MB 0024

ASSIGNMENT

Name S.AMEER ABBAS

Roll No. 520955311

Course MBA-Semester-1

SubjectSTATISTICS FOR MANAGEMENT

Subject Code MB0024-Set-1

Case 1ABC 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 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/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

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

You as an Assistant Branch Manager of the Bank are entrusted the task of selecting two account holders for sanctioning the loans. 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.

Ans.

We can take the probabilistic method of estimation of their ability to maintain average 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 η-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

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

1.Customer No. IV with probability of 84 and

2.Customer No. VI with probability of 77

ASSIGNMENT

Name S.AMEER ABBAS

Roll No. 520955311

Course MBA-Semester-1

SubjectSTATISTICS FOR MANAGEMENT

Subject Code MB0024-Set-2

1. What do you mean by sample survey? What are the different

sampling methods? Briefly describe them.

Ans .

Sampling is that part of statistical practice concerned with the

selection of individual observations intended to yield some knowledge about

a population of concern, especially for the purposes of statistical inference.

Each observation measures one or more properties (weight, location,

etc.) of an observable entity enumerated to distinguish objects or individuals.

Survey weights often need to be applied to the data to adjust for the sample

design. Results from probability theory and statistical theory are employed to

guide practice.

Sampling Methods

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 are selected from the population in some

nonrandom manner. These include convenience 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

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.

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 sampling technique is simplicity. Systematic sampling is

frequently used to select a specified number of records from a computer file.

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 sufficient number 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.

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 is often 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.

Judgment sampling is a common non probability method. The

researcher selects the sample based on judgment. This is usually and

extension of convenience sampling.

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 generate additional 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 use rank correlation and when

we 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,

ρ) 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 from independence. In this broad sense there are several

coefficients, measuring the degree of correlation, adapted to the nature of

the data. Correlation refers to the interdependence or co-relationship of

variables

In statistics, regression or regression analysis includes any

techniques for modeling and analyzing several variables, when the focus is

on the relationship between a dependent variable and one or more

independent variables. More specifically, regression analysis helps us

understand how the typical value of the dependent variable changes when

any one of the independent variables is varied, while the other independent

variables are held fixed. Most commonly, regression analysis estimates the

conditional expectation of the dependent variable given the independent

variables — that is, the average value of the dependent variable when the

independent variables are held fixed. Regression is a way of describing how

one variable, the outcome, is numerically related to predictor variables.

Rank correlation is the study of relationships between different

rankings on the same set of items. A rank correlation coefficient measures

the correspondence between two rankings and assesses its significance. An

increasing rank correlation coefficient implies increasing agreement between

rankings. The coefficient is inside the interval [-1,1] and assumes the value:

-1 if the disagreement between the two rankings is perfect; one

ranking is the reverse of the other.

0 if the rankings are completely independent.

1 if the agreement between the two rankings is perfect; the two

rankings are the same.

Pearson correlation coefficient (sometimes referred to as the

PMCC, and typically denoted by r is a measure of the correlation (linear

dependence) between two variables X and Y, giving a value between +1 and

−1 inclusive. It is widely used in the sciences as a measure of the strength of

linear dependence between two variables.

LINEAR REGRESSION — a statistical tool used for forecasting future price.

The concept behind linear regression is to find the best estimate of the trend

given a noisy sample of data points.

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 mode of business forecasting. Describe the method of moving averages.

Ans.

Business Forecasting involves making the best possible judgment

about some future event. It is no longer reasonable to rely solely on intuition,

or one’s feel for the situation, 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

management planning and decision making. Common types of forecasting

include trend analysis, regression analysis, Delphi technique, time series

analysis, correlation, exponential smoothing, and input-output analysis.

Business forecasting is used by:

Accountants - costs, revenues, tax-planning

Personnel Departments - recruitment of new employees

Financial Experts - interest rates

Production Managers - raw materials needs, inventories

Marketing Managers - sales forecasts for promotions

Different methods of Forecasting:

Subjective Methods

Sales Force Composites

Customer Surveys

Jury of Executive Opinions

Delphi Method

Quantitative Methods

Exponential smoothing family

Time series method

Time series methods use historical data as the basis of estimating

future outcomes. In statistics, signal processing, and many other fields.A

time series is a sequence of data points, measured typically at successive

times, spaced at (often uniform) time intervals. Time series analysis

comprises methods that attempt to understand such time series, often either

to understand the underlying context of the data points (Where did they

come from? What generated them?), or to make forecasts (predictions). Time

series forecasting is the use of a model to forecast future events based on

known past events; to forecast future data points before they are measured.

A standard example in econometrics is the opening price of a share of stock

based on its past performance.

The effectiveness of time series analysis lies in the factor that it is

used to distinguish a problem, firstly from more ordinary data analysis

problems (where there is no natural ordering of the context of individual

observations), and secondly from spatial data analysis where there is a

context that observations (often) relate to geographical locations

Moving Averages

In statistics, a moving average, also called rolling average, rolling

mean or running average, is a type of finite impulse response filter used to

analyze a set of data points by creating a series of averages of different

subsets of the full data set. A moving average is not a single number, but it is

a set of numbers, each of which is the average of the corresponding subset of

a larger set of data points. A moving average may also use unequal weights

for each data value in the subset to emphasize particular values in the

subset. This is the least used technique

A moving average is commonly used with time series data to smooth

out short-term fluctuations and highlight longer-term trends or cycles. The

threshold between short-term and long-term depends on the application, and

the parameters of the moving average will be set accordingly. For example, it

is often used in technical analysis of financial data, like stock prices, returns

or trading volumes. It is also used in economics to examine gross domestic

product, employment or other macroeconomic time series. Mathematically, a

moving average is a type of convolution 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 generic smoothing operation without any

specific connection to time, although typically some kind of ordering is

implied.

The moving average approach calculates an average of the sample

observations and then employs that average as the forecast for the next

period. The number of sample observations included in the calculation of the

average is specified at the start of this process. The term MOVING average

means that as a new observation becomes available a new average is

calculated by dropping the oldest observation in order to include the newest

one.

Advantages:1. Data requirements are small.

2. Better than using a simple arithmetic mean because it can be

adjusted 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 weight

is 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 the

limitations of Statistics?

Ans.

Statistics can be defined as a mathematical science pertaining to the

collection, analysis, interpretation or explanation, and presentation of data,

while others consider it to be a branch of mathematics concerned with

collecting and interpreting data. Statisticians improve the quality of data with

the design of experiments and survey sampling. Statistics also provides tools

for prediction and forecasting using data and statistical models. Statistics is

applicable to a wide variety of academic disciplines, including natural and

social sciences, government, and business.

It is actually a collection of methods for planning experiments,

obtaining data and then organizing, summarizing, presenting, analyzing,

interpreting and drawing conclusions based on data. It can also be termed as

“statistics are the numerical statement of facts capable of analysis and

interpretation and the science of statistics is 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

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 a phenomenon of nature.

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

Statistical helps in collecting an appropriate quantitative data.

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

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

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

Important limitations of statistics are :

Statistics laws are true on average. Statistics are aggregates of facts. So single 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 interpretation the data, statistical results might be misleading.

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

Some errors are possible in statistical decisions. Particularly the inferential statistics involves certain errors. We do not know whether an error has been committed or not.

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

the 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

must develop a written plan that sets forth a justification, including: goals

and objectives; potential users; the decisions the survey is designed to

inform; key survey estimates; the precision required of the estimates (e.g.,

the size of differences that need to be detected); the tabulations and analytic

results that will inform decisions and other uses; related and previous

surveys; steps taken to prevent unnecessary duplication with other sources

of information; when and how frequently users need the data; and the level

of detail needed in tabulations, confidential micro data , and public-use data

files.

Planning is an important prerequisite when designing a new survey or

survey system, 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 to prior surveys, survey goals and objectives (including priorities

within these goals and objectives), hypotheses to be tested, and definitions of

key variables. Consultations with potential users to identify their

requirements and expectations are also important at this stage of the

planning process.

2. A review of related studies, surveys, and reports of Federal and non-

Federal sources to ensure that part or all of the survey would not

unnecessarily duplicate available data from an existing source, or could not

be more appropriately obtained by adding questions to existing Federal

statistical surveys.

3. A review of all survey data items, the justification for each item, and how

each item can best be measured (e.g., through questionnaires, tests, or

administrative records). Agencies should assemble reasonable evidence that

these items are valid and can be measured both accurately and reliably, or

develop a plan for testing these items to assess their accuracy and reliability.

5. A plan for pre-testing the survey or survey system, if applicable

6. A plan for quality assurance during each phase of the survey process to

permit monitoring and assessing performance during implementation. The

plan should include contingencies to modify the survey procedures if design

parameters appear unlikely to meet expectations (for example, if low

response rates are likely). The plan should also contain general specifications

for an internal project management system that identifies critical activities

and key milestones of the survey that will be monitored, and the time

relationships among them.

7. A plan for evaluating survey procedures, results, and measurement error

8. An analysis plan that identifies analysis issues, objectives, key variables,

minimum substantively 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

information products, and the timing of their release.

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 or ungrouped 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

data may be collected for the whole population or for a sample only. It is

mostly collected on sample basis. Collection of data is very difficult job. The

enumerator or investigator 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

and published by organization for some purpose. They are most original data

in character and 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

already collected by some one (organization) for some purpose and are

available for the present study. The secondary data are not pure in character

and have undergone some treatment at least once.

Example: Economics survey of England is secondary data because these are

collected 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/herself and collects data from it. The data collected in this way is

usually accurate and reliable. This method of collecting data is only

applicable in case of small research projects.

Through Investigation: Trained investigators are employed to

collect the data. These investigators contact the individuals and fill in

questionnaire after asking the required information. Most of the

organizing implied this method.

Collection through Questionnaire: The researchers get the data

from local representation or agents that are based upon their own

experience. This method is quick but gives only rough estimate.

Through Telephone: The researchers get information through

telephone this method 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

mode of presentation of data?

Ans.

The process of arranging data into homogenous group or classes

according to some common characteristics present in the data is called

classification. Classification is a process of statistical analysis. For Example:

The process of sorting letters in a post office, the letters are classified

according to the cities and further arranged 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

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. It may 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

the data and usually contain either a row or column (or both) of headings that

organize the data. A table is generally less effective than a graph because it

only shows the data, whereas the graph shows an interpretation of the data,

which is easier for the audience to understand. When you are presenting a

table, you will need to provide the interpretation of the data for the audience.

One way to make certain cells stand out is to change the background color of

the cell or enhance the text by changing the color or making it bolder.

Column and/or row headings should be bolded to distinguish them from the

data. Most presentation software packages have a built-in table 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 and

relationships.

If a variable is continuous the table reveals a lot more information. It

may show the range, interval, and number of readings.

Tables with multiple variables can provide a lot of information. They

can be read by selecting and controlling factors to search for patterns

in the data.