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MB0024: Statistics forManagement[Assignment SET1 & SET2]

Name : P. Srinath

SMDUE ID : 520923307

Center : Mehbub College Campus, SecunderabadSubject Code : MB0024

Subject : Statistics for Management

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ASSIGNMENT MBA SEM I Subject Code:

MB0024 SET 1

1. Case 1

ABC Branch of XYZ Bank has decided to give 10 Lakh of loan

each on long term basis to only two of their customers

(accountholders), who are businessmen of the locality. About

20 businessmen had applied for loan in order to develop their

business further. In order to reject some of the applications (as

the fund was limited), the Bank decided that accountholder

who had maintained a minimum balance of 50000 INR would

only be considered for the loan. As a result, 10 applicationswere automatically rejected as they were not satisfying the

requirement of minimum balance. Now, the 10 applications

remained and it was found that monthly minimum balance in

all the cases were more than 50000 INR for the last 12 months.

Their account details of monthly minimum balance are given

below.

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You as an Assistant Branch Manager of the Bank are entrusted

the task of selecting two account holders for sanctioning theloans. How you will select the two individuals among the 10

applicants to give the loan using appropriate statistical

techniques? Give proper justification for your selection.

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Months Monthly Minimum Balance In INR

A/C

Holder

1

A/C

Holder

2

A/C

Holder

3

A/C

Holder

4

A/C

Holder

5

A/C

Holder

6

A/C

Holder

7

A/C

Holder

8

A/C

Holder

9

A/C

Holder

10

jan,2008 60000 56000 66000 86000 56000 59000 59000 52000 53000 56000

feb,2008 70000 76000 74000 96000 76000 96000 78000 73000 98000 76000

mar,2008 55000 110000 112000 190000 110000 120000 115000 112000 113000 120000

apr,2008 90000 89000 90000 98000 89000 97000 87000 93000 66000 89000

may,2008 56000 88000 84000 84000 88000 98000 90000 89000 87000 86000

jun,2008 80000 52000 57000 57000 52000 57000 55000 54000 59000 72000

jul,2008 82000 58000 96000 66000 58000 56000 86000 55000 98000 98000

aug,2008 79000 95000 55000 93000 95000 98000 99000 96000 59000 95000

sep,2008 51000 86000 76000 74000 86000 88000 89000 97000 87000 84000

oct,2008 95000 90000 95000 99000 90000 99000 95000 99000 95000 90000

nov,2008 82000 82000 87000 84000 82000 88000 87000 88000 86000 82000

dec,2008 83000 55000 56000 57000 55000 59000 59000 59000 52000 53000

Total 883000 937000 948000 1084000 937000 1015000 999000 967000 953000 1001000

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Use the weighted method for solution.

1st a/c holder Wx=883000, W=12

W.Avg.=883000/12

= 73583

2nd a/c holder Wx=937000, W=12

W.Avg.=937000/12

=78083.33

3rd a/c holder Wx=948000, W=12

W.Avg.=948000/12

= 790004th a/c holder Wx=1084000, W=12

W.Avg.=883000/12

= 90333.33

5th a/c holder Wx=937000, W=12

W.Avg.=937000/12

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Months Monthly Minimum Balance In INR

A/C

Holder

1

A/C

Holder

2

A/C

Holder

3

A/C

Holder 4

A/C

Holder

5

A/C

Holder 6

A/C

Holder

7

A/C

Holder

8

A/C

Holder

9

A/C

Holder

10

jan,2008 60000 56000 66000 86000 56000 59000 59000 52000 53000 56000

feb,2008 70000 76000 74000 96000 76000 96000 78000 73000 98000 76000

mar,2008 55000 110000 112000 190000 110000 120000 115000 112000 113000 120000

apr,2008 90000 89000 90000 98000 89000 97000 87000 93000 66000 89000

may,2008 56000 88000 84000 84000 88000 98000 90000 89000 87000 86000

jun,2008 80000 52000 57000 57000 52000 57000 55000 54000 59000 72000

jul,2008 82000 58000 96000 66000 58000 56000 86000 55000 98000 98000

aug,2008 79000 95000 55000 93000 95000 98000 99000 96000 59000 95000

sep,2008 51000 86000 76000 74000 86000 88000 89000 97000 87000 84000

oct,2008 95000 90000 95000 99000 90000 99000 95000 99000 95000 90000

nov,2008 82000 82000 87000 84000 82000 88000 87000 88000 86000 82000

dec,2008 83000 55000 56000 57000 55000 59000 59000 59000 52000 53000

Total 883000 937000 948000 1084000 937000 1015000 999000 967000 953000 1001000

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= 78083.33


W.Avg.=1015000/12

= 84583.33


W.Avg.=999000/12

= 83250


W.Avg.=967000/12

= 80583.333


W.Avg.=953000/12

= 79416.667

10th a/c holder Wx=1001000, W=12W.Avg.=1001000/12

= 83416.667

Table - B

A/c Holder Monthly

Avg Balance

1st a/c holder 73583

2nd a/c holder 78083

3rd a/c holder 790004th a/c holder 90333

5th a/c holder 78083





10th a/c

holder

83416

According to case ABC Branch of XYZ have decided to give 10

Lack of loan each on long term basis to only two of their customer or

accountholder, about 20 businessmen had applied for loan in order to

develop their business further. In order to reject some of the

application as (the fund was limited); the Bank decided that

accountholder who had maintained a minimum balance of 50000 INR

would only be considered for the loan. As a result, 10 applications were

automatically rejected as they were not satisfying the requirement of

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minimum balance. Now, the 10 applications remained and it was found

that monthly minimum balance in all the cases were more than 50000

INR for the last 12 month. If I were assistant manager XYZ Bank, I

would select from remained 10 applications choose 4th and 6th A/c

Holder for give loan .This is because they are only eligible who are

maintaining maximum balance more than remains Eight A/c Holders.

Only 4th and 6th A/c Holder has maximum average than remains eight

A/c Holder. So, it should be consider of them for give loan.

ASSIGNMENT MBA SEM I Subject Code:

MB0024 SET 2

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

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 the characteristics of the

population.

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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 context of survey sampling it most often refers

to a questionnaire used to measure the characteristics and/or attitudes

of people. The purpose of sampling is to reduce the cost and/or the

amount of work that it would take to survey the entire target

population. A survey that measures the entire target population is

called a census.

Sample survey can also be described as the technique used to

study about a population with 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 certain statistical

principles called sampling designs (this is for guaranteeing that a

representative sample is obtained for the study). Once the sampledecided 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 strict rules to follow, and the researcher must

rely on logic and judgment. The population is defined in keeping with

the objectives of the study.

Sometimes, the entire population will be sufficiently small, and

the researcher can include the entire population in the study. This type

of research is called a census study because data 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 probability samples, each member of the population

has a known non-zero probability of being selected. Probability

methods include random sampling, systematic sampling, and

stratified sampling. In non-probability sampling, members areselected from the population in some non-random manner. These

include convenience sampling, judgment sampling, quota

sampling, and snowball sampling. The advantage of probability

sampling is that sampling error can be calculated. Sampling error is

the degree to which a sample might differ from the population. When

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inferring to the population, results are reported plus or minus the

sampling error. In non-probability sampling, the degree to which the

sample differs from the population remains unknown.

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 very large 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 Nth name selection technique. After the

required sample size has been calculated, every Nth record is selected

from a list of population members. As long as the list does not contain

any hidden order, this sampling method is as good as the random

sampling method. Its only advantage over the random samplingtechnique is simplicity. 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 population that share at least one common

characteristic. Examples of stratums might be males and females, or

managers and non-managers. The researcher first identifies the

relevant stratums and their actual representation in the population.

Random sampling is then used to select a sufficientnumber of subjects

from each stratum. "Sufficient" refers to a sample size large enough for

us to be reasonably confident that the stratum represents the

population. Stratified sampling is often used when one or more of the

stratums in the population have a low incidence relative to the other

stratums.

Non Probability Methods

1. Convenience sampling is used in exploratory research

where the researcher is interested 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 selects the sample based on judgment. This is usually

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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 this method, the

researcher must be confident that the chosen sample is truly

representative of the entire population.

Quota sampling is the non-probability equivalent of stratified

sampling. Like stratified sampling, the researcher first identifies the

stratums and their proportions as they are represented in the

population. Then convenience or judgment sampling is used to select

the required number of subjects from each stratum. This differs from

stratified sampling, where the stratums are filled by random sampling.

Snowball sampling is a special non-probability method used

when the desired sample characteristic is rare. It may be extremely

difficult or cost prohibitive to locate respondents in these situations.

Snowball sampling relies on referrals from initial subjects to generateadditional subjects. While this technique can dramatically lower search

costs, it comes at the expense of introducing bias because the

technique itself reduces the likelihood that the sample will represent a

good cross section from the population.

2. What is the different between correlation and regression?What do you understand by Rank Correlation? When we userank correlation and when we use Pearsonian CorrelationCoefficient? Fit a linear regression line in the following data X 12 15 18 20 27 34 28 48 Y 123 150 158 170 180

184 176 130

CorrelationWhen two or more variables move in sympathy with other, then

they are said to be correlated. If both variables move in the samedirection then they are said to be positively correlated. If the variablesmove in opposite direction then they are said to be negativelycorrelated. If they move haphazardly then there is no correlationbetween them. Correlation analysis deals with 1) Measuring the

relationship between variables. 2) Testing the relationship for itssignificance. 3) Giving confidence interval for population correlationmeasure.

RegressionRegression is defined as, the measure of the average

relationship between two or more variables in terms of the originalunits of the data. Correlation analysis attempts to study therelationship between the two variables x and y. Regression analysis

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attempts to predict the average x for a given y. In Regression it isattempted to quantify the dependence of one variable on the other.The dependence is expressed in the form of the equations.

Difference between correlation and regressionCorrelation and linear regression are not the same. Consider

these differences: Correlation quantifies the degree to which two variables arerelated. Correlation does not find a best-fit line (that is regression). Yousimply are computing a correlation coefficient (r) that tells you howmuch one variable tends to change when the other one does.

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

With correlation, it doesn't matter which of the two variablesyou call "X" and which you call "Y". You'll get the same correlation

coefficient if you swap the two. With linear regression, the decision ofwhich variable you call "X" and which you call "Y" matters a lot, asyou'll get a different best-fit line if you swap the two. The line that bestpredicts Y from X is not the same as the line that predicts X from Y.

Correlation is almost always used when you measure bothvariables. It rarely is appropriate when one variable is something youexperimentally manipulate. With linear regression, the X variable isoften something you experimental manipulate (time, concentration...)and the Y variable is something you measure.

The correlation answers the STRENGTH of linear associationbetween paired variables, say X and Y. On the other hand, the

regression tells us the FORM of linear association that best predicts Yfrom the values of X.

(2a) Correlation is calculated whenever:* Both X and Y is measured in each subject and quantifies how

much they are linearly associated.* In particular the Pearson's product moment correlation

coefficient is used when the assumption of both X and Y are sampledfrom normally-distributed populations are satisfied

* or the Spearman's moment order correlation coefficient is usedif the assumption of normality is not satisfied.

* Correlation is not used when the variables are manipulated, for

example, in experiments.(2b) Linear regression is used whenever:* at least one of the independent variables (Xi's) is to predict the

dependent variable Y. Note: Some of the Xi's are dummy variables, i.e.Xi = 0 or 1, which are used to code some nominal variables.

* if one manipulates the X variable, e.g. in an experiment.

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

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

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One has to assign the same rank to each of the equal values. It isan 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.

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

Linear Regression Line for the above data can be plotted as :

Total Numbers : 8

Slope (b) :0.16701Y-Intercept (a) : 154.65 Regression Equation : 154.66 +

0.17x

3. What do you mean by business forecasting? What are the

different methods of business forecasting? Describe the

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effectiveness of time-series analysis as a mode of business

forecasting. Describe the method of moving averages.

Business forecasting refers to the analysis of past and present

economic conditions with the object of drawing inferences about

probable future business conditions. To forecast the future, variousdata, information and facts concerning to economic condition of

business for past and present are analyzed. The process of forecasting

includes the use of statistical and mathematical methods for long term,

short term, medium term or any specific term.

Following are the main methods of business forecasting:-

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 future

conditions, so they are also known as Business Barometers or

Economic Barometers. With the help of these business barometers

the trend of fluctuations in business conditions are made known and by

forecasting a decision can be taken relating to the problem. The

construction of business barometer consists of gross national product,

wholesale prices, consumer prices, industrial production, stock prices,

bank deposits etc. These quantities may be converted into relatives on

a certain base. The relatives so obtained may be weighted and theiraverage 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 index of business activity which refers to

weighted or composite indices of individual index business

activities. With the help of general index of business activity

long term trend and cyclical fluctuations in the economic

activities of a country are measured but in some specificcases the long term trends can be different from general

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

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business activity and these are constructed to measure 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 individual firm of an industry.

Time Series Analysis is also used for the purpose of making

business forecasting. The forecasting through time series analysis is

possible only when the business data of various years are available

which reflects a definite trend and seasonal variation.

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 aboutthe fluctuations of the figures, ii) Knowledge about the course of

events relating to the problem under consideration.

Regression Analysis

The regression approach offers many valuable contributions to

the solution of the forecasting problem. It is the means by which we

select from among the many possible relationships between variables

in a complex economy those which will be useful for forecasting.

Regression relationship may involve one predicted or dependent and

one independent variables simple regression, or it may involve

relationships between the variable to be forecast and several

independent variables under multiple regressions. Statistical

techniques to estimate the regression equations are often fairly

complex and time-consuming but there are many computer programs

now available that estimate simple and multiple regressions quickly

Modern Econometric Methods

Econometric techniques, which originated in the eighteenth

century, have recently gained in popularity for forecasting. The term

econometrics refers to the application of mathematical economictheory and statistical procedures to economic data in order to verify

economic theorems. Models take the form of a set of simultaneous

equations. The value of the constants in such equations are supplied

by a study of statistical time series

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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 found extremely useful in

short-term forecasting of inventories and sales.

Choice of a Method of Forecasting

The selection of an appropriate method depends on many factors

the context of the forecast, 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 the company,

and the time available for making the analysis.

Effectiveness of Time Series Analysis:

Time series analysis is also used for the purpose of makingbusiness forecasting. The forecasting through time series analysis is

possible only when the business data of various years are available

which reflects a definite trend and seasonal variation. By time series

analysis 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 mathematical model.

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 method calculates 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. The aim ofthis 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 to understand 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 the chart

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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 in his own

good.

We come across different types of moving averages, which are

based on the way these averages are computed. Still, the basis of

interpretation of averages is similar across all the types. The

computation of each type set itself different from other in terms of

weightage it lays 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. The historical closing prices over certain time

period are added. This sum is divided by the number of instances usedin summation. For example, if the moving average is calculated for 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 the trader 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 equal weightage. The difference between simple

average and linear average method is the weightage that is provided

to the position of the prices in the latter. Lets consider the above

example. In linear average method, the closing price on the 15th day is

multiplied by 15, the 14th day closing price by 14 and so on till the 1st

day closing price by 1. These results are totaled and then divided by

15.

The exponential moving average method shares some similarity

with the linear moving average method. This method lays emphasis on

the smoothing factor, there by weighing recent data with higher points

than the previous data. This method is more receptive to any market

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.

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4. What is definition of Statistics? What are the different

characteristics of statistics? What are the different functions

of Statistics? What are the limitations of Statistics?

According to Croxton and Cowden, Statistics is the science of

collection, presentation, analysis and interpretation of numerical data. Thus, Statistics contains the tools and techniques required for the

collection, presentation, analysis and interpretation of data. This

definition is precise and comprehensive.

Characteristic of Statistics:

a. 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 yield of paddy is the result of factors such as

fertility of soil, amount of rainfall, quality of seed used, 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) with required degree of accuracy.

The degree of accuracy differs from purpose to purpose. In measuring

the length of screws, an accuracy upto a millimeter may be required,

whereas, while measuring the heights of students in a class, accuracyupto a centimeter is enough.

e. Statistics are collected in a systematic manner: The facts should

be collected according to 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 purpose for collecting facts. E.g.: Movement of wholesale

price of a commodity.

g. Statistics are placed in relation to each other: The facts must be

placed in such a way that 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 data

2. It makes comparison easier

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3. It brings out trends and tendencies in the data

4. 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 withquantitative data.

2. Statistics does not deal with individual fact: Statistical methods

can be applied only to aggregate to facts.

3. Statistical inferences (conclusions) are not exact: Statistical

inferences are true only on 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: Onlystatisticians can handle statistics properly.

5. What are the different stages of planning a statistical survey?

Describe the various 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 to obtain certain estimates or to establish a theory or to verify anexisting statement to find relationship between characteristics etc.

3. The scope of investigation has to be made clear. It refers to area to becovered, identification of units to be studied, nature of characteristics to beobserved, accuracy of measurements, analytical methods, time, cost andother resources required.

4. Whether to use data collected from primary or secondary sourceshould be determined in advance.

5. The organization of investigation is the final step in the process. Itencompasses the determination of number of investigators required, their

training, supervision work needed, funds required etc.

Collection of primary data can be done by anyone of the followingmethods.

i. Direct personal observation

ii. Indirect oral interview

iii. Information through agencies

iv. Information through mailed questionnaires

v. Information through schedule filled by investigators

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6. What are the functions of classification? What are the

requisites of a good classification? 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 comprehensible

c. It facilitates comparison of characteristics

d. It renders the data ready for any statistical analysis

Requisites of good classification are:

i. Unambiguous: It should not lead to any confusion

ii. Exhaustive: every unit should be allotted to one and only one

class

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 investigation

vii. 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:-

a) To simplify complex data

b) To highlight important characteristics

c) To present data in minimum space

d) To facilitate comparison

e) To bring out trends and tendencies

f) To facilitate further analysis

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