Re: Solved assignment papers of ECO03, ECO05, ECO07, ECO12, ECO13,ECO14
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1. a) Long Range Planning concerned with making today’s, decisions with a better sense of
futurity.’’ Comment.
Solution : Yes Long Range Planning is concerned with making today’s, decisions with a better sense of futurity as Decisions exist only in the present." The question …is not what we should do tomorrow. It is what do we have to do today to be ready for an uncertain tomorrow? The question is not what will happen in the future. It is: what futurity do we have to factor into our present thinking and doing, what timespans do we have to consider, and how do we converge them into a simultaneous decision in the present?
We can make decisions only in the present; the rest are pious intentions. And yet we cannot make decisions for the present alone; the most expedient, most opportunist decision – let alone the decision not to decide – may commit us on a longrange basis, if not permanently and irrevocably. So idea of decision making as a “time machine” recognizes that future outcomes are wholly products of the complex interplay of decisions made by people in the present. Also that it is not only those decisions that are 'headlined' as strategic decisions that have potentially strategic implications for the organization.
b) What do you mean by span of control ? Discuss factors affecting span of control. (10+10)
Solution : The span of control means, simply, the number of subordinates or the units of work that an administrator personally direct. "The Span of control is the number of range of direct, habitual communication contacts between the chief executive of an enterprise and his principal fellowofficers". This concept is related to the principle of 'Span of attention’, Span of control is dependent upon span of attention. None of us can attend to more than a certain number of things at time
In all the activities you supervise, a principle of good organization that you should use is the maintenance of a suitable span of control. This principle implies that the greater number of people that one person must supervise, the more difficult it will be for that person to supervise effectively. A common rule you should use is that your immediate supervision should not extend over more than eight persons or less than four persons. However, the type of work being done, the capacity of a given supervisor, and the relationships between a supervisor and the subordinates are all factors that enter the picture. The location of subordinates in relation ship to the supervisor is also a consideration. Your layout should permit you to have frequent personal contact with those you directly supervise. There is also a time element involved with supervision. As was mentioned, you should assign responsibilities and delegate authority as much as possible without losing control of policy and pro cedars. Generally, your span of control should allow your subordinates to perform most of the routine work. This technique provides you wit h the time to supervise your people, to perform any work that is beyond the capacity of your subordinates, or to complete any work that has been assigned to you by your seniors
2. How can coordination be used as the instrument for effective management action? Discuss the various techniques through which coordination can be achieved. (6+14)
3. What do you mean by management development programmes? Explain the major techniques of management development programmes. (4+16)
Solution : Basically, management development is a term that describes any number of activities that reflect a planned effort to enhance employees’ ability in various individual and team management techniques. Very simply put, management development includes development of skills such as planning, organising, leading and developing resources. A key skill for any employees is the ability to manage their own work and control their career path. Highly motivated and selfdirected individuals can gain a massive amount of learning and other benefits for their organisation by implementing an aggressive management development programme.
Management development refers to the process of training and developing managerial talent within a company or organisation. But why do I need to waste time on training and development? Why not just hire the people I need when the time comes?
Nurturing inhouse management talent may not seem important, but it is one of the most important aspects of the development of any organisation. This is the case for several reasons, some of which are listed below:
1. Inhouse management development programmes give employees the chance to utilise special leadership skills that may posses. These employees will certainly bring an enhanced perspective to management as they will know the working of the company from the ground up as opposed to managerial talent that is brought in from outside the company.
2. Employees will feel more loyal towards the company as they will see that the company is also invested in promoting their career growth and progress.
3. Finally, the overall cost of developing management talent inhouse as opposed to trying to recruit talent from the outside world will be much less. A good management development programme may cost during the initial setting up phase, but will not cost much more after that. Individuals who have risen up from the management development programme will be happy to volunteer their time and mentor other employees. In general, a good management development programme will save a lot of money for any organisation.
Management development is a process that begins paying for itself very rapidly. You will begin to see the creation of a core team of individuals who are committed to the growth and progress of your organisation. In the long run, this can only mean increased efficiency and profitability as the management talent in your organisation grows stronger and stronger
4. Write short notes on the following:
a) BreakEven Analysis
Breakeven analysis is a technique widely used by production management and management accountants. It is based on categorizing production costs between those which are "variable" (costs that change when the production output changes) and those that are "fixed" (costs not directly related to the volume of production). Total variable and fixed costs are compared with sales revenue in order to determine the level of sales volume, sales value or production at which the business makes neither a profit nor a loss (the "breakeven point").
In its simplest form, the breakeven chart is a graphical representation of costs at various levels of activity shown on the same chart as the variation of income (or sales, revenue) with the same variation in activity. The point at which neither profit nor loss is made is known as the "breakeven point"
Fixed Costs
Fixed costs are those business costs that are not directly related to the level of production or output. In other words, even if the business has a zero output or high output, the level of fixed costs will remain broadly the same. In the long term fixed costs can alter  perhaps as a result of investment in production capacity (e.g. adding a new factory unit) or through the growth in overheads required to support a larger, more complex business.
Examples of fixed costs:
 Rent and rates
 Depreciation
 Research and development
 Marketing costs (non revenue related)
 Administration costs
Variable Costs
Variable costs are those costs which vary directly with the level of output. They represent payment outputrelated inputs such as raw materials, direct labour, fuel and revenuerelated costs such as commission.
A distinction is often made between "Direct" variable costs and "Indirect" variable costs.
Direct variable costs are those which can be directly attributable to the production of a particular product or service and allocated to a particular cost centre. Raw materials and the wages those working on the production line are good examples.
Indirect variable costs cannot be directly attributable to production but they do vary with output. These include depreciation (where it is calculated related to output  e.g. machine hours), maintenance and certain labour costs.
SemiVariable Costs
Whilst the distinction between fixed and variable costs is a convenient way of categorising business costs, in reality there are some costs which are fixed in nature but which increase when output reaches certain levels. These are largely related to the overall "scale" and/or complexity of the business. For example, when a business has relatively low levels of output or sales, it may not require costs associated with functions such as human resource management or a fullyresourced finance department. However, as the scale of the business grows (e.g. output, number people employed, number and complexity of transactions) then more resources are required. If production rises suddenly then some shortterm increase in warehousing and/or transport may be required. In these circumstances, we say that part of the cost is variable and part fixed.
b) Statistical Quality Control
Quality Control has been with us for a long time. It is safe to say that when manufacturing began and competition accompanied manufacturing, consumers would compare and choose the most attractive product (barring a monopoly of course). If manufacturer A discovered that manufacturer B's profits soared, the former tried to improve his/her offerings, probably by improving the quality of the output, and/or lowering the price. Improvement of quality did not necessarily stop with the product  but also included the process used for making the product.
The process was held in high esteem, as manifested by the medieval guilds of the Middle Ages. These guilds mandated long periods of training for apprentices, and those who were aiming to become master craftsmen had to demonstrate evidence of their ability. Such procedures were, in general, aimed at the maintenance and improvement of the quality of the process.
In modern times we have professional societies, governmental regulatory bodies such as the Food and Drug Administration, factory inspection, etc., aimed at assuring the quality of products sold to consumers. Quality Control has thus had a long history.
c) Chain of Command
The continuous chain of authority that links the most junior private to the Commander in Chief and vice versa. Many argue that the U. S. implementation of the chain of command is the most important strategy employed by our military forces. In other armies the loss of a commander would throw the entire organization into disorder while in the U. S. military, the next most senior person present just assumes command. It is taught that whenever two Marines are walking together, one is in charge.
d) King Pin function (4x5)
5. Briefly comment on the following:
a) Orders will be obeyed if they make sense.
b) Delegated duties are always a part of the subordinate normal duties.
c) Tactical planning is carried out under more risky conditions than strategical planning.
d) Directing simply mean instructing others what they should do. (4x5)
IGNOU B.Com ECO07 Solved Assignment Paper
1. “All statistics are numerical statements of facts but all numerical
statements of facts are not statistics” comment. (20).
Solution: According to this definition the numerical facts (data) should possess the following
characteristics to be treated as statistics.
(i) Aggregate of facts:
Single, isolated or unrelated figures are not statistics, because they are not comparable. These
figures tell nothing about any problem. For example the age of a student or the price of a
commodity is not statistics. Because they are just abstract numbers. But when we consider age
of a group of students, or the prices of a basket of commodities it is statistics as they
comparable. Statistics must be expressed as aggregate of facts relating to any particular
enquiry. Thus ‘not a datum’ but the data represent statistics.
(ii) Affected by multiplicity of causes :
Numerical facts should be affected by a number of factors to become statistics.These may
include both normal as well as exceptional factors. For example, the yield of rice depends on a
number of factors like the rainfall, fertility of the soil, method of cultivation, quality of seeds used
etc.Some of these factors are normal and some are exceptional. Hence the data relating to the
yield of rice over a period of time become statistics. On the other hand if we write numericals
l,2,3,4,5,6,7,8,9,and 10, they are not statistics. Because they are not affected by any factors.
(iii) Numerically expressed:
Statistics are quantitative phenomena. Mostly, statistical techniques deal with quantitative
factors than with qualitative aspect. So statistics should be always numerically expressed. For
example, ‘there are 30 districts in Orissa’, is a numerical statement. But the standard of living of
the people of Orissa have improved over the years’ is not a numerical statement. Here the first
statement is statistical where as the second is not. So the subjective statements relating to
qualitative information like honesty, beauties etc. are not statistics. Only statements which can
be expressed numerically are statistics.
(iv) Enumerated accurately:
In an enquiry statistics (data) should be collected with a reasonable standard of accuracy. This
affects the findings of the enquiry. The degree of accuracy of statistics depends on the nature
and purpose of the enquiry. Generally data are collected in two ways  by enumerating all the
units of the population (complete enumeration method) or enumerating some units (sampling
Method) and the result is generalized for the whole group. No doubt the first method involves
more time and cost but provides more accurate information than the second. Depending on the
nature of enquiry and the degree of accuracy desired only one of the above two methods is
employed. But the collected statistics should be as far as possible accurate.
(v) Collected in a systematic manner :
Information (data) constitute the basis of any statistical enquiry. They should be collected in a
scientific and systematic manner. For this, the purpose of the enquiry must be decided in
advance. The purpose should be specific and well defined. The information should be collected
by trained, skilled and unbiased investigators. Other wise irrelevant and unnecessary
information may be collected and the very purpose of statistics is defeated.
(vi) Collected for a predetermined purpose :
Statistics relating to an enquiry are always collected with a predetermined purpose. So it is
essential to define clearly the purpose or the objective of the enquiry before actually collecting
data. This ensures the inclusion of all essential information and the exclusion of all irrelevant
and confusing data. This will make the analysis specific and result oriented.
(vii) Placed in relation to each other :
Statistics should be comparable. They may be compared with respect to time of occurrence or
place of collection. This requires the data should be homogeneous and are placed in relation to
each other. Because heterogeneous data are not comparable.For example, data relating to
production of rice and the number of students taking admission in a class are not statistics.
Because they are not comparable. On the other hand, the food grain production of a state for
the last ten years constitute statistics as they are comparable. So statistical data should express
some phenomenon. In other words, “All statistics are numerical statements of facts but all
numerical statements of facts are not statistics”.
2. (a) What is statistical table? How is it constructed? Discuss the requisites of a
good statistical table.
Solution: These tables are prepared twice each year, with one volume reporting data
for the 12month period ending June 30, and the other volume reporting data for the
calendar year ending December 31.Detailed statistical tables address the work of the
U.S. courts of appeals, district courts and bankruptcy courts, as well as the federal
probation and pretrial services system.The Judicial Caseload Indicators table compares
data for the current 12month period to that for the same period 1, 5, and 10 years
earlier.
Constructed: In general, a statistical table consists of the following eight parts. They are as
follows:
(i) Table Number: Each table must be given a number. Table number helps in distinguishing
one table from other tables. Usually tables are numbered according to the order of their
appearance in a chapter. For example, the first table in the first chapter of a book should be
given number 1.1 and second table of the same chapter be given 1.2 Table number should be
given at its top or towards the left of the table.
(ii) Title of the Table: Every table should have a suitable title. It should be short & clear. Title
should be such that one can know the nature of the data contained in the table as well as where
and when such data were collected. It is either placed just below the table number or at its right.
(iii) Caption: Caption refers to the headings of the columns. It consists of one or more column
heads. A caption should be brief, concise and selfexplanatory, Column heading is written in the
middle of a column in small letters.
(iv)Stub: Stub refers to the headings of rows.
(v) Body This is the most important part of a table. It contains a number of cells. Cells are
formed due to the intersection of rows and column. Data are entered in these cells.
(vi) Head Note: The headnote (or prefactory note) contains the unit of measurement of data. It
is usually placed just below the title or at the right hand top corner of the table.
(vii) Foot Note A foot note is given at the bottom of a table. It helps in clarifying the point which
is not clear in the table. A foot note may be keyed to the title or to any column or to any row
heading. It is identified by symbols such as *,+,@,£ etc.
Requisites of Good Statistical Table: You have studied the parts of a statistical table. Now let
us discuss the features of a statistical table. There are certain general guidelines in preparing a
good statistical table. They are as follows:
I) A good table must present the data in a clear and simple manner.
2) It should have a brief and clear title. The title should be selfevplanatory and should
represent the description of the contents of the table.
3) The stub, stub entries, captions and caption heads should be brief and clear. The columns
may be numbered to facilitate easy reference in the text.
4) The headnote should be precise and complete as it relates to the unit of the data.
5) The totals and subtotals should be given at the appropriate places.
6) The references should be clearly stated so that the reliability of the data could be verified if
needed.
7) If necessary, the derived data (ratios, percentages, averages, etc.) may also be incorporated
in the tables.
8) .As far as possible abbreviations should be avoided in a statistical table. If it is essential to
use abbreviations, their meaning must be explained in footnotes.
9) Wherever necessary, proper ruling should be provided in a table. Normally, the columns
are separated from one another by lines. These lines make the table more readable and
attractive, and also show the relations of the data more clearly. Always lines are drawn at
the top and bottom of the table, and also below the captions.
10) Use of ditto mark should be avoided.
11) Columns and rows which are to be compared with one another should be placed side by
side.
12) If it is necessary to emphasise the relative significance of certain categories, different kinds
of type spacing and indentation should be used.
13) All the column figures should be properly aligned. Decimal points and plusminus signs
also should be in perfect alignment.
14) Generally not more than four to five characteristics may be shown at a time in a table,
otherwise it will become too complex.
(b) What is skewness? Explain the various methods of measuring skewness.
Solution: In probability theory and statistics, skewness is a measure of the asymmetry of
the probability distribution of a realvalued random variable. The skewness value can be positive
or negative, or even undefined. Qualitatively, a negative skew indicates that the tail on the left
side of the probability density function is longer than the right side and the bulk of the values
(possibly including the median) lie to the right of the mean. A positive skew indicates that
the tail on the right side is longer than the left side and the bulk of the values lie to the left of the
mean. A zero value indicates that the values are relatively evenly distributed on both sides of
the mean, typically (but not necessarily) implying a symmetric distribution. Some distributions of
data, such as the bell curve are symmetric. This means that the right and the left are perfect
mirror images of one another. But not every distribution of data is symmetric. Sets of data that
are not symmetric are said to be asymmetric. The measure of how asymmetric a distribution
can be is called skewness. As we will see, data can be skewed either to the right or to the left.
The mean, median and mode are all measures of the center of a set of data. The skewness of
the data can be determined by how these quantities are related to one another.
Measures of Skewness:
It’s one thing to look at two set of data and determine that one is symmetric while the other is
asymmetric. It’s another to look at two sets of asymmetric data and say that one is more skewed
than the other. It can be very subjective to determine which is more skewed by simply looking at
the graph of the distribution. This is why there are ways to numerically calculate the measure of
skewness.
One measure of skewness, called Pearson’s first coefficient of skewness, is to subtract the
mean from the mode, and then divide this difference by the standard deviation of the data. The
reason for dividing the difference is so that we have a dimensionless quantity. This explains why
data skewed to the right has positive skewness. If the data set is skewed to the right, the mean
is greater than the mode, and so subtracting the mode from the mean gives a positive number.
A similar argument explains why data skewed to the left has negative skewness. Pearson’s
second coefficient of skewness is also used to measure the asymmetry of a data set. For this
quantity we subtract the mode from the median, multiply this number by three and then divide
by the standard deviation.
1. Introduction: In an introductory level statistics course, instructors spend the first part of the
course teaching students three important characteristics used when summarizing a data set:
center, variability, and shape. The instructor typically begins by introducing visual tools to get a
“picture” of the data.
2. Visual Displays: A textbook discussion would typically begin by showing the relative
positions of the mean, median, and mode in smooth population probability density functions.
The explanation will mainly refer to the positions of the mean and median. There may be
comments about tail length and the role of extreme values in pulling the mean up or down. The
mode usually gets scant mention, except as the “high point” in the distribution.
3. Skewness Statistics: Since Karl Pearson (1895), statisticians have studied the properties of
various statistics of skewness, and have discussed their utility and limitations. This research
stream covers more than a century. For an overview, see Arnold and Groenveld (1995),
Groenveld and Meeden (1984), and Rayner, Best and Matthews (1995). Empirical studies have
examined bias, mean squared error, Type I error, and power for samples of various sizes drawn
from various populations.
4. Type I Error Simulation: We obtained preliminary critical values for Sk2 using Monte Carlo
simulation with Minitab 16. We drew 20,000 samples of N(0,1) for n = 10 to 100 in increments of
10 and computed the sample mean ( x ), sample median (m), and sample standard deviation
(s). For each sample size, we calculated Sk2 and its percentiles. Upper and lower percentiles
should be the same except for sign, so we averaged their absolute values (effectively 40,000
samples).
5. Type II Error Simulation: Type II error in this context occurs when a sample from a nonnormal
skewed distribution does not lead to rejection of the hypothesis of a symmetric normal
distribution. There are an infinite number of distributions that could be explored, including “real
world” mixtures that do not resemble any single theoretical model. Just to get some idea of the
comparative power of Sk2 and G1, we will illustrate using samples from two nonnormal,
unimodal distributions.
6. Summary and Conclusions: Visual displays (e.g., histograms) provide easily understood
impressions of skewness, as do comparisons of the sample mean and median. However,
students tend to take too literal a view of these comparisons, without considering the effects of
binning or the role of sample size.
3. Differentiate between the following:
(a) Primary data and Secondary data:
Solution: Primary Data and Secondary Data
The data which is collected for the first time for your own use is known as primary data. The
source happens to be primary if the data is collected for the first time by you as original data. On
the other hand, if you are using data which has been collected, classified and analysed by
someone else, then such data is known as secondary data. The sources of secondary data are
called secondary sources. For instance, national income data collected by the Government in
a country is primary data for that Government. But the same data becomes secondary for those
research workers who use it later. We may, thus, state that primary data is in the shape of raw
materials to which statistical methods are applied for analysis. At the same time secondary data
is in the shape of finished products since it has already been treated in some form or the other
by statistical methods. In case you have decided to collect primary data for your survey, you
have to identify the sources from which you can collect that data. Big enquiries like population
census involve very large number of persons to be surveyed but in case of small enquiries like
cost of living of industrial workers in a city, the persons to be surveyed may be few. If you have
decided to use secondary data, it is necessary for you to edit and scrutinize such data.
Otherwise it may not have the desired level of accuracy or it may not be suitable or
adequatefor'your purpose. If you do not edit and scrutinise the secondary data before you use it
in your survey, the results of your investigation may not be fully correct. Therefore, secondary
data should always be used with great caution. Bowley writes: It is never safe to take
published statistics at their face value without knowing their meaning and limitations.
(b) Sampling and NonSampling errors:
Solution: Sampling Errors: The errors caused by drawing inference about the
population on the basis af samples are termed as sampling errors. The sampling errors result
from the bias in the selection of sample units. These errors occur because the study is based on
a portion of the population. If the whole population is taken, sampling error can be eliminated. If
two or more sample units are taken from a population by random sampling method, their results
need not be identical and the results of both of them may be different from the result of the
population. This is due to the fact that the selected two sample items will not be identical. Thus,
sampling error means precisely the difference between the sample result and that of the
population when both the results are obtained by using the same procedure or method of
calculation. The exact amount of sampling error will differ from sample to sample. The sampling
errors are inevitable even if utmost care is taken in selecting the sample. However, it is possible
to minimise the sampling erfors by designing the survey appropriately. Sampling errors are of
two types: (i) biased sampling errors, and (ii) unbiased sampling errors.
Nonsampling Errors:
These nonsampling errors can occur in any survey, whether it be a complete ,
enumeration or sampling. Nonsampling errors include biases as well as mistakes.
These are not chance errors. Most of the factors causing bias in complete enumeration are
similar to the one described above under sampling errors. They also include careless definition
of population, a vague conception regarding the information sought, inefficient method
of interview and so on. Mistakes arise as a result ofimproper coding, computations and
processing. More specifially, nonsampling errors may arise because of one or more of
the following reasons:
i) Improper and ambiguous data specifications which are not consistent with the
census or survey objectives.
ii) Inappropriate sampling methods, incomplete quextionnaire and incorrect way of
interviewing.
iii) Personal bias of the investigators or informants.
iv) Lack of trained and qualified investigators.
v) Errors in compilation and tabulation.
This list is not exhaustive, but it indicates some of the main possible reasons.
(c) Dispersion and Skewness:
Solution: Dispersion: In statistics, the dispersion is the variation of a random variable
or its probability distribution. It is a measure of how far the data points lie from the central value.
To express this quantitatively, measures of dispersion are used in descriptive statistic.
Variance, Standard Deviation, and Interquartile range are the most commonly used measures
of dispersion. If the data values have a certain unit, due to the scale, the measures of dispersion
may also have the same units. Interdecile range, Range, mean difference, median absolute
deviation, average absolute deviation, and distance standard deviation are measures of
dispersion with units. In contrast, there are measures of dispersion which has no units, i.e
dimensionless. Variance, Coefficient of variation, Quartile coefficient of dispersion, and Relative
mean difference are measures of dispersion with no units. Dispersion in a system can be
originated from errors, such as instrumental and observational errors. Also, random variations in
the sample itself can cause variations. It is important to have a quantitative idea about the
variation in data before making other conclusions from the data set.
Skewness: In statistics, skewness is a measure of asymmetry of the probability distributions.
Skewness can be positive or negative, or in some cases nonexistent. It can also be considered
as a measure of offset from the normal distribution. If the skewness is positive, then the bulk of
the data points is centred to the left of the curve and the right tail is longer. If the skewness is
negative, the bulk of the data points is centred towards the right of the curve and the left tail is
rather long. If the skewness is zero, then the population is normally distributed. In a normal
distribution, that is when the curve is symmetric, the mean, median, and mode have the same
value. If the skewness is not zero, this property does not hold, and the mean, mode, and
median may have different values. Pearson’s first and second coefficients of skewness are
commonly used for determining the skewness of the distributions. Pearson’s first skewness
coffeicent = (mean – mode) / (standard deviation) Pearson’s second skewness coffeicent =
3(mean – mode) / (satndard deviation) In more sensitive cases, adjusted FisherPearson
standardized moment coefficient is used. G = {n / (n1)(n2)} ∑ni=1 ((y )/s)3
(d) Geometric mean and Harmonic mean:
Solution: Geometric mean is a kind of average of a set of numbers that is different from the
arithmetic average. The geometric mean is well defined only for sets of positive real numbers.
This is calculated by multiplying all the numbers (call the number of numbers n), and taking the
nth root of the total. A common example of where the geometric mean is the correct choice is
when averaging growth rates.
Formula:
Geometric Mean :
Geometric Mean = ((X1)(X2)(X3)........(XN))1/N
where
X = Individual score
N = Sample size (Number of scores)
Harmonic Mean: Probably the least understood, the harmonic mean is best used in
situations where extreme outliers exist in the population. The harmonic mean can be manually
calculated; however, most people will find it much easier to just use Excel. In Excel, the
harmonic mean can be calculated by using the HARMEAN() function. There are plenty of
online resources (see Wikipedia) that cover the mathematical derivation of the harmonic
mean; we are going to focus on when one should use it. If the population (or sample) has a
few data points that are much higher than the rest (outliers), the harmonic mean is the
appropriate average to use. Unlike the arithmetic mean, the harmonic mean gives less
significance to highvalue outliers–providing a truer picture of the average.
5. Write short notes on the following:
(a) Probability Sampling:
Solution: Probability sampling Methods:
In the case of probability sampling method, each and every item in the population has
a probability or chance of being included in the sample. Thus, in,this method every
member of the population has an equal chance of selection into the sample. Under this
probability sampling, there are various methods such as:
1 Simple random sampling
2 Systematic sampling
3 Stratified sampling
4 Cluster sampling
5 Area sampling
6 Multistage sampling
1 Simple Random Sampling: This method is also known as chance or lottery sampling
method. In this case each and every item in the population has an equal chance of
inclusion in the sample and each one of the possible samples has the same probability
of being selected. This is the most common method used when the population is a
homogeneous group. To identify the sample unit, normally, random numbers are
used.
2 Systematic Sampling: Under this method, population is arranged in alphabetical,
serial order etc. Then the sample units appearing at flxed intervals are selected.
Thus, you may select every 14th name on a list, every 10th house on the side of a
street and so on. Element of randomness is introduced into this method of sampling
by using random numbers to pick up the first unit with which to start. Thus, in this
method, the selection process starts by picking some random point in the list of .
population, and the'units are to be selected until the desired number is secured.
3 Stratified Sampling: This method is generally used when population is not a
homogeneous group. Under this method, population is divided into a number of
homogeneous subpopulations or strata. While doing this, care should be taken to
avoid overlapping. After stratification, the sample items are randomly selected from '
each stratum either on proportionate or equal basis.
4 Cluster Sampling: This method involves grouping the population into heterogeneous
groups called 'clusters' and then selecting a few of such groups (or the clusters) by
simple random sampling method. All the items in the selected clusters are studied for
accomplishing the survey work.
5 Area Sampling: This method is very close to cluster sampling. 1t is generally followed
when the total geographical area to be covered under the survey is spread very
widely. In this sampling method, the geographical area is first divided into anumber
of smaller areas and then a suitable number of these smaller areas are randomly
selected. All units of these selected small areas are then studied and examined for
accomplishing the survey work.
6 Multistage Sampling: This method is suitable for big surveys extending to a
considerably large geographical area or the population is heterogeneous,,For
instance, in a survey you want to select some families from all over the country.
Under this multistage sampling method, the first stage may be to randomly select a
few states. At the next stage, from each sample state.you can randomly select a few
districts. Then at the third stage you can select a few towns from each of the selected
districts. Finally, certain families may be randomly selected within the selected
towns. Thus, in this method stratification is done at four stages to constitute a final
sample. It may be noted that in this multistage sampling, each and every item of the
population has a chance of being selected but this chance need not be same for all
items.
(b) Statistical Derivatives:
Solution: when one or more numbers are being compared with another number, the
figure which is taken as the standard for comparison is known as the base. Which type
of base should be chosen would depend upon the situation. Any derivative by itself is
generally not meaningful for the analysis of a given problem. For instance, it is stated
that a company earned 18% return on its investment during the current year. What 
does this signify? You may ask whether or not this is a high rate of return. Any
meaningful use of derivatives requires comparison with some standard yardstick so that
their significance can be evaluated. The return of 18% can be either compared with last \
year's return or with another competing firm's return on investment, if they are
comparable. While the derivatives are used to compare different groups, it is a common practice
to reduce them to a common denominator and thereby the comparisons are made simple
and more meaningful. Suppose, two business firms were started with a capital of
Rs. 50,000 and Rs. 1,20,000 respectively. At the end of the year, the first business firm
made a profit of Rs. 20,000 and the second business firm earned a profit of Rs. 40,000.
It apparently shows that the second business has made double the profit of the first
business. But by reducing them to a common denominator of 100, it can be seen that
the first business has made a profit of 40% of the capital and the second business firm
mad6 a profit of 33% of the capital. The impression which you gather by looking at the
absolute numbers is reversed now. Thus, profit as a percentage of capital is really more
meaningful. The derivatives are also useful in estimating the unknown quantity. For instance,
the birth rate in a particular region is known and it can be assumed to be fairly constant over
a period of time. If you know the total number of births, at aspecific point of time, you
can estimate the population at that point of time. Thus, thederivatives are useful in the
estimation of unknown quantities, over and above simplifying the data and increasing
their comparability.
(c) Diagrams:
Solution: The following guideline should be
kept in mind while preparing diagrams :
1) A diagram is to be prepared on the graphic axes')(' axis and 'Y' axis. However, it is not
necessary to use a graph paper. While taking scales on these two axes, it must be
emured that the data is being presented in a meaningful manner. The scale on the two axes
should be clearly set up.
2) Whenever the data are to be presented on the 'Y' axis (vertical scale), the scale should start
from zero. Generally, the vertical scale is not broken.
3) A diagram must always have a concise and selfexplanatory title.
4) Colours and shades should be used to exhibit various components of a diagram and a key ,
be provided.
5) To make the diagram attractive, leave reasonable margin on all sides of the diagram. The
diagram should not be too small or too big.
6) If a number of diagrams are to be prepared, it is desirable to number them for the purpose
of reference.
TYPES OF DIAGRAMS:
Diagrams are generally classified on the basis of length, breadth and height. Broadly, diagrams
are classified as : 1) one dimensional diagram, 2) two dimensional diagram, and 3) three
dimensional diagram. Besides these diagrams, the data can also be presented in the form of
maps and pictographs.
(d) An Ideal Average:
Solution: An ideal average should possess the following characteristics:
1) Easy to understand and simple to compute: It should be easy to make out an average
and its computation should also be simple.
2) Rigidly defined: An average should be rigidly defined by a mathematical formula so
that the same answer is dived by different persons who try to compute if. It should not
depend on the personal prejudice or bias of a person computing it.
3) Based on all items in the data: For calculating an average, each and every item of the
data set should be included. Not a single item should be dropped, otherwise the vqhe of
the 'average may change.
4) Not to be unduly affected by extreme items: A single extreme value i.e., a maximum
value or a minimum value, can unduly affect the average. A too small item can reduce
the value of an average, and a too big item can inflate its value to a large extent. If the
average is chaniing with the inclusion or exclusion of an extreme item, them is not a
truly representative value of the data set.
5) Capable of further algebraic treatment: An average should be amenable to further
algebraic treatment. That should add to its utility. For example, if we are given the
averages of three data sets of similar type, it should be possible to obtain the combined
average of all those three data sets.
6) Sampling stability: The average should have the same 'sampling stability'. This means
that if we take different samples from the aggregate, the average of any sample should
approximated turn out to be the same as those of other samples.
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Answered By StudyChaCha Member
