mb 0024 assingment set1 set2

8/9/2019 MB 0024 Assingment Set1 Set2

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ASSIGNMENTS - MBA - I SEMESTER

MB0024

SET 1

Statistics For Management

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 arebusinessmen of the locality. About 20 businessmen had applied for loan in

order to develop their business further. In order to reject some of theapplications (as the fund was limited), the Bank decided that accountholder

who had maintained a minimum balance of 50000 INR would only beconsidered for the loan. As a result, 10 applications were 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.

Months

Monthly Minimum Balance in INR

A/CHolder 1

A/CHolder 2

A/CHolder3

A/CHolder4

A/CHolder 5

A/CHolder 6

A/CHolder7

A/CHolder8

A/CHolder9

A/CHolder10

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

Sept,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


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You as an Assistant Branch Manager of the Bank are entrusted the task ofselecting two account holders for sanctioning the loans. How you will select

the two individuals among the 10 applicants to give the loan usingappropriate statistical techniques? Give proper justification for your

selection.

Ans.

We can take the probabilistic method of estimation of their ability to maintainaverage balance and more.

1. Authentic mean of each A/C holder=

Am= x/n

2.Standard dividend of the each monthly balance from the mean

(x-x-)2-1

3.Calculate z variable (normal distribution)

For each a/c holders z = required monthly balance x-

Standard distribution x n

4.Convert z variable into probabilities and select two a/c holder with the highest

probability


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So by these assumptions and justifications ,we can give loan to the a/c holders withhighest probability. They are

1.Customer No. IV with probability of 84and

2.Customer No. VI with probability of 77


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ASSIGNMENTS - MBA - I SEMESTER

MB0024

SET 2

Statistics For Management

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

Ans .

Sampling is that part ofstatistical practice concerned with the selection of individualobservations intended to yield some knowledge about a population of concern,

especially for the purposes ofstatistical inference.

Each observation measures one or more properties (weight, location, etc.) of anobservable entity enumerated to distinguish objects or individuals. Survey weightsoften need to be applied to the data to adjust for the sample design. Results fromprobability theory and statistical theory are employed to guide practice.

Sampling Methods

Sampling methods are classified as eitherprobabilityor non probability. Inprobability samples, each member of the population has a known non-zeroprobability of being selected. Probability methods include random sampling,

systematic sampling, and stratified sampling. In non probability sampling, membersare selected from the population in some nonrandom manner. These includeconvenience sampling, judgment sampling, quota sampling, and snowball sampling.The advantage of probability sampling is that sampling error can be calculated.

Random sampling is the purest form of probability sampling. Each memberof the population has an equal and known chance of being selected. When there arevery large populations, it is often difficult or impossible to identify every member ofthe population, so the pool of available subjects becomes biased.

Systematic sampling is often used instead of random sampling. It is alsocalled 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 longas the list does not contain any hidden order, this sampling method is as good as therandom sampling method. Its only advantage over the random sampling technique issimplicity. Systematic sampling is frequently used to select a specified number ofrecords from a computer file.

Stratified sampling is commonly used probability method that is superior torandom sampling because it reduces sampling error. A stratum is a subset of thepopulation that share at least one common characteristic. Examples of stratums
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might be males and females, or managers and non-managers. The researcher firstidentifies the relevant stratums and their actual representation in the population.Random sampling is then used to select a sufficientnumber of subjects from eachstratum. "Sufficient" refers to a sample size large enough for us to be reasonablyconfident that the stratum represents the population. Stratified sampling is oftenused when one or more of the stratums in the population have a low incidence

relative to the other stratums.

Convenience sampling is used in exploratory research where the researcheris interested in getting an inexpensive approximation of the truth. As the nameimplies, the sample is selected because they are convenient. This non probabilitymethod is often used during preliminary research efforts to get a gross estimate ofthe results, without incurring the cost or time required to select a random sample.

Judgment sampling is a common non probability method. The researcherselects the sample based on judgment. This is usually and extension of conveniencesampling.

Quota sampling is the non probability equivalent of stratified sampling. Likestratified sampling, the researcher first identifies the stratums and their proportionsas they are represented in the population. Then convenience or judgment samplingis used to select the required number of subjects from each stratum. This differsfrom stratified sampling, where the stratums are filled by random sampling.

Snowball sampling is a special non probability method used when thedesired sample characteristic is rare. It may be extremely difficult or cost prohibitiveto locate respondents in these situations. Snowball sampling relies on referrals frominitial subjects to generate additional subjects. While this technique can dramaticallylower search costs, it comes at the expense of introducing bias because thetechnique itself reduces the likelihood that the sample will represent a good crosssection from the population.

2. What is the different between correlation and regression? What do you

understand by Rank Correlation? When we use rank correlation and whenwe use Pearsonian Correlation Coefficient? 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

Ans.

In statistics, correlation (often measured as a correlation coefficient, )indicates the strength and direction of a relationship between two random variables.

The commonest use refers to a linear relationship. In general statistical usage,correlation or co-relation refers to the departure of two random variables fromindependence. In this broad sense there are several coefficients, measuring thedegree of correlation, adapted to the nature of the data. Correlation refers to theinterdependence or co-relationship of variables

In statistics, regression or regression analysis includes any techniques formodeling and analyzing several variables, when the focus is on the relationship
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between a dependent variable and one or more independent variables. Morespecifically, regression analysis helps us understand how the typical value of thedependent variable changes when any one of the independent variables is varied,while the other independent variables are held fixed. Most commonly, regressionanalysis estimates the conditional expectation of the dependent variable given theindependent variables that is, the average value of the dependent variable when

the independent variables are held fixed. Regression is a way of describing how onevariable, the outcome, is numerically related to predictor variables.

Rank correlation is the study of relationships between different rankings onthe same set of items. A rank correlation coefficient measures thecorrespondence between two rankings and assesses its significance. An increasingrank correlation coefficient implies increasing agreement between rankings. Thecoefficient is inside the interval [-1,1] and assumes the value:

-1 if the disagreement between the two rankings is perfect; one ranking is thereverse of the other.

0 if the rankings are completely independent.

1 if the agreement between the two rankings is perfect; the two rankings arethe same.

Pearson correlation coefficient (sometimes referred to as the PMCC, andtypically denoted by r is a measure of the correlation (linear dependence) betweentwo variablesXand Y, giving a value between +1 and 1 inclusive. It is widely usedin the sciences as a measure of the strength of linear dependence between twovariables.

LINEAR REGRESSION a statistical tool used for forecasting future price. Theconcept behind linear regression is to find the best estimate of the trend given anoisy sample of data points.

3.What do you mean by business forecasting? What are the differentmethods of business forecasting? Describe the effectiveness of time-series

analysis as a mode of business forecasting. Describe the method of movingaverages.

Ans.

Business Forecasting involves making the best possible judgment about some futureevent. It is no longer reasonable to rely solely on intuition, or ones feel for thesituation, in projecting sales, inventory needs,personnel requirements, and other important economic or business variables.

Forecasting is an operational research technique used as a basis for managementplanning and decision making. Common types of forecasting include trend analysis,regression analysis, Delphi technique, time series analysis, correlation, exponentialsmoothing, and input-output analysis.

Business forecasting is used by:
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Accountants - costs, revenues, tax-planningPersonnel Departments - recruitment of new employeesFinancial Experts - interest ratesProduction Managers - raw materials needs, inventoriesMarketing Managers - sales forecasts for promotions

Different methods of Forecasting:

Subjective MethodsSales Force CompositesCustomer SurveysJury of Executive OpinionsDelphi Method

Quantitative MethodsExponential smoothing family

Time series method

Time series methods use historical data as the basis of estimating futureoutcomes. In statistics, signal processing, and many other fields.A time series is asequence of data points, measured typically at successive times, spaced at (oftenuniform) time intervals. Time series analysis comprises methods that attempt tounderstand such time series, often either to understand the underlying context of thedata points (Where did they come from? What generated them?), or to makeforecasts (predictions). Time series forecasting is the use of a model to forecastfuture events based on known past events; to forecast future data points before theyare measured. A standard example in econometrics is the opening price of a share ofstock based on its past performance.

The effectiveness of time series analysis lies in the factor that it is used todistinguish a problem, firstly from more ordinary data analysis problems (wherethere is no natural ordering of the context of individual observations), and secondlyfrom spatial data analysis where there is a context that observations (often) relate togeographical locations

Moving Averages

In statistics, a moving average, also called rolling average, rolling meanor running average, is a type offinite impulse response filter used to analyze a setof data points by creating a series ofaverages of different subsets of the full data

set. A moving average is not a single number, but it is a set of numbers, each ofwhich is the average of the corresponding subset of a larger set of data points. Amoving average may also use unequal weights for each data value in the subset toemphasize particular values in the subset. This is the least used technique

A moving average is commonly used with time series data to smooth outshort-term fluctuations and highlight longer-term trends or cycles. The thresholdbetween short-term and long-term depends on the application, and the parametersof the moving average will be set accordingly. For example, it is often used in
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technical analysis of financial data, like stock prices, returns or trading volumes. It isalso used in economics to examine gross domestic product, employment or othermacroeconomic time series. Mathematically, a moving average is a type ofconvolution and so it is also similar to the low-pass filter used in signal processing.When used with non-time series data, a moving average simply acts as a genericsmoothing operation without any specific connection to time, although typically some

kind of ordering is implied.

The moving average approach calculates an average of the sampleobservations and then employs that average as the forecast for the next period. Thenumber of sample observations included in the calculation of the average is specifiedat the start of this process. The term MOVING average means that as a newobservation becomes available a new average is calculated by dropping the oldestobservation in order to include the newest one.

Advantages:1. Data requirements are small.2. Better than using a simple arithmetic mean because it can beadjusted to reflect the observable patterns in the data.

Disadvantages:

1. The past n sample observations must be available.2. Equal weights are given to all past observations and no weightis given to observations earlier than period t-n+1.3. Assumes that the data has a stationary distribution (not always true).

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

statistics? What are the different functions of Statistics? What are thelimitations of Statistics?

Ans.

Statistics can be defined as a mathematical science pertaining to thecollection, analysis, interpretation or explanation, and presentation ofdata, whileothers consider it to be a branch ofmathematics concerned with collecting andinterpreting data. Statisticians improve the quality of data with the design ofexperiments and survey sampling. Statistics also provides tools for prediction andforecasting using data and statistical models. Statistics is applicable to a wide varietyofacademic disciplines, including natural and social sciences, government, andbusiness.

It is actually a collection of methods for planning experiments, obtaining dataand then organizing, summarizing, presenting, analyzing, interpreting and drawingconclusions based on data. It can also be termed as statistics are the numericalstatement of facts capable of analysis and interpretation and the science of statisticsis the study of the principles and the methods applied in collecting, presenting,analysis and interpreting the numerical data in any field of inquiry.

Characteristics of Statistics
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Some of its important characteristics are given below:

Statistics are aggregates of facts. Statistics are numerically expressed. Statistics are affected to a marked extent by multiplicity of causes. Statistics are enumerated or estimated according to a reasonable standard of

accuracy. Statistics are collected for a predetermine purpose. Statistics are collected in a systemic manner. Statistics must be comparable to each other.

Functions of Statistics

Statistics helps in providing a better understanding and exact description of aphenomenon of nature.

Statistical helps in proper and efficient planning of a statistical inquiry in anyfield of study.

Statistical helps in collecting an appropriate quantitative data.

Statistics helps in presenting complex data in a suitable tabular, diagrammaticand graphic form for an easy and clear comprehension of the data.

Statistics helps in understanding the nature and pattern of variability of aphenomenon through quantitative observations.

Statistics helps in drawing valid inference, along with a measure of theirreliability about the population parameters from the sample data.

Important limitations of statistics are:

Statistics laws are true on average. Statistics are aggregates of facts. Sosingle observation is not a statistics, it deals with groups and aggregates only.

Statistical methods are best applicable on quantitative data.

Statistical methods cannot be applied to heterogeneous data.

Its sufficient care is not exercised in collecting, analyzing and interpretationthe data, statistical results might be misleading.

Only a person who has an expert knowledge of statistics can handlestatistical data efficiently.

Some errors are possible in statistical decisions. Particularly the inferentialstatistics involves certain errors. We do not know whether an error has beencommitted or not.


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

Ans.

To Plan a statistical survey:

Agencies initiating a new survey or major revision of an existing survey mustdevelop a written plan that sets forth a justification, including: goals and objectives;potential users; the decisions the survey is designed to inform; key surveyestimates; the precision required of the estimates (e.g., the size of differences thatneed to be detected); the tabulations and analytic results that will inform decisionsand other uses; related and previous surveys; steps taken to prevent unnecessaryduplication with other sources of information; when and how frequently users needthe data; and the level of detail needed in tabulations, confidential micro data , andpublic-use data files.

Planning is an important prerequisite when designing a new survey or surveysystem, or implementing a major revision of an ongoing survey.

Key planning statistical survey activities include the following:

1. A justification for the survey, including the rationale for the survey, relationship toprior surveys, survey goals and objectives (including priorities within these goals andobjectives), hypotheses to be tested, and definitions of key variables. Consultationswith potential users to identify their requirements and expectations are alsoimportant at this stage of the planning process.2. A review of related studies, surveys, and reports of Federal and non-Federalsources to ensure that part or all of the survey would not unnecessarily duplicateavailable data from an existing source, or could not be more appropriately obtainedby adding questions to existing Federal statistical surveys.

3. A review of all survey data items, the justification for each item, and how eachitem can best be measured (e.g., through questionnaires, tests, or administrativerecords). Agencies should assemble reasonable evidence that these items are validand can be measured both accurately and reliably, or develop a plan for testingthese items to assess their accuracy and reliability.5. A plan for pre-testing the survey or survey system, if applicable6. A plan for quality assurance during each phase of the survey process to permitmonitoring and assessing performance during implementation. The plan shouldinclude contingencies to modify the survey procedures if design parameters appearunlikely to meet expectations (for example, if low response rates are likely). Theplan should also contain general specifications for an internal project managementsystem that identifies critical activities and key milestones of the survey that will bemonitored, and the time relationships among them.

7. A plan for evaluating survey procedures, results, and measurement error8. An analysis plan that identifies analysis issues, objectives, key variables, minimumsubstantively significant effect sizes, and proposed statistical tests.9. An estimate of resources and target completion dates needed for the survey cycle.10. A dissemination plan that identifies target audiences, proposed major informationproducts, and the timing of their release.


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Methods for collecting data in a statistical survey:

Statistical Data:A sequence of observation, made on a set of objects included in the sample

drawn from population is known as statistical data.

(1) Ungrouped Data: Data which have been arranged in a systematic order are called raw data orungrouped data.

(2) Grouped Data:

Data presented in the form of frequency distribution is called grouped data.

Collection of Data:

The first step in any enquiry (investigation) is collection of data. The datamay be collected for the whole population or for a sample only. It is mostly collectedon sample basis. Collection of data is very difficult job. The enumerator orinvestigator is the well trained person who collects the statistical data. The

respondents (information) are the persons whom the information is collected.

Types of Data:

There are two types (sources) for the collection of data. (1) Primary Data (2) Secondary Data

(1) Primary Data: The primary data are the first hand information collected, compiled andpublished by organization for some purpose. They are most original data in characterand have not undergone any sort of statistical treatment.Example: Population census reports are primary data because these are collected,complied and published by the population census organization.

(2) Secondary Data: The secondary data are the second hand information which are alreadycollected by some one (organization) for some purpose and are available for thepresent study. The secondary data are not pure in character and have undergonesome treatment at least once.Example: Economics survey of England is secondary data because these arecollected by more than one organization like Bureau of statistics, Board of Revenue,the Banks etc

Methods of Collecting Primary Data:

Primary data are collected by the following methods:

Personal Investigation: The researcher conducts the survey him/herselfand collects data from it. The data collected in this way is usually accurateand reliable. This method of collecting data is only applicable in case of smallresearch projects.

Through Investigation: Trained investigators are employed to collect thedata. These investigators contact the individuals and fill in questionnaire afterasking the required information. Most of the organizing implied this method.


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Collection through Questionnaire: The researchers get the data from localrepresentation or agents that are based upon their own experience. Thismethod is quick but gives only rough estimate.

Through Telephone: The researchers get information through telephone thismethod is quick and give accurate information

Methods of Collecting Secondary Data:The secondary data are collected by the following sources:

Official: e.g. The publications of the Statistical Division, Ministry of Finance,the Federal Bureaus of Statistics, Ministries of Food, Agriculture, Industry,Labor etc

Semi-Official: e.g. State Bank, Railway Board, Central Cotton Committee,Boards of Economic Enquiry etc

Publication of Trade Associations, Chambers of Commerce etc

Technical and Trade Journals and Newspapers.

Research Organizations such as Universities and other institutions.

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 modeof presentation of data?

Ans.

The process of arranging data into homogenous group or classes according tosome common characteristics present in the data is called classification.Classification is a process of statistical analysis. For Example: The process of sortingletters in a post office, the letters are classified according to the cities and furtherarranged according to streets

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

e.

Requisites of a good classification are

i. Unambiguous: It should not lead to any confusion


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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 be remain stable through out the investigation

vii. Homogeneity: Similar units are essential features of the collected data.

TABLE:

The process of placing classified data into tabular form is known as tabulation.A table is a symmetric arrangement of statistical data in rows and columns.Rows are horizontal arrangements whereas columns are vertical arrangements. Itmay be simple, double or complex depending upon the type of classification.

The basic structure of a table is a set of columns and rows that contain thedata and usually contain either a row or column (or both) of headings that organizethe data. A table is generally less effective than a graph because it only shows thedata, whereas the graph shows an interpretation of the data, which is easier for theaudience to understand. When you are presenting a table, you will need to providethe interpretation of the data for the audience. One way to make certain cells standout is to change the background color of the cell or enhance the text by changing thecolor or making it bolder. Column and/or row headings should be bolded todistinguish them from the data. Most presentation software packages have a built-intable creation tool that will serve most purposes quite well.

A table works best when:

--It is used to look up individual values--It is used to compare individual values--The values must be expressed precisely

Uses of a table in presentation are:

To simplify complex data

To highlight important characteristics

To present data in minimum space

To facilitate comparison

To bring out trends and tendencies

To facilitate further analysis

A table helps organise information so it is easier to see patterns andrelationships.


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If a variable is continuous the table reveals a lot more information. It mayshow the range, interval, and number of readings.

Tables with multiple variables can provide a lot of information. They can beread by selecting and controlling factors to search for patterns in the data.

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