ADL 07 Quantitative Techniques in Management V1

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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 &#8805; 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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