38593356 Assignement QTM Quantitive Techique Mgt (2)

8/2/2019 38593356 Assignement QTM Quantitive Techique Mgt (2)

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AMITY SCHOOL OF DISTANCE LEARNINGPost Box No. 503, Sector 44,

Noida 201 303

ASSIGNMENT No. ADL07

Subject Name & Code : QUANTITATIVE TECHNIQUESStudy Centre : NOIDA

Enroll No. : 17070105327

Date :

Course MBA (EFT) IV Semester

ASSIGNMENT INSTRUCTION

(a) Total weightage given to these assignments is 30%.

(b) All assignments are to be completed in your own hand writing.

(c) All questions are required to be attempted.

(d) Three assignments i.e A, B & C are to be answered. Assignments A will

carry Five subjective questions (10 marks). Assignment B will carry

three subjective questions with a (10 marks) and Assignment C will

carry Forty objective type questions (10 marks)

(e) All the three assignments are to be completed by due dates (specified from time

to time) and mailed / given by hand for evaluation at the ASODL office Noida /

your Study Centre.

(f) The evaluated assignments can be collected from your study center / ASODLOffice after Six week. Thereafter these will be destroyed at the end of each

semester.Signature :

Name : NIMIT GUPTA

Date : ---------------------------------------------------

() Tick mark in front of the assignments submitted

Assignment A Assignment B Assignment C


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ASSIGNMENT A

Q. 1 Define quantitative technique. Name the two major divisions in whichyou can divide these techniques. Explain the modus of operandi of

each and give names of a few technique under each category.

Ans. Quantitative techniques attempts to provide a systematic & rational approach

to the fundamental problems involved in the control of system by making

decisions, a sense achieve the best results considering all the information that

can be profitably used. Thus it is scientific method employed for problem

solving & decision making by the management.

Quantitative analysis is now extended & several alias of business operation& responsibilities probably the most effective approach to handling of some

types of decision problems. A significant benefit of attaining some degree

of profiency with quantitative methods is exhibited in the way problems are

formulated. A problem has to well defined before it can be formulated in awell structure framework for solution.

The 2 different divisions of quantitative techniques are:-

1) Business statistics

2) Operative Research

BUSINESS STATISTICS

Statistical data & statistical method are of immense helping the proper

understanding of the economic problem & in the formulations of economic

policies as well as evaluating of their effect for example in order to check the

overgrowing population, if emphasis has been placed on family planning

methods one can ascertain statistically the efficiency of such methods in

attaining the desired goals.

OPERATION RESEARCH

It is the application of scientific methods, technique & tools to problems

involving the operation of system. So as to provide these in control ofoperation & optimum solution to the problem.


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The modus of operandi of each are:-

37.formulate the problem

38.analyse the data & collection of data

39.analyse the dataa. central tendency

i) mean

ii) median

iii) mode

b. Dispersion

i) Standard deviation

ii) Mean deviation

iii) Skewness

CORRELATION, REGRESSION ANALYSIS ETC.

Testing

Hypothesis be it data & accurate to what extent

Interpret the result

Complement the result

Q. 2 State and illustrate Addition and Multiplication Theorem ofprobability.

Ans. Addition Theorem----

A compound event is any event combining two or more simple events.The notation for addition rule is: P(A or B) = P(event A occurs or event B occurs or they bothoccur).When finding the probability that event A occurs or event B occurs, find the total numbers ofways A can occurs and the number of ways B can occurs, but find the total in such a way thatno outcome is counted more than once.General addition rule is :P(A or B) = P(A) + P(B) - P(A and B), where P(A and B) denotes that A and B both occur at the

same time as an outcome in a trial procedure.It is a special addition rule that shows that A and B cannot both occur together, so P(A and B)becomes 0:If A and B are mutually exclusive, then P(A) or P(B)= P(A or B) = P(A) + P(B)

Addition Rule

The addition rule is a result used to determine the probability that event A or event B

occurs or both occur.


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The result is often written as follows, using set notation:

where:

P(A) = probability that event A occurs

P(B) = probability that event B occurs

= probability that event A or event B

occurs

= probability that event A and event B

both occur

Formutually exclusive events, that is events which cannot occur together:

= 0

The addition rule therefore reduces to

= P(A) + P(B)

Forindependent events, that is events which have no influence on each other:
http://l/http://l/http://l/http://l/http://l/http://l/


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The addition rule therefore reduces to

Example

Suppose we wish to find the probability of drawing either a king or a spade in a single draw

from a pack of 52 playing cards.

We define the events A = 'draw a king' and B = 'draw a spade'

Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we

have:

= 4/52 + 13/52 - 1/52 = 16/52

So, the probability of drawing either a king or a spade is 16/52 (= 4/13).

See also multiplication rule.

Multiplication Rule

The multiplication rule is a result used to determine the probability that two events, A and

B, both occur.

The multiplication rule follows from the definition of conditional probability.

The result is often written as follows, using set notation:
http://l/http://l/


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where:

P(A) = probability that event A occurs

P(B) = probability that event B occurs

= probability that event A and event B occur

P(A | B) = the conditional probability that event A occurs given that event B hasoccurred already

P(B | A) = the conditional probability that event B occurs given that event A has

occurred already

For independent events, that is events which have no influence on one another, the rulesimplifies to:

That is, the probability of the joint events A and B is equal to the product of the individual

probabilities for the two events.

Q. 3A Calculate the mean, median & standard deviation of the following

data:

Ans.

Wages No. of workers Mid values Fx

0 15 12 7.5 90

15 30 18 22.5 405


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30 45 35 37.5 1312.5

45 60 42 52.5 2205

60 75 50 67.5 3375

75 90 45 82.5 3712.5

90 105 20 97.5 1950

105 120 08 112.5 900

Mean =

1395060.65

N 230

fx= =

Median = 60 +

230 10715 62.4

50

=

X F 76.5

12u x=

Fu U2 Fu2

7.5 12 4 48 16 192

22.5 18 3 54 09 162

37.5 35 2 70 4 140

52.5 42 1 42 1 42

67.5 50 0 0 0 0

82.5 45 1 45 1 45

97.5 20 2 40 4 80

112.5 08 3 24 9 72

Fu=105 fu2=733

C =

22

15 fx fx

n n

=

2

733 10515

230 230x

= 15 1.72

= 25.9


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Also calculate

(a) Coefficient of correlation

(b) Interquartile Range (Q3 Q1)

A) Coefficient of correlation

X y xy x 2 y2

15 12 180 225 144

30 30 900 900 900

45 65 2925 2025 4225

60 107 6420 3600 11449

75 157 11775 5625 24649

90 202 18180 8100 40804

105 222 23310 11025 49284

120 230 27600 14400 52900

x=540 y=1025 xy=9120 x2=45900 y2=185399

Coefficient of correlation

R = xy Nx y

=

2 2

2 2N N

x yx y

= 91290

( )540 1025

8

=

2 2

540 102545900 185399

8 8

= 0.978

B. Interquartile Range (Q3 Q1)


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A. Quartile = < + j

N

4 Pef ilf

For Q1, j = 1

N = 230 ,

N

4 = 57.5

This falls in the range of 3045.

< 30 + 57.5

3015

35

= 4178

for Q3, j = 3

N = 230,

3N

172.54 =

Range 7590, < = 75, Pef = 157, j 45

Q3 = 75 + 1725 157

15

45

= 80.166

Interquartile Range

= Q3 Q1

= 80.166 4178

= 38.386

Q.4A There are three companies A,B and C manufacturing 40%, 35%, 25

% bolts respectively. All these companies are manufacturing 3%, 5%

and 8% defective bolts respectively. If one bolt is selected find the

probability that this bolt is taken from company B.

Ans.

B. Answer the following questions:


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1. The income of a person in a particular week is Rs.50 per day, find

mean deviation of his income for the week.

Ans. Income

Day 1 50

Day 2 50

Day 3 50

Day 4 50

Day 5 50

Day 6 50

Day 7 50

I = 350

Mean deviation =

I350

N =

2) The median & variance of a distribution are35 2.56 respectively.Find median &variance of each observation is multiplied by 3.

Median = 35 3

= 105

New 6 = 1.6 3

= 4.8

Variance= (4.8) 2

= 23.04

3) The mode & standard deviation of a distribution are 55 &4.33

respectively. Find mode & std. deviation of 8 is added to eachobservation.

Mode = 55 + 8 = 63

Standard Deviation= 4.33 (no change)


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4) The mean & std. deviation of a distribution are 15 2 respectively.Find std. distribution of each observation & multiplied by 5.

Mean = 15 5 = 75

Std. Deviation = 2 5 = 10

Q. 5(A) A random sampling of 200 tins of oil gave an average weight of 4.95

kgs with a SD of 21 kg . Do we accept the hypothesis of weight of 5 kg

per tin at 1% level(The value of Z at 1% level is 2.58).

(B) Find minimized cost for following matrix using VAM method.

ASSIGNMENT B

Q. 1 Calculate the Rank correlation & coefficient.

Ans.

Juices Manu (x) Sonu (y) D = xy D2

A 2 1 1 1

B 1 3 2 4

C 4 2 2 4

D 3 4 1 1

E 5 5 0 0

F 7 6 1 1

G 6 7 1 1

D2 = 12

Rank Correlation

Coefficient = 1 6

2

2

D

( 1)n n

Where D = R1R2 Ranks ofx &y


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r=

6(12)1

7(49 1)

=

6(12)1 0.785

7(48) =

Yes the relationship is significant as ris a +ve value (+ 0.785)

Q. 2 Fit a straight line trend by the method of least square to the following

data:

Taking u = x1993 v = y255

Ans.

u v uv u2

2 1.5 30 41 0 0 10 30 0 01 5 5 1

2 25 50 4

0 15 85 10v = na + bu

15 = 5(a) + 0

a = 3

Multiplying (1) both sides by u

v u = 4 a + bu2

= 8.5 = 0 + b(10)

b = 8.5

Hence equation

u = a + bu

v = 3 + 8.5u

Substituting back the value ofu & v

(y255) = 3 + 8.5 (x1993)

y255 = 3 + 8.5 16940.4


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[y = 8.5 16688.5]

b. Likely production for the year 2000

y = 8.5 (2000)

16688.5

= 311.5

c. Double production that of year 1993

2(225) = 8.5x16688.5

year 2016

Q. 3 a) The income of a group of 10,000 persons was found to be normally

distributed with mean Rs.750 PM & standard deviation = Rs.50. Showthat of this group 95% had income exceeding Rs.668 & only 5% had

income exceeding Rs.832.

Ans. Standard Normal Price

2 =6

x x

Herex = 668, x = 750, 6 = 50

2 = 668

750

50

= 1.64

Area to the right of the ordinate at 1.64 is

(0.4495 + 0.5000) = 0.9495 = 95%.

The member of persons getting above Rs.832

= 832 75050

= 1.64

Area to the right of ordinate at 1.64 is (0.5000) 0.4495 = 0.0505

= 5.70 Approx.


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Q.3 b) In a locality, out of 5000 people residing 1200 are above 30 years of

age & 3000 are females out of the 1200 who are above 30,200 are

females . Suppose after a person is chosen you are told that the person

is a female. Whats the possibility that she is above 30 years of age.

Ans. 5000 people 3000 females above 30 years, 1200 people : 200 femaleschoose one : female

Probability that shes above 30 eyars

(s) = 3000

(f) = 200

So, the required probability is

200

300

=

1

15


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ASSIGNMENT 2

CASE STUDY

Q. 1 Arrange in ascending order

01 112 127 133 141

04 116 128 134 141

05 117 129 138 145

10 125 130 139 146

11 125 131 140 150

Q. 2 Grouped frequency distribution

Class Intervals Frequency

100 110 3

110 120 5

120 130 5

130 140 6

140 150 6

f= 25

Q. 3 (a) Relative Frequency

12

20

20

2424

(b) Cumulative frequency (


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More than 110 22 88

More than 120 17 68

More than 130 12 48

More than 140 06 24

Q. 4 (a)

Class Interval Frequency

100 110 3

110 120 5

120 130 5

130 140 6

140 150 6

A) HISTOGRAM

6-

5-

4-

3-

2-

1-

0100 110 120 130 140 150


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40.Frequency Polygon

6-

5-

4-

3-

2-

1-100 110 120 130 140 1500


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Assignment 3

1. Quantitative Techniques facilitate classification and comparison of dataTrue / False

2. If the data is written down as collected it is calleda. Ordered Datab. Raw Datac. An Array

3. Any characteristic which can assume different values can be called avariable True /False

4. A discrete variable can takea. Only whole number values b. An infinite number of values

5. Number of children in a family is an example ofa. Continuous variable b. Discrete variable

6. Heights of Models in a beauty contest is an example ofa. Continuous variable b. Discrete variable

7. Rule determining the area is written as A=X2 where A is a function of

Variable X, then A is calleda. Independent Variable b. Dependent Variable

8. The Absolute Value of a real number isO if X = 0

[X] = X if X > 0

X if X < 0 True / False


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9. If the revenue function is TR = 50 Q0.5 Q2Then Marginal Function MR = 50 Q True / False

10. If the Total cost function TC = 500+300 Q5Q2 Then Marginal Cost FunctionMC = 500 10Q True / False

11. Conditions for Local Maxima areFirst order Function dy/dx=0 Second Order Function d2y/dx2>0 True / False

12. Conditions for local Maxima areFirst order Function dy/dx=0 Second Order Function d2y/dx2


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42.Extreme values in a data having a strong effect upon the ModeTrue /

False

24. If the value of mean = 35.4 and value of media = 35 the shape of the curve

skewed is right. True /False

25. If gives equal weightage to all previous monthsa. Exponential Smoothingb. Moving Averagec. Weighted Average

26. The value most often repeated in a series of observations is calleda. Median b. Mode c. Mean

27. The difference between the largest and the smallest observation is calleda. Geometric Mean b. The Range c. The Mode

28. The middle most value in a series of observations arranged in an array iscalleda. Mode of the series b. Median of the series

29. When the value of two variables move in the same direction, the correlationis said to be positive. True /

False

30. Value of correlation lies between

a. 0 to 1 b. 1 to 1

31. Kari Parsons coefficient of correlation is given by

r =

Cov(X,Y)

x y

32. Line of best fit is determined by Method of Lease Squaresa. True b. False

33. A decision tree is a graphic model of a decision processa. True b. False

34. A time series is a set of observations taken ata. Specified Intervals b. Not necessary at equalintervals


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35. Quartiles are those which divide the total data intoa. Four Equal Parts b. Ten Equal Parts c. Hundred equal parts

36. Regular variation include only seasonal variations True / False

43.Yearly data are independent of the effects of seasonal variationsTrue / False

38. For index numbers, base year should be a year of normalcy True / False

39. GM = SQ ROOT OF (AM * HM) True / False

40. Variances are additive True / False

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38593356 Assignement QTM Quantitive Techique Mgt (2)