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ADL 07 Quantitative Techniques in Management V1

Assignment – A

Question 1. Define Quantitative Techniques. Name the two major divisions in

which you can divide these techniques. Explain the modus oprendii of each and

give names of a few techniques under each category.

Question 2. a. Show for the following function f(x) = x + 1/x has its Min value

greater that its Max value.

Question 2. b. An enquiry into the faculty budgets of middle class families gave

the following information given below.

Expenses onFoodClothingFuelRentMiscellaneous

%age of Expenditure3515102020

Price in 1999 (Rs.)7045208040

Price in 2000 (Rs.)9050257030

Compute the price index using

(a). weighted A. M. of price relatives &

(b). weighted G.M. Of price relatives

Question 3. a. Calculate the Mean, Median and Standard Deviation of the

following data

Wages Up to (Rs.)153045607590105120

No. of Workers123065107157202222230

Question 3. b. Also calculate

(a). Coefficient of correlation

(b). Interquartile Range (Q3-Q1)

(c). Skewness

Question 4. a. Two brands of tyres are tested with the following results.

Life (in thousands of Kms)Brand ABrand B

20-2586

25-301520

30-351232

35-401830

40-451312

45-5090

Which brand of tyre would you use on the fleet of trucks and why?

Question 4. 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.

2. The median and variance of a distribution are 35 & 2.56 per day. Find

median and variance if each observation is multiplied by 3.

3. The mode and standard deviation of a distribution are 55 and 4.33

respectively.

Find mode and standard deviation if 8 is added to each observation.

4. The mean and standard deviation of a distribution are 15 & w

respectively. Find mean and standard distribution if each observation is

multiplied by 5.

5. a. Define the following Matrix with an example of each.

a. Row Mat rixb. Column Matrixc. Zero or Null Matrix

d. Square Matrixe. Diagonal Matrixf. Scalar Matrix

g. Unit or Identity Matrixh. Upper Triangular Matrixi. Lower Triangular

Matrix

j. Comparable Matrixk. Equal Matrix

5. b. Solve the following equations using MATRIX method.

-2x + y + 3z = 9

x + y + x = 6

x – y + z = 2

Assignment – B

Question 1. Two women customers are randomly selected in a super ma rket and are

asked to taste 7 different types of juices and rank them in order of preference

from 7(best) to 1(least desirable). The results are as follows.

JuicesABCDEFG

MANU2143576

SONU1324567

1. Calculate the Rank Correlation and Coefficient.

2. Is the relationship significant?

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

following data.

YearProduction

1991240

1992255

1993225

1994260

1995280

b. Estimate the likely production for the year 2000.

c. When will the production be double that of year 1993?

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

distributed with mean Rs.750PM and standard deviation =Rs.50 show that of this

group 95% had income exceeding Rs.668 and only 5% had income exceeding RS.832.

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

years of age and 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 is the probability that she is above 30 years of age?

Case Study

For determining IQ of students, standard tests were conducted and scores

recorded. The recorded scores of 25 students are given below

105145130150110

127138112141140

125131117101139

104134128146141

133125111116129

Questions to be answered:

Question 1. Arrange data into ordered array.

Question 2. Construct grouped frequency distribution with suitable class

intervals.

Question 3. Compute for the data:

–Relative frequency

–Cumulative frequency (<) & Cumulative Relative Frequency (<)

–Cumulative frequency (>) & Cumulative Relative Frequency (>)

Question 4. Construct for the data

a. A histogram

b. A frequency polygon

c. Cumulative relative ogive (<)

d. Cumulative relative ogive (>)

Question 5. How many students have IQ <130 and How many students have IQ ≥ 130.

Assignment – C

1. Quantitative Techniques facilitate classification and comparison of data

True /False

2. If the data is written down as collected it is called

(a). Ordered Data

(b). Raw Data

(c). An Array

3. Any characteristic which can assume different values can be called a variable

True /False

4. A discrete variable can take

(a). Only whole number values

(b). An infinite number of values.

5. Number of children in a family is an example of

(a). Continuous Variable

(b). Discrete Variable

6. Heights of Models in a beauty contest is an example of

(a). Continuous Variable

(b). Discrete Variable

7. Rule determining the area is written as A = X

where A is a function of Variable X.

Then A is called

(a). Independent Variable

(b). Dependent Variable

8. The Absolute Value of a real number is True / False

9. If the revenue function is TR = 50Q – 0.5Q2 then Marginal Function MR = 50 –

Q

True / False

10. If the Total Cost Function TC = 500 + 300Q – 5Q2 Then Marginal Cost Function

MC=500-10Q

True / False

11. Conditions for Local Maxima are

First order Function d2y/dx2 > 0

True / False

12. Conditions for local Minima are

First order Function dy/dx = 0 Second Order Function d2y / dx2 < 0

True / False

13. Derivative of product of two functions

d/dx(uv) = u d/dx (v) + v d/dx

True / False

14. Derivative of loge

d/dx (loge u) = 1/u log e du/dx

True / False

15. A matrix is an array of m x n numbers arranged in m-columns and n-rows

True / False

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

True / False

17. [4 1 2 7] is a

(a). 4 x 1 matrix

(b). 1 x 4 matrix

18. Then A 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 whim tt1e

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 tt1e horizontal axis the distribution is said to be

positively skewed.

True /False

23. Extreme values in a data have 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. It gives equal weightage to all previous months

(a). Exponential Smoothing

(b). Moving Average

(c). Weighted Average

26. The value most often repeated in a series of observations is called

(a). Median

(b). Mode

(c). Mean

27. The difference between the largest and the smallest observations is called

(a). Geomet ric Mean

(b). the Range

(c). the Mode

28. The middle most value in a series of observations arranged in an array is

called.

(a). 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 between

(a). 0 to 1

(b). -1 to 1

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

32. “Line of best fit” is determined by “Method of Least Squares”

True /False

33. A decision tree is a graphic model of a decision process

True /False

34. A time series is a set of observations taken at

(a). Specified Intervals

(b). Not necessary at equal intervals

35. Quartiles are those which divide the total data into

(a). 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 effect s 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

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