.
Describe the application of Econometrics in Economics?
Answer:
Origin Of Econometrics:

  • Economists tried to support their ideas with facts and figures in ancient times.
  • Irving Fisher is the first person, developed mathematical equation in the quantity theory of money with help of data.
  • Ragnar Frisch, a Norwegian economist and statistician named the integration of three subjects such that mathematics, statistical methods and economics as Econometrics” in 1926. Ragnar Anton Kittil Frisch Noble Memorial Prize in 1969.
  • The term econometrics is formed from two words of Greek origin, ‘oukovouia’ meaning economy and ‘uetpov’ meaning measure. Econometrics emerged as an independent discipline studying economics phenomena.
  • Econometrics may be considered as the integration of economics, Statistics and Mathematics.
  • Econometrics is an amalgamation of three subjects which can be easily understood by following Venn diagram and picture representation.
  • Economics + Mathematics = Mathematical Economics
  • Mathematical Economics + Statistical Data & Its Technique = Econometrics
  • {Economics + Statistics + Mathematics} + Empirical Data = Econometrics

Definitions:

  • In the words of Arthur S. Goldberger, “Econometrics may be defined as the social science in which the tools of economic theory, mathematics and statistical inference are applied to the analysis of economic phenomena”.
  • Gerhard Tinbergen points out that “Econometrics, as a result of certain outlook on the role of economics, consists of application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results”.
  • H Theil“Econometrics is concerned with the empirical determination of economic laws”
  • In the words of Ragnar Frisch “The mutual penetration of quantitative econometric theory and statistical observation is the essence of econometrics”.
  • Econometrics means economic measurement. Econometrics deals with the measurement of economic relationships.

Objectives Of Econometrics:
The general objective of Econometrics is to give empirical content to economic theory. The specific objectives are as follows:

  1. It helps to explain the behaviour of a forthcoming period that is forecasting economic phenomena.
  2. It helps to prove the old and established relationships among the variables or between the variables
  3. It helps to establish new theories and new relationships.
  4. It helps to test the hypotheses and estimation of the parameter.