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ADL-07-Quantitative Techniques in Management-AM2

Assignment - A

Question 1: Define quantitative techniques. Name the two major divisions in which you can divide these techniques. Explain the modus oprendi of each and give names of a few techniques under each category.

Question 2: State and illustrate Addition & Multiplication Theorem of Probability.

Question 3 (a) Calculate the Mean Median and Standard Deviation of the following data

Wages upto (Rs.)	15	30	45	60	75	90	105	120
No of workers	12	30	65	107	157	157	202	230

Question 3 (b) Also calculate: (i) Coefficient of correlation (ii) Interquartile Range

Question 4 (a) There are three companies A, B, and C manufacturing 40%, 35% and 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.

Question 4 (b) Answer the following questions:
          (i) The income of a person in a particular week is Rs. 50.00 per day. Find mean deviation of his income for the week.
          (ii) The median and variance of a distribution are 35 & 2.56 respectively. Find median and variance if each observation is multiplied by 3.
          (iii) The mode and standard deviation of a distribution are 55 and 4.33 respectively.
          (iv) The mean and standard deviation of a distribution are 15 and 2 respectively. Find mean and standard distribution if each observation is multiplied by 5.

Question 5 (a) A random sample of 200 tins of oil gave an average weight of 4.95 kgs with a SD of 21kg. 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):

Question 5 (b) Find minimize cost for following matrix using VAM methods.

Factories	Warehouse 1	Warehouse 2	Warehouse 3	Supply
F1	16	20	12	200
F2	14	8	18	169
F3	26	24	16	90
Demand	180	120	150

Assignment - B

Question 1: Two women customers are randomly selected in a super market and are asked to taste 7 different types of juices and rank them in order of preference from 7 (best) to 1 (lcast desirable). The results are as follows:

Juices	A	B	C	D	E	F	G
MANU	2	1	4	3	5	7	6
SONU	1	3	2	4	5	6	7

a. Calculate t he Rank Correlation and Coefficient

b. Is the relationship significant?

Question 2: Fit a straight line trend by the method of least square to the following data

Year	Production
1991	240
1992	255
1993	225
1994	260
1995	280

(a) Estimate the likely production for the year 2000

(b) 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 manually distributed with mean Rs. 750 per months and standard deviation equal to 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. When is the probability that she is above 30 years of age?

Case Study

For determining IQ of students, standard test were conducted and scores recorded. The recorded scores of 25 students are given below:

… …

Question 1. Arrange data into an ordered array.

Question 2. Construct a 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. The data is written down as collected it is called:

2. A discrete variable can take

3. Number of children in a family is an example of:

4. Heights of models in a beauty contest is an example of:

5. It gives equal weightage to all precious months:

6. Irregular vario us is a component of

7. The value most often repeated in a series of observation is called:

8. The difference between the largest and the smallest observations is called:

9. The middle most value in a series of observations arranged in an array is called:

10. Value of correlation lies between:

11. A time series is a set of observation taken at:

12. Quartiles are those which divide the total data into:

13. Extreme values in a data have a strong effect upon the Modes:

14. If the value of mean = 35.4 and value of median = 35 the shape of the curve skewed is "rig ht"

15. When the value of two var iables mo ve in the same direction, the correlation is said to be positive:

16. Linear pro gramming deals with only minimization problems:

17. Graphical methods fails where any of the constraints is parallel is objective function:

18. Dual of dual is notprimal:

19. Quantitative methods involve decision making through data analysis:

20. Operation Research emerged during Second World War

21. One of the objective of averag ing is compar ison:

22. Standard Deviation is simplest measure of dispersion

23. Probability lies between 0 and 1:

24. Coefficient of correlation is independent of change of origin and scale:

25. In a pie diagram the whole is represented by 180 degrees:

26. Skewness is lack of symmetry in a curve;

27. Conditional probability of an event A when B has already occurred is P(A/B)
= P (A 7 B)/P (B):

28. Probability of 53 Sunday in a leap year is 2/7:

29. Measure of Central Tendency is a data set refers to the extent to which the observations are scattered:

30. The value of all obser vations in the data set is taken into account when we calculate its mean:

31. If the curve of a certain distribution tails off towards the right end of the measur ing scale on the ho rizontal axis the distr ibution is said to be positively skewed:

32. "Line of the best fit" is determined by "Method of least Squares":

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

34. Regular variation includes only seasonal var iation:

35. Year ly data are independent of the effects of seasonal variatio n:

36. Statistical results are always misleading:

37. GM - Square Root of (AM * IIM):

38. Variances are additive:

39. Quantitative techniques facilitate classification and comparison of data:

40.Any characteristic which can assume different values can be called a Variable: