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 / ASODL

Office 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”

ASSIGNMENT – ‘A’

Q. 1 Define quantitative technique. Name the two major divisions in which you 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 a well structure framework for solution.

The 2 different divisions of quantitative techniques are:-

1) Business statistics2) 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 of operation & optimum solution to the problem.The modus of operandi of each are:-

1. formulate the problem2. analyse the data & collection of data3. analyse the data

a. central tendencyi) meanii) medianiii) mode

b. Dispersioni) Standard deviationii) Mean deviationiii) Skewness

CORRELATION, REGRESSION ANALYSIS ETC.Testing

Hypothesis be it data & accurate to what extentInterpret the resultComplement the result

Q. 2 Show for the following function f(x) = x + has its minimum value

greater than its max. value.

Ans. f(x) = x +

Let y = f(x)

y = x +

Differentiating on both sides w.r.t. x

(1)

For Maximum & minimum

x2 = 1x = + 1

now find

Diff. (1) with respect to x on both sides.

for maximum

< 0

> 0

This is satisfied when x = 1Hence maximum value of x is

x +

= 1 + = 2

And minimum value of x is

x +

= 1 + = 1

for f(x) = x + minimum value is greater than minimum value.

Computer the price Index using(a) weighted A.M. of price relatives &(b) weighted G.M. of price relatives

A. weighted A.M. year 1999

% of expenditure (x) Price (1999) (w) wx

Food 35 70 2450

Clothing 15 45 675

Fuel 10 20 200

Rent 20 80 1600

Misc. 30 40 800

w = 255 wx = 5725

For the year 1999 A.M. =

weighted A.M. – year 2000(x)% of expenditure Price (2000)w wx

Food 35 90 3150

Clothing 15 50 750

Fuel 10 25 250

Rent 20 70 1400

Misc. 20 30 600

w = 265 wx = 6150

For the year 2000 A.M. =

= 23.20

B. Weighted G.M. Year 1999 x% of expenditure (x) Prices 1999 log x F log

Food 35 70 1.8451 64.

Clothing 15 45 1.6532 24.

Fuel 10 20 1.3010 13.0

Rent 20 80 1.9031 38.

Misc. 20 40 1.6021 32.09

G.M. = Antilog

= Antilog

= 52.84

weighted G.M. : Year 2000

x% of expenditure (x) Prices 2000 log x F log

Food 35 90 1.954 68.39

Clothing 15 50 1.6990 251.41

Fuel 10 25 1.3979 13.97

Rent 20 70 1.845 36.90

Misc. 20 30 1.477 29.50

x = 100 f log x =174.30

G.M. = Antilog

= Antilog

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

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 =

Median = 60 +

X F 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 =

=

= 15 1.72

= 25.9Also calculate(a) Coefficient of correlation(b) Interquartile Range (Q3 – Q1)(c) Skewness

A) Coefficient of correlation

X y xy x2 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

=

= 91290

=

= 0.978B. Interquartile Range (Q3 – Q1)

A. Quartile = < + j Pef ilf

For Q1, j = 1

N = 230 , = 57.5

This falls in the range of 3045.

< 30 + 57.5

= 4178for Q3, j = 3

N = 230,

Range 7590, < = 75, Pef = 157, j – 45

Q3 = 75 + 1725 157

= 80.166Interquartile Range= Q3 Q1

= 80.166 4178

= 38.386

C) Skewness

Skewness = mean

Mode = < + fm f I (2fm f 1 f2 h

f1 = 60, fm = 50, f1 = 42, f2 = 45, h = 15

Mode =

= 69.23

Skewness = 60.65

= 0.33

Q.4A Which of brand of tyre would you use on the fleet of trucks & why?

Ans.

Class Interval

Freq. Mid point

fd

0-25 08 22.5 2 1 32

25-30 15 27.5 1 15 13

30-35 12 32.5 0 0 0

35-40 18 37.5 1 18 18

40-45 13 42.5 2 26 52

45-50 9 47.5 3 27 81

N=75 fd=40 fd2=118

C =

=

= 7.67 (Brand A)

Brand B

Class Interval

Freq. Mid point

fd

0-25 06 22.5 2 12 24

25-30 20 27.5 1 20 20

30-35 32 32.5 0 0 0

35-40 30 37.5 1 30 30

40-45 12 42.5 2 24 48

45-50 0 47.5 3 0 0

fd=22 fd2=122

C =

=

= 5.412 (Brand B)Hence, Std. Deviation of Brand B isles than Brand A. It has a high degree of uniformity of observation as well as homogeneity of a series. So Brand B, of tyres would be a better choice.

B. Answer the following questions: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. IncomeDay 1 50Day 2 50Day 3 50Day 4 50Day 5 50Day 6 50Day 7 50

I = 350

Mean deviation =

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

Median = 35 3

= 105New 6 = 1.6 3

= 4.8Variance = (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 each observation.

Mode = 55 + 8 = 63Standard Deviation= 4.33 (no change)

4) The mean & std. deviation of a distribution are 152 respectively. Find std. distribution of each observation & multiplied by 5.

Mean = 15 5 = 75

Std. Deviation = 2 5 = 10

Q. 5 Define the following matrix with an example of each.

A. Row Matrix

Ans. A matrix having only one row is called a row matrix for example:[4 1 2 7] is a 1 4 matrix or row matrix having 4 elements.

B. Column Matrix

Ans. A matrix having only one column is called a column matrix for example:

is a 31 matrix having 3 elements

C. Zero or Null Matrix

Ans. A matrix (square or rectangular has all its elements equal to 0 is called a NULL

The Matrix is a 23 null matrix

D. Square Matrix

Ans. When due number or rows of a matrix is equal to its member of columns, it is said to be as a square matrix. For example:

is a square matrix

E. Diagonal Matrix

Ans. A square matrix a = (a i j) n k n is said to be diagonal matrix if a i j = 0 for I = j for example, the matrix

is a 33 diagonal matrix.

The elements of a i j of matrix A, for I = j are called the diagonal elements & the line along which they lie is called the principal diagonal.

F. Scalar Matrix

Ans. A diagonal matrix in which its diagonal elements are equal is called a scalar matrix. For example:

is a 33 scalar matrix

G. Unit or Identity Matrix

Ans. A scalar matrix is which all its diagonal elements are unity is called on Identity matrix.

is a 33 Identity Matrix

H. Upper Triangular Matrix

Ans. A square matrix A = (a i j) is said to be upper diagonal if a i j = 0 for I > j

is a Lower Triangular

J. Comparable Matrix

Ans. In this both A & B elements are of the same order. Both the elements of A & B should be equal to each other in no.

Q.5 B Solve the following equations using Matrix method:2x + y + 32 = 9

x + y + x = 6 x + y + 2 = 2

= 2(1 + 1) + 1 (1 1) + 3 (1 + 1)

= 4 6 = 10

= 9(2) (4) + 3(8)

= 18 4 + 24

= 10

= 8 12 = 20

= 16 + 4 18 = 30

x =

y =

z =

ASSIGNMENT – B

Q. 1 Calculate the Rank correlation & coefficient.

Ans.

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

Where D = R1 R2 Ranks of x & y

r =

=

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

Q. 2 Fit a straight line trend by the method of least square to the following data:Taking u = x 1993

v = y 255

Ans.u v uv u2

2 1.5 30 41 0 0 10 30 0 01 5 5 12 25 50 40 15 85 10

v = na + bu15 = 5(a) + 0

a = 3Multiplying (1) both sides by u

vu = 4a + bu2

= 8.5 = 0 + b(10)b = 8.5

Hence equationu = a + buv = 3 + 8.5u

Substituting back the value of u & v(y 255) = 3 + 8.5 (x 1993)

y 255 = 3 + 8.5 16940.4

[y = 8.5 16688.5]

b. Likely production for the year 2000y = 8.5 (2000) 16688.5

= 311.5

c. Double production that of year 19932(225) = 8.5x 16688.5

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. Show that of this group 95% had income exceeding Rs.668 & only 5% had income exceeding Rs.832.

Ans. Standard Normal Price

2 =

Here x = 668, = 750, 6 = 50

2 = 668

= 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

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

= 5.70 Approx.

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. What’s the possibility that she is above 30 years of age.

Ans. 5000 people 3000 females above 30 years, 1200 people : 200 females choose one : femaleProbability that she’s above 30 eyars

(s) = 3000(f) = 200

So, the required probability is

=

ASSIGNMENT – 2

CASE STUDY

Q. 1 Arrange in ascending order01 112 127 133 14104 116 128 134 14105 117 129 138 14510 125 130 139 14611 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 Frequency1220202424

(b) Cumulative frequency (<) & cumulative relative frequency (<)

Class Interval Cum. Freq. Cum rel. freq.

More than 0 25 100

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

B) Frequency Polygon

Assignment – 3

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

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

3. Any characteristic which can assume different values can be called a variable 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 > 0X if X < 0 True / False

9. If the revenue function is TR = 50 Q0.5 Q2

Then Marginal Function MR = 50 Q True / False

10. If the Total cost function TC = 500+300 Q5Q2 Then Marginal Cost Function MC = 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<0 True / False

13. Derivative of product of two functionsd/dx (u v) = u d/dx (v) + v d/dx True / False

14. Derivative of loge u

d/dx(loge u) = 1/u loge du/dx True / False

15. A matrix is an array of m x n numbers arranged in m columns & n rowsTrue / False

16. A square matrix is one where number of rows = (number of columns)2

True /False

17. [4 1 2 7] is a a. 4 1 matrix b. 1 4matrix

18. if A = [2 3 4] A2 = [21 6][1 4 5] [3 4 7] [6 7 8] [4 5 8]

Then A2 is called the TRANSPOSE OF A True / False

19. The INVERSE of the INVERSE MATRIX is the original matrix. True / False

20. Measure of Central Tendency is a data set refers to the extent to which the observations are scattered. True / False

21. The value of all observations in the data set is taken into account when we calculate its mean. True / False

22. If the curve of a certain distribution tails off towards the right end of the measuring scale on the horizontal axis the distribution is said to be positively skewed. True / False

23. Extreme values in a data having a strong effect upon the Mode True / 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 is calleda. Mode of the series b. Median of the series

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

30. Value of correlation lies betweena. 0 to 1 b. 1 to 1

31. Kari Parson’s coefficient of correlation is given by

“r” =

32. “Line of best fit” is determined by “Method of Lease Squares”a. 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 equal intervals

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

37. Yearly data are independent of the effects of seasonal variations True / 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