# ECO 07 Solved Assignment 2021 – 22

## Maximum Marks: 100

Attempt all the questions:

Q.1 What do understand by statistics? Discuss the importance, functions and limitations of statistics. (20)

Ans: Statistics: The word Statistics seems to have been derived from the Latin word “status” or the Italian word Statista. All word means a political state. In early year “statistics” equipped a
collection of facts about the people in the state for administration or political purpose.

A comprehensive definition was given by Prof. Horace Secrist, which is a follows: “By Statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically
expressed, enumerated or estimated according to a reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other.”

Characteristics of Statistics:

(i) Statistics are aggregates of facts. Single and isolated figures are not statistics because they cannot be compared.

(ii) Statistics must be numerically expressed. Statistical methods are applicable only to those data which can be numerically expressed.

(iii) Statistics should be capable of comparison and connected to each other.

(iv) Statistics should be collected in a systematic manner.

(v) Statistics should be collected for a definite purpose: The purpose should be specific and well defined.

Following are the need and importance or use of statistics:

a)    Statistics helps in understanding the modern literature in education and psychology.

b)   By using statistical methods, the teachers and educator can collect, arrange, tabulate, compare and interpret the educational results.

c)   Statistics helps in determining the standard of knowledge, intelligence, abilities of student.

d)    Many of the theories and principles of education and psychology are based on statistics.

e)   Statistical methods are used in selection, classification, and promotion of the students.

f)    It can be very useful for higher studies and research studies on educational and psychological problems.

g)   It simplifies complex data.

h)   It permits the most exact kind of desire phenomena and exact kind of description.

i)     It helps the educators and administrators to compare the functioning and development of one educationalinstitution with the other.

j)     It enables the teachers to know about the individual differences of his students.

k)   It helps us to summarize results in a meaningful and convenient form.

l)     It enables us to analyze some of the casual factors underlying complex and otherwise bewildering events.

The functions of statistics are as follows:

(i) It presents fact in a definite form. Numerical expressions of data are convincing.

(ii) It simplifies mass of figures. The data presented in the form of table, graph or diagram, average or coefficients are simple to understand.

(iii) It facilitates comparison. Once the data are simplified they can be compared with other similar data.

(iv) It helps in prediction. Plans and policies of organisations are invariably formulated in advance at the time of their implementation.

(v) It helps in the formulation of suitable policies. Statistics provide the basic material for framing suitable policies.

Limitations of statistics are as follows:

(i) Statistics deals only with quantitative characteristics. Data Which cannot be expressed in numbers are incapable of statistical analysis. Qualitative characteristics like honesty, efficiency, intelligence etc. cannot be studied directly.

(ii) Statistics deals with aggregates not with individuals.

(iii) Statistical laws are not perfectly accurate.

(iv) Statistical results are only an average. Statistical results reveal only the average behavior.

(v) Statistics is only one of the methods of studying a problem. Statistical tools do not provide the best solution under all circumstances.

(vi) Statistics can be misused. The data placed to an inexperienced person may reveal wrong results. Only persons having fundamental knowledge of statistical methods can handle the data
properly.

Q.2 Compute unweighted means of the salaries of teachers in towns A and B. Compare them with weighted means. 20

 Schools Town A Town B No. of teachers Rate of salary No. of teachers Rate of salary 1. Municipal school 25 30 34 40 2. Government school 26 50 35 60 3. Aided school 20 43 12 25 4. Non-aided school 19 35 11 20 5. Night school 10 32 8 25 Total 100 190 100 170

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Q.3 a) Discuss any two types of frequency distribution graphs with example. (10)

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b) What is classification? Discuss the various methods of classification with example? (10)

Ans: Classification of Data

The process of arranging the data in groups or classes according to their common characteristics is technically known as classification. Classification is the grouping of related facts into classes. It is the first step in tabulation.

In the words of Secrist, “Classification is the process of arranging data into sequences and groups according to their common characteristics or separating them into different but related parts.”

Essentials of classification

a)    The classification must be exhaustive so that every unit of the distribution may find place in one group or another.

b)    Classification must conform to the objects of investigation.

c)    All the items constituting a group must be homogeneous.

d)    Classification should be elastic so that new facts and figures may easily be adjusted.

e)    Classification should be stable. If it is not so and is changed for every enquiry, then the data would not fit for an enquiry.

f)     The data must not overlap. Each item of the data must be found in one class.

Methods of Classification of Data

There are two methods of classification: i) classification according to attributes, and ii) classification according to variables.

Classification According to Attributes

An attribute is a qualitative characteristic which cannot be expressed numerically. Only the presence or absence of an attribute can be known. For example, intelligence, religion, caste, sex, etc., are attributes. You cannot quantify these characteristics. When classification is to be done on the basis of attributes, groups are differentiated either by the presence or absence of the attribute
(e.g. male and female) or by its differing qualities. The qualities of an attribute can easily be differentiated by means of some natural line of demarcation. Based on this natural difference, we can determine the group into which a particular item is placed. For instance, if we select colour of hair as the basis of classification, there will be a group of brown haired people and another group of black haired people. There are two types of classification based on attributes.

1) Simple Classification: In simple classification the data is classified on the basis of only one attribute. The data classified on the basis of sex will be an example of simple classification.

2) Manifold Classification: In this classification the data is classified on the basis of more than one attribute. For example, the data relating to the number of students in a university can be classified on the basis of their sex and marital.

Classification According to Variables

According to Variables, data may be classified as:

1.    Univariate data: Univariate data is a data in which there is only one variable. It is simplest form of data and deals with only change in quantity. It does not deal with cause and effect relationship between two or more variables. The main purpose of univariate data is to find the pattern exist in given data. Examples of univariate data is age of 10 workers in a factory, marks scored by 50 students in mathematics etc. Pattern exists in univariate data can be analysed with the help of various tools of measures of central tendency and dispersion. Also diagrams and graphs
can be used to analyse univariate data.

2.    Bivariate data: Bivariate data is a data in which there are two different variables. It deals with cause and effect relationship between two variables and analysis of data is done to find the relationship between two variables. Example of Bivariate data is age and weight of workers, demand and supply of a product, marks of students in two different subjects, temperature and sales of woolen products etc.

3.    Multivariate data: Multivariate data is data in which there are three or more variables. Example of multivariate data is suppose a manufacturer wants to compare the sales data of his product in five different areas. Some of the common tool used to analysed multivariate data is correlation and regression analysis, multivariate analysis of variance etc.

4.    Time series data: Time series data is the study of behaviour of single variable at different intervals. This data is analysed to find the trend. Example of time series data is the sales of product X over a period of 10 years.

5.    Cross sectional data: Cross sectional data is the study of behaviour of more than one variable at different interval.  Example of cross sectional data is the sales of product X over a period of 10 years in four different states.

Q.4 a) Find the combined mean and combined standard deviation of the given series:     10

 Series A Series B Mean 50 40 Standard deviation 5 6 No. of items 100 150

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b) Consider the following distribution and answer whether the given statements are true or false:      10

 Distribution A Distribution B Mean 100 90 Median 90 80 Standard deviation 10 10

i) Distribution A has the same degree of variation as distribution B.

ii) Both the distributions have same degree of skewness.

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Q.5 Write short notes on the following: (5×4=20)

a. Multistage sampling

Ans: Multi-Stage sampling:  This is not a favoured procedure of sampling.  In this items are selected in different stages at random.  For example, if we wish to know per acre yield of various crops in U.P., we shall begin by studying a single crop in one study.  Here we shall begin by making at random selection of 5 districts in the first instance, and then of these 5 districts, 10 villages per districts will be chosen in the same manner. Now in the final stage, again by random selection 5 fields out of every village. Thus we shall examine per acre yield in 250 farms all over U.P. this number can have increased or decreased depending upon the opinion of experts.

b. Types of ratios

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c. Pie diagrams

Ans: Pie diagram are very popularly used in practice to show percentages breakdowns. For example, with the help of pie diagram we can show how the expenditure of the government is distributed over different heads like agriculture, irrigation, industry, transport, defence, etc. Similarly, through a pie diagram we can show how the expenditures incurred by an industry are divided over different heads like raw materials, wages and salaries, selling costs, distribution expenses etc. The pie chart is so called because the entire graph looks like a pie, and the components resemble slices cut from pie.

While making comparison, pie diagram should be used on a percentage basis and not on an absolute basis, since a series of pie diagram showing absolute figures would require that larger totals be
represented by larger cycle. Such presentation involves difficulties of two-dimensional comparisons. However, when pie diagrams constructed on a percentage basis, percentages can be presented by circles equal in size. In may be noted that this problem does not arise in the use of a single pie diagram.

d. Harmonic mean

Ans: H.M.: It is defined as the reciprocal of the arithmetic mean of the reciprocal of the individual observations.

Merits of H.M.:

(i)  Like AM and GM, it is also based on all observations.

(ii)   It is most appropriate average under conditions of wide variations among the items of a series since it gives larger weight to smaller items.

(iii)    It is capable of further algebraic treatment.

(iv)   It is extremely useful while averaging certain types of rates and ratios.

Demerits of H.M.:

(i)     It is difficult to understand and to compute.

(ii)   It cannot be computed when one of the values is 0 or negative.

(iii)   It is necessary to know all the items of a series before it can be calculated.

(iv)  It is usually a value which may not be a member of the given set of numbers.

Uses of H.M.: If there are two measurements taken together to measure a variable, HM can be used. For example, tonne mileage, speed per hour. In the above example tonne mileage, tonne is one measurement and mileage is another measurement. HM is used to calculate average speed.

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