MB0024+Assignment+Set2

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ASSIGNMENT STATISTICS FOR MANAGEMENT CODE MB0024SET-2

1. What do you mean by sample survey? What are the different sampling methods?Briefly describe them.

Ans:

Sample is a finite subset of a population drawn from it to estimate the characteristics of the population. Sampling is a tool which enables us to draw conclusions about thecharacteristics of the population.

Survey sampling describes the process of selecting a sample of elements from a target population in order to conduct a survey.

A survey may refer to many different types or techniques of observation, but in the contextof survey sampling it most often refers to a questionnaire used to measure thecharacteristics and/or attitudes of people. The purpose of sampling is to reduce the costand/or the amount of work that it would take to survey the entire target population. Asurvey that measures the entire target population is called a census.

Sample survey can also be described as the technique used to study about a populationwith the help of a sample. Population is the totality all objects about which the study is

proposed. Sample is only a portion of this population, which is selected using certainstatistical principles called sampling designs (this is for guaranteeing that a representativesample is obtained for the study). Once the sample decided information will be collected

from this sample, which process is called sample survey.

It is incumbent on the researcher to clearly define the target population. There are no strictrules to follow, and the researcher must rely on logic and judgment. The population isdefined in keeping with the objectives of the study.

Sometimes, the entire population will be sufficiently small, and the researcher can includethe entire population in the study. This type of research is called a census study becausedata is gathered on every member of the population.

Usually, the population is too large for the researcher to attempt to survey all of its

members. A small, but carefully chosen sample can be used to represent the population.The sample reflects the characteristics of the population from which it is drawn.

Sampling methods are classified as either probability or non-probability . In probabilitysamples, each member of the population has a known non-zero probability of beingselected. Probability methods include random sampling, systematic sampling, andstratified sampling . In non-probability sampling, members are selected from the

population in some non-random manner. These include convenience sampling, judgmentsampling, quota sampling, and snowball sampling. The advantage of probabilitysampling is that sampling error can be calculated. Sampling error is the degree to which asample might differ from the population. When inferring to the population, results arereported plus or minus the sampling error. In non-probability sampling, the degree towhich the sample differs from the population remains unknown.

ASSIGNMENT STATISTICS FOR MANAGEMENT CODE MB0024 SET 2 1


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Probability Sampling Methods

1. Random sampling is the purest form of probability sampling. Each member of the population has an equal and known chance of being selected. When there are verylarge populations, it is often difficult or impossible to identify every member of the

population, so the pool of available subjects becomes biased.2. Systematic sampling is often used instead of random sampling. It is also called an

N th name selection technique. After the required sample size has been calculated,every N th record is selected from a list of population members. As long as the listdoes not contain any hidden order, this sampling method is as good as the randomsampling method. Its only advantage over the random sampling technique issimplicity. Systematic sampling is frequently used to select a specified number of records from a computer file.

3. Stratified sampling is commonly used probability method that is superior to random

sampling because it reduces sampling error. A stratum is a subset of the populationthat share at least one common characteristic. Examples of stratums might be malesand females, or managers and non-managers. The researcher first identifies therelevant stratums and their actual representation in the population. Random samplingis then used to select a sufficient number of subjects from each stratum. " Sufficient "refers to a sample size large enough for us to be reasonably confident that the stratumrepresents the population.

Stratified sampling is often used when one or more of the stratums in the population have alow incidence relative to the other stratums.

Non Probability Methods

1. Convenience sampling is used in exploratory research where the researcher isinterested in getting an inexpensive approximation of the truth. As the name implies,the sample is selected because they are convenient. This non-probability method isoften used during preliminary research efforts to get a gross estimate of the results,without incurring the cost or time required to select a random sample.

2. Judgment sampling is a common non-probability method. The researcher selectsthe sample based on judgment. This is usually extension of convenience sampling.For example, a researcher may decide to draw the entire sample from one

"representative" city, even though the population includes all cities. When using thismethod, the researcher must be confident that the chosen sample is trulyrepresentative of the entire population.

3. Quota sampling is the non-probability equivalent of stratified sampling. Likestratified sampling, the researcher first identifies the stratums and their proportions asthey are represented in the population. Then convenience or judgment sampling isused to select the required number of subjects from each stratum. This differs fromstratified sampling, where the stratums are filled by random sampling.

4. Snowball sampling is a special non-probability method used when the desiredsample characteristic is rare. It may be extremely difficult or cost prohibitive tolocate respondents in these situations. Snowball sampling relies on referrals frominitial subjects to generate additional subjects. While this technique can dramatically



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lower search costs, it comes at the expense of introducing bias because the techniqueitself reduces the likelihood that the sample will represent a good cross section fromthe population.

2. What is the difference between correlation and regression? What do youunderstand by Rank Correlation? When we use rank correlation and when weuse Pearsonian Correlation Coefficient? Fit a linear regression line in thefollowing data

X 12 15 18 20 27 34 28 48Y 123 150 158 170 180 184 176 130

Correlation

When two or more variables move in sympathy with other, then they are said to becorrelated. If both variables move in the same direction then they are said to be positivelycorrelated. If the variables move in opposite direction then they are said to be negativelycorrelated. If they move haphazardly then there is no correlation between them.Correlation analysis deals with1) Measuring the relationship between variables.2) Testing the relationship for its significance.3) Giving confidence interval for population correlation measure.

RegressionRegression is defined as, the measure of the average relationship between two or morevariables in terms of the original units of the data. Correlation analysis attempts to studythe relationship between the two variables x and y. Regression analysis attempts to predictthe average x for a given y. In Regression it is attempted to quantify the dependence of onevariable on the other. The dependence is expressed in the form of the equations.

Difference between correlation and regression

Correlation and linear regression are not the same. Consider these differences: Correlation quantifies the degree to which two variables are related. Correlation does

not find a best-fit line (that is regression). You simply are computing a correlationcoefficient (r) that tells you how much one variable tends to change when the other one does.

With correlation you don't have to think about cause and effect. You simply quantifyhow well two variables relate to each other. With regression, you do have to think about cause and effect as the regression line is determined as the best way to predict Yfrom X.

With correlation, it doesn't matter which of the two variables you call "X" and whichyou call "Y". You'll get the same correlation coefficient if you swap the two. Withlinear regression, the decision of which variable you call "X" and which you call "Y"matters a lot, as you'll get a different best-fit line if you swap the two. The line that



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best predicts Y from X is not the same as the line that predicts X from Y.

Correlation is almost always used when you measure both variables. It rarely isappropriate when one variable is something you experimentally manipulate. Withlinear regression, the X variable is often something you experimental manipulate(time, concentration...) and the Y variable is something you measure.

The correlation answers the STRENGTH of linear association between pairedvariables, say X and Y. On the other hand, the regression tells us the FORM of linear association that best predicts Y from the values of X.

(2a) Correlation is calculated whenever:

- Both X and Y is measured in each subject and quantifies how much they arelinearly associated.

- In particular the Pearson's product moment correlation coefficient is used when the

assumption of both X and Y are sampled from normally-distributed populations aresatisfied

- Or the Spearman's moment order correlation coefficient is used if the assumption of normality is not satisfied.

- Correlation is not used when the variables are manipulated, for example, inexperiments.

(2b) linear regression is used whenever:

- At least one of the independent variables (Xi's) is to predict the dependent variableY. Note: Some of the Xi's are dummy variables, i.e. Xi = 0 or 1, which are used tocode some nominal variables.

- If one manipulates the X variable, e.g. in an experiment.

Linear regression are not symmetric in terms of X and Y. That is interchanging X andY will give a different regression model (i.e. X in terms of Y) against the original Y interms of X.On the other hand, if you interchange variables X and Y in the calculation of correlation coefficient you will get the same value of this correlation coefficient.

The "best" linear regression model is obtained by selecting the variables (X's) with atleast strong correlation to Y, i.e. >= 0.80 or


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In principle, is simply a special case of the Pearson product-moment coefficient in whichtwo sets of data X i and Y i are converted to rankings xi and yi before calculating thecoefficient. In practice, however, a simpler procedure is normally used to calculate . Theraw scores are converted to ranks, and the differences d i, between the ranks of eachobservation on the two variables are calculated.

If there are no tied ranks, then is given by:

Where:d i = xi yi = the difference between the ranks of corresponding values X i and Y i, andn = the number of values in each data set (same for both sets).If tied ranks exist, classic Pearson's correlation coefficient between ranks has to be usedinstead of this formula.

One has to assign the same rank to each of the equal values. It is an average of their positions in the ascending order of the values.

Conditions under which P.E can be used :

1. Samples should be drawn from a normal population.

2. The value of r must be determined from sample values.

3. Samples must have been selected at random.



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3. What do you mean by business forecasting? What are the different methods of business forecasting? Describe the effectiveness of time-series analysis as a modeof business forecasting. Describe the method of moving averages.

Business forecasting refers to the analysis of past and present economic conditions with theobject of drawing inferences about probable future business conditions. To forecast the

future, various data, information and facts concerning to economic condition of businessfor past and present are analyzed. The process of forecasting includes the use of statisticaland mathematical methods for long term, short term, medium term or any specific term.

Following are the main methods of business forecasting:-

1. Business Barometers

Business indices are constructed to study and analyze the business activities on the basis of which future conditions are predetermined. As business indices are the indicators of futureconditions, so they are also known as Business Barometers or Economic Barometers .With the help of these business barometers the trend of fluctuations in business conditionsare made known and by forecasting a decision can be taken relating to the problem. Theconstruction of business barometer consists of gross national product, wholesale prices,consumer prices, industrial production, stock prices, bank deposits etc. These quantitiesmay be converted into relatives on a certain base. The relatives so obtained may beweighted and their average be computed. The index thus arrived at in the business

barometer.

The business barometers are of three types:

i. Barometers relating to general business activities : it is also known as general indexof business activity which refers to weighted or composite indices of individualindex business activities. With the help of general index of business activity longterm trend and cyclical fluctuations in the economic activities of a country are



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measured but in some specific cases the long term trends can be different fromgeneral trends. These types of index help in formation of country economic

policies.ii. Business barometers for specific business or industry : These barometers are used as

the supplement of general index of business activity and these are constructed tomeasure the future variations in a specific business or industry.

iii. Business barometers concerning to individual business firm : This type of barometer is constructed to measure the expected variations in a specific individualfirm of an industry.

2. Time Series Analysis is also used for the purpose of making business foreca sting. Theforecasting through time series analysis is possible only when the business data of various years are available which reflects a definite trend and seasonal variation.

3. Extrapolation is the simplest method of business forecasting. By extrapolation, a businessman finds out the possible trend of demand of his goods and about their future

price trends also. The accuracy of extrapolation depends on two factors:i) Knowledge about the fluctuations of the figures,ii) Knowledge about the course of events relating to the problem under consideration.

4. Regression AnalysisThe regression approach offers many valuable contributions to the solution of theforecasting problem. It is the means by which we select from among the many possiblerelationships between variables in a complex economy those which will be useful for forecasting. Regression relationship may involve one predicted or dependent and oneindependent variables simple regression, or it may involve relationships between thevariable to be forecast and several independent variables under multiple regressions.

Statistical techniques to estimate the regression equations are often fairly complex andtime-consuming but there are many computer programs now available that estimate simpleand multiple regressions quickly.

5. Modern Econometric MethodsEconometric techniques, which originated in the eighteenth century, have recently gainedin popularity for forecasting. The term econometrics refers to the application of mathematical economic theory and statistical procedures to economic data in order toverify economic theorems. Models take the form of a set of simultaneous equations. Thevalue of the constants in such equations is supplied by a study of statistical time series.

6. Exponential Smoothing Method

This method is regarded as the best method of business forecasting as compared to other methods. Exponential smoothing is a special kind of weighted average and is foundextremely useful in short-term forecasting of inventories and sales.

7. Choice of a Method of ForecastingThe selection of an appropriate method depends on many factors the context of theforecast, the relevance and availability of historical data, the degree of accuracy desired,the time period for which forecasts are required, the cost benefit of the forecast to thecompany, and the time available for making the analysis.

Effectiveness of Time Series Analysis:



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Time series analysis is also used for the purpose of making business forecasting. Theforecasting through time series analysis is possible only when the business data of variousyears are available which reflects a definite trend and seasonal variation. By time seriesanalysis the long term trend, secular trend, seasonal and cyclical variations are ascertained,analyzed and separated from the data of various years.

Merits:

i) It is an easy method of forecasting.ii) By this method a comparative study of variations can be made.iii) Reliable results of forecasting are obtained as this method is based on mathematicalmodel.

Method of Moving Averages

One of the most simple and popular technical analysis indicators is the moving averages

method. This method is known for its flexibility and user-friendliness. This methodcalculates the average price of the currency or stock over a period of time.

The term moving average means that the average moves or follows a certain trend. Theaim of this tool is to indicate to the trader if there is a beginning of any new trend or if there is a signal of end to the old trend. Traders use this method, as it is relatively easy tounderstand the direction of the trends with the help of moving averages.

Moving average method is supposed to be the simplest one, as it helps to understand thechart patterns in an easier way. Since the currencys average price is considered, the

prices volatile movements are evened. This method rules out the daily fluctuation in the

prices and helps the trader to go with the right trend, thus ensuring that the trader trades inhis own good.

We come across different types of moving averages, which are based on the way theseaverages are computed. Still, the basis of interpretation of averages is similar across all thetypes. The computation of each type set itself different from other in terms of weightage itlays on the prices of the currencies. Current price trend is always given a higher weightage.The three basic types of moving averages are viz. simple, linear and exponential.

A simple moving average is the simplest way to calculate the moving price averages. Thehistorical closing prices over certain time period are added. This sum is divided by the

number of instances used in summation. For example, if the moving average is calculatedfor 15 days, the past 15 historical closing prices are summed up and then divided by 15.This method is effective when the number of prices considered is more, thus enabling thetrader to understand the trend and its future direction more effectively.

A linear moving average is the less used one out of all. But it solves the problem of equalweightage. The difference between simple average and linear average method is theweightage that is provided to the position of the prices in the latter. Lets consider theabove example. In linear average method, the closing price on the15th day is multiplied by 15, the 14th day closing price by 14 and so on till the 1 st dayclosing price by 1. These results are totalled and then divided by 15.

The exponential moving average method shares some similarity with the linear movingaverage method. This method lays emphasis on the smoothing factor, there by weighing



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recent data with higher points than the previous data. This method is more receptive to anymarket news than the simple average method. Hence this makes exponential method more

popular among traders.

Moving averages methods help to identify the correct trends and their respective levels of resistance.

4. What is definition of Statistics? What are the different characteristics of statistics? What are the different functions of Statistics? What are the limitationsof Statistics?

According to Croxton and Cowden, Statistics is the science of collection, presentation,analysis and interpretation of numerical data. Thus, Statistics contains the tools andtechniques required for the collection, presentation, analysis and interpretation of data.This definition is precise and comprehensive.

Characteristic of Statisticsa. Statistics Deals with aggregate of facts: Single figure cannot be analyzed.

b. Statistics are affected to a marked extent by multiplicity of causes: The statistics of yieldof paddy is the result of factors such as fertility of soil, amount of rainfall, quality of seedused, quality and quantity of fertilizer used, etc.c. Statistics are numerically expressed: Only numerical facts can be statistically analyzed.Therefore, facts as price decreases with increasing production cannot be called statistics.d. Statistics are enumerated or estimated according to reasonable standards of accuracy:The facts should be enumerated (collected from the field) or estimated (computed) withrequired degree of accuracy. The degree of accuracy differs from purpose to purpose. In

measuring the length of screws, an accuracy upto a millimetre may be required, whereas,while measuring the heights of students in a class, accuracy upto a centimetre is enough.e. Statistics are collected in a systematic manner: The facts should be collected accordingto planned and scientific methods. Otherwise, they are likely to be wrong and misleading.f. Statistics are collected for a pre-determined purpose: There must be a definite purposefor collecting facts.Eg. Movement of wholesale price of a commodityg. Statistics are placed in relation to each other: The facts must be placed in such a waythat a comparative and analytical study becomes possible.Thus, only related facts which are arranged in logical order can be called statistics.

Functions of Statistics

1. It simplifies mass data2. It makes comparison easier 3. It brings out trends and tendencies in the data4. It brings out hidden relations between variables.5. Decision making process becomes easier.

Major limitations of Statistics are :

1. Statistics does not deal with qualitative data. It deals only with quantitative data.

2. Statistics does not deal with individual fact: Statistical methods can be applied only toaggregate to facts.

3. Statistical inferences (conclusions) are not exact: Statistical inferences are true only on



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an average. They are probabilistic statements.4. Statistics can be misused and misinterpreted: Increasing misuse of Statistics has led to

increasing distrust in statistics.5. Common men cannot handle Statistics properly: Only statisticians can handle statistics

properly.

5. What are the different stages of planning a statistical survey? Describe thevarious methods for collecting data in a statistical survey.

The planning stage consists of the following sequence of activities.

1. Nature of the problem to be investigated should be clearly defined in an un-ambiguous manner.

2. Objectives of investigation should be stated at the outset. Objectives could be toobtain certain estimates or to establish a theory or to verify a existing statement to find

relationship between characteristics etc.3. The scope of investigation has to be made clear. It refers to area to be covered,identification of units to be studied, nature of characteristics to be observed, accuracyof measurements, analytical methods, time, cost and other resources required.

4. Whether to use data collected from primary or secondary source should be determinedin advance.

5. The organization of investigation is the final step in the process. It encompasses thedetermination of number of investigators required, their training, supervision work needed, funds required etc.

Collection of primary data can be done by anyone of the following methods.

i. Direct personal observationii. Indirect oral interviewiii. Information through agenciesiv. Information through mailed questionnaires

iv. Information through schedule filled by investigators

6. What are the functions of classification? What are the requisites of a goodclassification? What is Table and describe the usefulness of a table in mode of

presentation of data?

The functions of classification are:

a. It reduce the bulk data b. It simplifies the data and makes the data more comprehensiblec. It facilitates comparison of characteristicsd. It renders the data ready for any statistical analysis

Requisites of good classification are:

i. Unambiguous: It should not lead to any confusionii. Exhaustive: every unit should be allotted to one and only one class



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iii. Mutually exclusive: There should not be any overlapping.iv. Flexibility: It should be capable of being adjusted to changing situation.v. Suitability: It should be suitable to objectives of survey.

vi. Stability: It should remain stable throughout the investigationvii. Homogeneity: Similar units are placed in the same class.

viii. Revealing: Should bring out essential features of the collected data.

Table is nothing but logical listing of related data in rows and columns.

Objectives of tabulation are:-

i. To simplify complex dataii. To highlight important characteristicsiii. To present data in minimum spaceiv. To facilitate comparisonv. To bring out trends and tendenciesvi. To facilitate further analysis

Parts of a Table.

i. Table number: Identifies the table for reference.

ii. Title: It indicates the scope and the nature of contents in concise form.

iii. Captions: They are the headings and subheading of columns.

iv. Stubs: They are the headings and subheadings of rows.

v. Body of the table: It contains numerical information

vi.Ruling and Spacing: They separate columns and rows. However totals are separated from

main body by thick lines.

vii. Head Note: It is given below the title of the table to indicate the units of measurement

of

the data and enclosed in brackets.

viii. Source Note: It indicates the source from which data is taken

Tables are classified on the basis of

a. Purpose of investigation : Consists of two types.

i. General purpose table or also known as reference table . It facilitates easy reference to

the collected data. They are formed without specific objective, but can be used for any



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