MB0040 Statistics for Management Set1

Statistics for Management | Set 1 Page 1 of 9

Sikkim Manipal University | MBA-Spring 2010 | MB0040 Statistics for Management | Sem 1

ASSIGNMENT – 01/02NameAyaz Anis AnsariRegistration No.511025251Learning CentreKarrox Technologies

(Borivali Centre, Mumbai) Learning Centre Code03092CourseMBASubjectStatistics for Management - Set

1SemesterSemester 1Module No.MB0040Date of SubmissionMay 8, 2010Marks AwardedDirectorate of Distance Education

Sikkim Manipal UniversityII Floor, Syndicate House,

Manipal – 576 104

_________________Signature of Coordinator

__________________

Signature of Center

_________________

Signature of Evaluator


Q. 1. Elucidate the functions of Statistics.

Ans. Statistics is a mathematical science involving the collection, interpretation, analysis, and presentation of

data. It is often used to make predictions based on data. It is widely applicable in various social and natural

sciences as such as political science and medicine as well as in business such as the insurance industry.

For example, statistics are a very important part of political campaigns as they lead up to elections. Every time a

scientific poll is taken, statistics are used to calculate and illustrate the results in percentages and to calculate

the margin for error.

Statistics are also used in psychology. People’s behavior can be measured on a bell curve. Most people fall

within acceptable ranges of the bell curve. However the people who fall outside "the norm" or on the "fringe" of

the bell curve may be considered unstable.

Statistics are very important in various aspects of business; a terrific example is the insurance industry. It is the

job of an actuarial scientist to determine how long people will live (statistically), how likely they are to have an

accident, and how likely is it their home will burn down or be damaged in a hurricane? These risks are all rated

based solely on statistical data and policies are priced accordingly.

Definition of Statistics:

A.L. Bowley defined statistics as “statistics is the science of counting”. This definition places the entries stress

on counting only. A common man also thinks as if statistics is nothing but counting. This used to be the situation

but very long time ago. Statistics today is not mere counting of people, counting of animals, counting of trees

and counting of fighting force. It has now grown to a rich methods of data analysis and interpretation.

A.L. Bowley has also defined as “science of averages”. This definition is very simple but it covers only some

area of statistics. Average is very simple important in statistics. Experts are interested in average deaths rates,

average birth rates, average increase in population, and average increase in per capita income, average

increase in standard of living and cost of living, average development rate, average inflation rate, average

production of rice per acre, average literacy rate and many other averages of different fields of practical life. But

statistics is not limited to average only. There are many other statistical tools like measure of variation, measure

of correlation, measures of independence etc… Thus this definition is weak and incomplete and has been

buried in the past.

Prof: Boddington has defined statistics as “science of estimate and probabilities”. This definition covers a major

part of statistics. It is close to the modern statistics. But it is not complete because it stress only on probability.

There are some areas of statistics in which probability is not used.



A definition due to W.I. King is “the science of statistics is the method of judging collection, natural or social

phenomena from the results obtained from the analysis or enumeration or collection of estimates”. This

definition is close to the modern statistics. But it does not cover the entire scope of modern statistics. Secrist

has given a detailed definition of statistics in plural sense. His definition is given on the previous. He has not

given any importance to statistics in singular sense. Statistics both in the singular and the plural sense has been

combined in the following definition which is accepted as the modern definition of statistics.

“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.”

Functions or Uses of Statistics

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

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

Statistics 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.

It simplifies mass data.

It makes comparison easier.

It brings out trends and tendencies in data.

It brings out hidden relations in variables.

Decision making process becomes easier.



2. What are the methods of statistical survey? Explain briefly.

Ans. Following are the methods of statistical survey for collection of primary data:

Direct personal observation: Most evaluation teams conduct some fieldwork, observing what's actually going

on at assistance activity sites. Often, this is done informally, without much thought to the quality of data

collection. Direct observation techniques allow for a more systematic, structured process, using well-designed

observation record forms.

The main advantage of direct observation is that an event, institution, facility, or process can be studied

in its natural setting, thereby providing a richer understanding of the subject.

Direct observation may be useful:

When performance monitoring data indicate results are not being

Accomplished as planned, and when implementation problems are suspected, but not understood. Direct

observation can help identify whether the process is poorly implemented or required inputs are absent.

When details of an activity's process need to be assessed, such as whether tasks are being implementing

according to standards required for effectiveness.

When an inventory of physical facilities and inputs is needed and not available from existing sources.

When interview methods are unlikely to elicit needed information accurately or reliably, either because the

respondents don't know or may be reluctant to say.

Indirect oral interview / investigation: Here the interviewer / investigator contacts third party capable of

supplying necessary information. It is generally adopted in those cases where the information to be obtained is

of complex nature and the informants are reluctant to respond if approached directly, e.g. information regarding

addiction to drug, alcohol, HIV infected persons, etc.

Information through agencies: Here the investigator appoints local agents or correspondents in different

place to collect information. Newspaper agencies generally adopt this method. However, the information may be

affected by the personal prejudice and bias of the correspondent.

Information through mailed questionnaires: Here, a list of questions pertaining to the survey is prepared and

sent to the various informants by post.

Information through schedule filled by investigators: Schedules (is the name usually applied to a set of

questions which are asked and filled in a face-to-face situation with another person) are sent through

investigators or enumerators to get replies of the questions in the schedule from the respondents.



Q. 3. Tabulate the following data:

Age: 20-40; 40-60; 60-above

Departments: English, Hindi, Political science, History, sociology

Degree level: Graduates, Post graduates; PhD

Total students in age group and in degree level.

Solution.

DepartmentsAge 20 - 4040 - 6060 - aboveTotalAGraduatesB

Post GraduatesCPhDA

GraduatesBPost GraduatesC

PhDAGraduatesB

Post GraduatesC

PhDEnglish1040101015512113116Hindi103010121478102103Political

Science1525101014574494History103010812695191Sociology52510015766579Total50150504070304236154

83



Q. 4. The data given below is the distribution of employees of a business

according to their efficiency. Find the mean deviation and coefficient of

mean deviation from Mean and Median:

Efficiency Index 22-26 26-30 30-34 34-38 38-42

Employees 25 35 15 5 2

Solution.

The table below displays the frequency distribution of employees to calculate the mean deviation from mean

and mean deviation from median.

Frequency distribution of employees

Efficiency Index

Employees

(f)Mid value

(x)fdF |x -28.29| Cf|x – Med|F |(x – Med)|22 – 262524-2-50107.25253.8395.7526 – 303528-1-

3510.15600.175.9530 – 3415320055.65754.1762.5534 – 385361538.55808.1740.8538 –

422402423.428212.1724.3482-76.00235.02229.44

The assumed mean (A) is 32. Then the Arithmetic Mean is calculated as:

= 32 – 3.71 = 28.29

The Arithmetic Mean = 28.29

Mean Deviation from Mean is calculated as:

M.D. () =

Median Class is 26 – 30



Median =

Mean Deviation from Median =

Co-efficient of Mean Deviation from Mean = =

Co-efficient of Mean Deviation from Median =

Therefore,

Mean deviation from Mean = 2.87

Co-efficient of Mean Deviation from Mean = 0.1014

Mean deviation from Median = 2.80

Co-efficient of Mean Deviation from Median = 0.1006



Q. 5. What is conditional probability? Explain with an example

Ans. Probability Definitions:

Probability is a numerical value measure which indicates the chance of occurrence of an event ‘A’. It is denoted

by p(A). It is the ratio between the favorable outcomes of an event ‘A’ (m) to the total outcomes of the

experiment (n). In other words:

P(A) =

Where, ‘m’ is the number of favorable outcomes of an event ‘A’ and ‘n’ is the total number of outcomes of the

experiment.

For discrete math, we focus on the discrete version of probabilities.

For each random experiment, there is assumed to be a finite set of discrete possible results, called outcomes.

Each time the experiment is run, one outcome occurs. The set of all possible outcomes is called the sample

space.

Conditional Probability:

If event F occurs, what is the probability that event E also occurs?

This probability is called conditional probability and denoted as .

Definition of Conditional Probability:

If p(F) > 0, then

=

Example:

An urn contains 8 red balls and 4 white balls. We draw 2 balls from the urn without replacement. What is the

probability that both balls are red?

Solution:

Let E be the event that both balls drawn are red. Then,

p(E) =

or, we can solve the problem using conditional probability approach, Let E1 and E2 denote, respectively, the

events that the first and second balls drawn are red. Then,

p(E1E2) = p(E1) p(E2 | E1 ) =



Q. 6. The probability that a football player will play Eden garden is 0.6 and

on Ambedkar Stadium is 0.4. The probability that he will get knee injury

when playing in Eden is 0.07 and that in Ambedkar stadium is 0.04. What

is the probability that he would get a knee injury if he played in Eden.

Solution.

P(E) = Probability of football player playing at Eden garden = 0.6

P(A) = Probability of football player playing at Ambedkar stadium = 0.4

P(IE) = Probability of player getting injured while playing at Eden garden = 0.07

P(IA) = P(E) = Probability of player getting injured while playing at Ambedkar stadium = 0.04

And

Hence, the probability that the player would get a knee injury if he played in Eden is 0.7241


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MB0040 Statistics for Management Set1