Assignment QT Col MBA Semester 1

Assignment No. 1

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((55556644))

Executive MBA/MPA (Col)

ZAHID NAZIR Roll.No. AB523655 Semester:Autumn 2008

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Question 1

a). Explain the use of Quantitative Techniques in Business

and Management?

Marks: 10

b). What are limitations of Statistics?

Marks: 10

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a).

QUATITATIVE TECHNIQUES

Quantitative techniques refers to the group of statistical and

operations research techniques. All these techniques require

preliminary knowledge of certain topics in mathematics.

Quantitative Techniques

Statistical Techniques Operations Research

Techniques

USE OF QUANTITATIVE TECHNIQUES IN BUSINESS AND MANAGMENT

Due to increasing complexity in business and industry, decision

making based on intuition has become highly questionable especially

when the decision involves the choice among several courses of

action each of which can achieve several management actions. So

there is need for training the people who can manage a system

efficiently and creatively.

Quantitative Techniques now have a major role in effective decision

making in various functional areas of management i.e. marketing,

finance, production and personnel. These techniques are also widely

used in planning, transportation, public health, communication,

military, agriculture etc. Quantitative techniques are also used

extensively as an aid in business decision making.

Some of the areas where quantitative techniques can be used are:

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MANAGEMENT

i). Marketing

• Analysis of marketing research information

• Statistical records for building and maintaining an

extensive market

• Sales forecasting

ii). Production

• Production planning, control and analysis

• Evaluation of machine performance

• Quality control requirement (to analyze the data/trends)

• Inventory control measures

iii). Finance, Accounting and Investment

• Financial forecast, budget preparation

• Financial investment decisions

• Selection of securities

• Auditing function

• Credit policies, credit risk and delinquent accounts

iv). Personnel

• Labour turn over rate

• Employment trends

• Performance appraisal

• Wage rates and incentive plans

ECONOMICS

• Measurement of gross national product and input-output

analysis

• Determination of business cycle, long term growth and

seasonal fluctuations

• Comparison of market prices, cost and profits of individual

firms

• Analysis of population, land economies and economic

geography

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• Operational studies of public utilities

• Formulation of appropriate economic policies and evaluation

of their effect

RESEARCH & DEVELOPMENT

• Development of new product lines

• Optimal use of resources

• Evaluation of existing products

NATURAL SCIENCE

• Diagnosis of disease based on data like temperature, pulse rate,

blood pressure etc.

• Judging the efficiency of a particular drug for curing a certain

disease

• Study of plant life

In the competitive and dynamic business world, firms/companies

who likes to succeed and survive are those which are capable of

maximizing the use of tools of management like quantitative

techniques.

b)

LIMITATIONS OF STATISTICS

Statistics with all its wide application in every sphere of human activity

has its own limitations. Some of them are given below.

1. STATISTICS IS NOT SUITABLE TO THE STUDY OF QUALITATIVE PHENOMENON:

Since statistics is basically a science and deals with a set of numerical

data, it is applicable to the study of only these subjects of enquiry,

which can be expressed in terms of quantitative measurements. As a

matter of fact, qualitative phenomenon like honesty, poverty,

beauty, intelligence etc, cannot be expressed numerically and any

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statistical analysis cannot be directly applied on these qualitative

phenomenons. Nevertheless, statistical techniques may be applied

indirectly by first reducing the qualitative expressions to accurate

quantitative terms. For example, the intelligence of a group of

students can be studied on the basis of their marks in a particular

examination.

2. STATISTICS DOES NOT STUDY INDIVIDUALS:

Statistics does not give any specific importance to the individual

items; in fact it deals with an aggregate of objects. Individual items,

when they are taken individually do not constitute any statistical data

and do not serve any purpose for any statistical enquiry.

3. STATISTICAL LAWS ARE NOT EXACT:

It is well known that mathematical and physical sciences are exact.

But statistical laws are not exact and statistical laws are only

approximations. Statistical conclusions are not universally true. They

are true only on an average.

4. STATISTICS TABLE MAY BE MISUSED:

Statistics must be used only by experts; otherwise, statistical

methods are the most dangerous tools on the hands of the inexpert.

The use of statistical tools by the inexperienced and untraced

persons might lead to wrong conclusions. Statistics can be easily

misused by quoting wrong figures of data.

5. STATISTICS IS ONLY, ONE OF THE METHODS OF STUDYING A PROBLEM:

Statistical method do not provide complete solution of the problems

because problems are to be studied taking the background of the

countries culture, philosophy or religion into consideration. Thus the

statistical study should be supplemented by other evidences.

References: www.textbooksonline.tn.nic.in/

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Question 2

a). Different types of functions are introduced and used in

CACULUS, briefly explain them?

Marks: 10

b). Graph and find domain of

f(x) = 2x2

if x < 0

3x + 1 if x > 0

Marks: 10

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a).

TYPES OF FUNCTION

Different types of functions that are introduced and used in calculus

are:

i). Linear Function

ii). Polynomial Function

iii). Absolute Value Function

iv). Inverse Function

v). Step Function

vi). Algebraic Function

i). LINEAR FUNCTION

A linear function is one in which the power of independent variable is

1, it is also called single variable function.

The general expression of linear function having only one

independent variable is:

y = f(x) = a + bx

where a and b are given real numbers and x is an independent

variable taking all numerical values in an interval.

Single variable function can be linear and non-linear, for example

y = 3 + 2x (Linear single variable function)

and

y = 2 + 3x – 5x2 + x

2 (non-linear single variable function)

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A linear function with one variable can always be graphed in a two

dimensional plane. This graph can always be plotted by giving

different values to x and calculating corresponding values of y. The

graph of such functions is always a straight line.

ii). POLYNOMIAL FUNCTION

Polynomial functions are functions with x as an input variable, made

up of several terms, each term is made up of two factors, the first

being a real number coefficient, and the second being x raised to

some non-negative integer power.

Polynomial functions are functions that have this form:

y = f(x) = anxn + an-1x

n-1 + ... + a1x

1 + a0

The value of n must be a nonnegative integer. That is, it must be

whole number; it is equal to zero or a positive integer.

an, an-1, ..., a1, a0 are called coefficients. These are real numbers.

The degree of the polynomial function is the highest value for n

where an is not equal to 0.

If n = 1, then the polynomial function is of degree 1 and is called a

linear function and if n = 2 then the polynomial function is of degree

2 and is called quadratic function and usually written as:

y = ax2 + bx + c

iii). ABSOLUTE VALUE FUNCTION

The absolute value function is the real-valued function defined as

follows.

y = │x │

Where │x │ is known as magnitude or absolute value of x. By

absolute value means that whether x is positive or negative, its

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absolute value will remain positive. For example │7 │= 7 and │-6 │

= 6. The graph of given function is like this:

iv). INVERSE FUNCTION

Take the function y = f(x). Then the value of y can be uniquely

determined for given values of x as per the functional

relationship. . Sometimes it is required to consider x as a of y,

so that for given values of y, the values of x can be determined

as per the functional relationship. This is called the inverse

function and is also donated by x = f -1

(y). For example

consider the linear function:

y = ax + b

Expressing this in terms of x, we get

x = y - b / a

= y/a - b/a = cy – d

where c = 1/a, and d = - b/a

This is also a linear function and is denoted by x = f -1

(y).

v). STEP FUNCTION

For different values of an independent variable x in an interval,

the dependant variable y = f(x) takes a constant value, but takes

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different values in different intervals. In such cases the given function

y = f(x) is called a step function.

vi). ALGEBRAIC & TRANSCENDENTAL FUNCTIONS

Functions can also be classified with respect to the mathematical

operations (addition, subtraction, multiplication, division, powers

and roots) involved in the functional relationship between

dependant variable and independent variables. When only finite

number of terms are involved in a functional relationship and

variables are affected only by the mathematical operations, then the

function is called an algebraic function otherwise transcendental

function. The following functions are algebraic functions of x.

i). y = 2x3 + 5x

2 - 3x + 9

ii). y = √x + 1/x2

iii). Y = x3 - 1/ √x + 2

The subclasses of transcendental functions are:

i). Exponential Function

ii). Logarithmic Function

b).

DOMAIN:

Domain consists of all real numbers except zero.

Now consider

f (x) = 2x2 where x < 0

Supposed the values of x are -1, -3, -5, then

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f (-1) = 2(-1)2 = 2

f(-3) = 2(-3)2 = 18

f(-5) = 2(-5)2 = 50

Its graph is as follows;

0

10

20

30

40

50

60

-1-2-3-4-5-6

Y-A

xis

X-Axis

f (x) = 2x2

Now consider f (x) = 3x + 1 if x > 0

Suppose value of x are 1, 3, 5, so

f (1) = 3(1) + 1 = 4

f (3) = 3(3) + 1 = 10

f (5) = 3(5) + 1 = 16

Its graph will be as follows;

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024

681012

141618

123456

Y-A

xis

X-Axis

f (x) = 3x + 1

Reference:

http://www.themathpage.com

http://oregonstate.edu

Quantitative Techniques (AIOU)

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Question 3

a). Given the following input-output table, calculate the

gross output so as to meet the final demand of 200

units of Agriculture and 800 units of industry.The

following data relates to the sales of 100 companies

is given below:

Consumer Sector

Producer Sector Agriculture Industry Final Demand Total Output

Agriculture 300 600 100 1000 Industry 400 1200 400 2000

Marks: 10

b). Discriminate between the census and sampling

methods of data collection and compare their merits and

demerits. Why is the sampling method unavoidable in

certain situations?

Marks: 10

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Solution:

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b).

CENSUS

Census is a complete enumeration of an entire population of

statistical units in a field of interest. It is also called complete

enumeration survey.

For example, population census canvases every household in a

country to count for the number of permanent residents and

other characteristics; census of manufacturing canvases all

establishments engaging in manufacturing activities.

Data from the census serve as base-year or benchmark data.

Requirement: A complete and up-to-date register of all

statistical units in the field of inquiry is required.

Advantages: Census provides the most reliable statistics if

done professionally and with integrity.

Disadvantages: Very costly to enumerate and to process data.

Timeliness is low: data is available for use only many months,

even years after. Census is normally carried every five or ten

years.

SAMPLING METHOD

When the investigator studies only a representative part of the

total population and makes inferences about the population on

the basis of that study. It is known as sampling method or

Survey.

In both methods, the investigator is interested in studying

some characteristics of the population.

Advantages: Provide more up-to-date statistics, which are

reliable if scientifically designed and professionally

implemented, less costly than census. Sampling errors can also

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be obtained. Surveys are normally carried out weekly, monthly,

quarterly or annually.

Disadvantages: Timeliness requires prompt data processing,

thus less information may be asked.

SITUATIONS IN WHICH SAMPLING METHOD IS UNAVOIDABLE

Sampling method is unavoidable in following situations

• Unlimited population

• Distractive population nature

• Unapproachable population e.g. Mobilink users

• In quality control, such as finding the tensile strength of

a steel specimen by stretching it till it breaks. Another

example is in process checking in the manufacturing of

pharmaceuticals where it is not possible to check the

each and every tablet or injection. Secondly quality

testing results in destruction of items itself.

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Question 4

a). The following data relates to the sales of 100

companies is given below:

Sales

(Lakhs)

No. of Complaints Sales

(Lakhs)

No. of Complaints

5-10 5 25-30 18

10-15 12 30-35 15

15-20 13 35-40 10

20-25 20 40-45 7

Draw less than and more than ogives. Determine the

number of companies whose sales are (i) less than

Rs.13 Lakhs (ii) more than Rs.36 Lakhs and (iii)

between Rs.13 lakhs and Rs.36 lakhs.

Marks: 10

b). Briefly explain the following important concepts:

i). Continuous Data

ii). Discrete Data

iii). Frequency Distribution

iv). Qualitative Data

v). Quantitative Data

Marks: 10

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a).

OGIVE

“An ogive is a specialized line graph which shows how many items

there are which are below a certain value.”

The horizontal axis shows the upper class boundaries marked on the

scale, just like a histogram.

The vertical axis shows the cumulative frequency, which is just a

fancy name for a running total. Some line graphs are actually ogives.

First we calculate the cumulative frequency. We start at 5.

Next line: 5 + 12 = 17

Next line: 17 + 13 = 30

Next line: 30 + 20 = 50 and so on.

i). Less than Rs. 13 Lakhs = 12 companies (Graph - I)

ii). More than Rs. 36 Lakhs = 15 companies (Graph - II)

iii). B/w 13 and 36 Lakhs = 73 companies (Graph - I)

Sales

X

(Lakhs)

No. of

Companies

(f)

Cumulative

Frequency

Decumulative

Frequency

5-10 5 Less than 10 5 More than 5 100








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b).

i). CONTINUOUS DATA

Continuous data is information that can be measured on a

continuum or scale. Continuous data can have almost any numeric

value and can be meaningfully subdivided into finer and finer

increments, depending upon the precision of the measurement

system.

In contrast to discrete data like good or bad, off or on, etc.,

continuous data can be recorded at many different points (length,

size, width, time, temperature, cost, etc.).

Let's say you are measuring the size of a marble. To be within

specification, the marble must be at least 25mm but no bigger than

27mm. If you measure and simply count the number of marbles that

are out of spec (good v/s bad) you are collecting attribute data.

However, if you are actually measuring each marble and recording

the size (i.e. 25.2mm, 26.1mm, 27.5mm, etc) that's continuous data,

and you actually get more information about what you're measuring

from continuous data than from attribute data.

Data can be continuous in the geometry or continuous in the range

of values. The range of values for a particular data item has a

minimum and a maximum value. Continuous data can be any value in

between.

ii). DISCRETE DATA

Discrete data is information that can be categorized into a

classification. Discrete data is based on counts. Only a finite number

of values is possible, and the values cannot be subdivided

meaningfully. For example, the number of parts damaged in

shipment.

Example . A 5 question quiz is given in a Math class. The number of

correct answers on a student's quiz is an example of discrete data.

The number of correct answers would have to be one of the

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following: 0, 1, 2, 3, 4, or 5. There are not an infinite number of

values, therefore this data is discrete. Also, if we were to draw a

number line and place each possible value on it, we would see a

space between each pair of values.

iii). FREQUENCY DISTRIBUTION

Frequency distribution is a way of summarizing a set of data. It is a

record of how often each value (or set of values) of the variable in

question occurs. It may be enhanced by the addition of percentages

that fall into each category.

A frequency table is used to summarize categorical, nominal, and

ordinal data. It may also be used to summarize continuous data once

the data set has been divided up into sensible groups.

Example

Suppose that in thirty shots at a target, a marksman makes the

following scores:

5 2 2 3 4 4 3 2 0 3 0 3 2 1 5

1 3 1 5 5 2 4 0 0 4 5 4 4 5 5

The frequencies of the different scores can be summarized as:

Score Frequency Frequency (%)

0 4 13%

1 3 10%

2 5 17%

3 5 17%

4 6 20%

5 7 23%

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iv). QUALITATIVE DATA

Qualitative data is extremely varied in nature. It includes virtually any

information that can be captured that is not numerical in nature.

Qualitative data are generally (but not always) of less value to

scientific research than quantitative data, due to their subjective and

intangible nature. It is possible to approximate quantitative data

from qualitative data

Qualitative methods are ways of collecting data which are concerned

with describing meaning, rather than with drawing statistical

inferences. What qualitative methods (e.g. case studies and

interviews) lose on reliability they gain in terms of validity. They

provide a more in depth and rich description.

v). QUATITATIVE DATA

Information that can be counted or expressed numerically. This type

of data is often collected in experiments, manipulated and

statistically analyzed. Quantitative data can be represented visually in

graphs and charts.

Quantitative methods are those which focus on numbers and

frequencies rather than on meaning and experience. Quantitative

methods (e.g. experiments, questionnaires and psychometric tests)

provide information which is easy to analyze statistically and fairly

reliable. Quantitative methods are associated with the scientific and

experimental approach and are criticized for not providing an in

depth description.

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Reference:

http://www.stats.gla.ac.uk/

en.wikipedia.org

www.isixsigma.com

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Question 5

a). What are the Quantiles? Explain and illustrate the

concepts of Quartiles, deciles and Percentiles?

Marks: 10

b). The geometric mean of 10 observations on a certain

variable was calculated to be 16.2. It was later discovered

that one of the observations was wrongly recorded as

10.9, when in fact it was 21.9. Apply appropriate

correction and calculate the correct geometric mean.

Marks: 10

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a).

QUANTILE

“Quantiles are points taken at regular intervals from the

cumulative distribution function (CDF) of a random variable”

For example quantiles divide distribution into four parts.

QUARTLE

“A quartile is any of the three values which divide the sorted

data set into four equal parts, so that each part represents one

fourth of the sampled population.”

Each quartile contains 25% of the total observations. Generally,

the data is ordered from smallest to largest with those

observations falling below 25% of all the data analyzed

allocated within the 1st quartile, observations falling between

25.1% and 50% and allocated in the 2nd quartile, then the

observations falling between 51% and 75% allocated in the 3rd

quartile, and finally the remaining observations allocated in

the 4th quartile.

Its formula is:

Quartiles = l + h(2n/4 - pcf) f where

l = lower class boundary of specific class

h = class interval

f = frequency of specific class

n = total frequecy i.e. ∑ f = n

pcf = cumulative frequency of preceding class

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DECILES

Any one of the numbers or values in a series dividing the

distribution of the individuals in the series into ten groups of

equal frequency.

Since nine points divide the distribution into ten equal parts,

we shall have nine deciles denoted by D1, D2, ………. D9.

The formula of decile is:

Decile (DL) = l + h(2n/10 - pcf) f where


h = class interval




PERCENTILES

Those values which divide the total data into hundred equal

parts are called percentiles.

Since 99 points divide the distribution into hundred equal parts,

we shall have 99 percentiles denoted by P1,P2, ………… P99.

Its formula is:

Percentile (Pi) = l + h(2n/100 - pcf) f where


h = class interval




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b).

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Assignment QT Col MBA Semester 1