Amity dbm assignments solution
Section A
 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.
 a. Show for the following function f(x) = x + 1/x has its Mi value greater that its ax value.
 An enquiry into the faculty budgets of middle class families gave the following information given below.
 a. Calculate the Mean, Median and Standard Deviation of the following data
Wages Up to (Rs.) 15 30 45 60 75 90 105 120
No. of Workers 12 30 65 107 157 202 222 230
 Also calculate
 Coefficient of correlation
 Interquartile Range (Q3Q1)
 Skewness
 a. Two brands of tyres are tested with the following results.
Life (in thousands of Kms) Brand A Brand B
2025 8 6
2530 15 20
3035 12 32
3540 18 30
4045 13 12
4550 9 0
Which brand of tyre would you use on the fleet of trucks and why?
 Answser the following guestions.
 The income of a person in a particular week is Rs.5o per day. Find mean deviation of his income for the week.
 The median and variance of a distrthution are 35 & 2.56 per day. Find median and variance if each observation is multiplied by 3.
 The mode and standard deviation of a distrnbution are 55 and 4.33 respectively. Find mode and standard deviation if 8 is added to each observation.
 The mean and standard deviation of a distribution are 15 & w respectively. Find meamn and standard distribution if each observation is multiplied by 5.
 a. Define the following Matrix with an example of each.
 Row Matrix b. Column Matrix c. Zero or Null Matnx
 square Matrix e. Diagonal Matrix f. Scalar Matrix
 unit or dentity Matrix h. Upper Triangular Matrix i. Lower Triangular Matrix
 Comparable Matrix k. Equal Matrix
 b. Solve the following equations using MATRIx method.
2x ÷ y + 3z = 9
x.+.y.+.x =6.
xo.y.+.z =2.
_{Section B}
 _{ 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(least 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 } 
 _{ Calculate the Rank Correlation and Coefficient. }
 _{ Is the relationship significant? }
_{ }
 _{ a. 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 }
 _{ Estimate the likely production for the year 2o0o. }
 _{ when will the production be double that of year 1993? }
_{ CASE STUDY }
_{ }
_{Case Study}
_{The marks obtained by seven students in Statistics and Accountancy are as follows:}
_{Age(X) 56 42 36 47 49 42 60 72 63 55 }
_{ }
_{Blood 147 125 118 128 145 140 155 160 149 150}
_{Pressure(Y) }
_{ }
 _{Given the form of the scattered diagram, does it appear that a straight line provides an accurate}
_{ model for the data?}
 _{Find the correlation coefficient between Age(X) and Blood Pressure(Y) and discuss its nature.}
 _{Find the two lines of regression.}
 _{Estimate the blood pressure of a woman whose age is 45}
_{
}
_{Assignment – C }
_{ (Objective type Questions) Total Marks 10 }
Ques.1 a sequence of interrelated decisions made either simultaneously or over several time periods called dynamic decisions.
 dynamic decisions
 static decisions
 Both
 None
Ques.2 Stocking of an item for sale in a certain trade fair, illustrates a
 Static decision
 Where uncertainly exists
 Nature is opponent.
 All of above
Ques.3 Quantitative analysis is also called
 Operations research
 Management science
 Quantitative techniques
 All the above
Ques.4 Quantitative research provides the fundamental connection between
 empirical observation and mathematical expression
 empirical observation and qualitative expression
 empirical observation and social expression
 empirical observation and all expression
Ques.5 Most of the business decisions can be made on the basic of
 Rule of thumb
 Commonsense
 Snap judgment.
 Quantitative Techniques
Ques.6 Statistics is a branch of
 applied physics
 applied mathematics
 applied commerce
 Dramatics
Ques.7 The mean of 7, 12, 24, 20, 19 is
 14
 16
 15.4
 16.4
Ques.8 ∑ (X/c) =
 ∑ ( X)/n c
 ∑ ( X)/∑ c
 ∑ ( X)/c
 X/c.
Ques.9 Midterm exam scores for a small advanced neuroanatomy class are provided below. Scores represent percent of items marked correct on the exam.
87,99,75,87,94,75,35,88,87,93
The mode of the distribution
 75
 87
 88
 94
Ques.10 Which measure of Central tendency is most efficient
 Mean
 Median
 Mode
 All are equal
Ques.11 Mean Deviation can be calculated from
 Mean
 Median
 All the three
Ques.12 Qualitative data are
 Nonnumeric
 Numeric
 Can be both
 None
Ques.13 The numeric data that have a finite number of possible values is called
 Continuous data
 Discrete data
 Datum
 None
Ques.14 The Coefficient of Variance is expressed as
 CV = .S . X 100
X_{mean}
 CV = .S .
X_{mean}
 CV = . X_{mean} . X 100
S
 CV = (X – X_{mean )}
Ques.15 Which one is unaffected by extreme scores
 Mean
 Median
 Mode
 Range
Ques.16 A storeowner kept a tally of the sizes of suits purchased in her store. Which measure of central tendency should the storeowner use to describe the average suit sold?
 Mean
 Median
 Mode
 None
Ques.17 The correlation coefficient, r = 1, implies
 Perfect negative
 Perfect positive
 No correlation
 Limited correlation
Ques.18 If two variables changes in the opposite direction and in the same proportion, the correlation between the two is
 Perfect positive
 Limited positive
 Limited Negative
 Perfect negative
Ques.19 The value of ‘r’ gives the magnitude of correlation and its sign denotes its
 Value
 Direction
 Both
 None
Ques.20 By the Rank method the value of R is 0.73 it suggests a
 fairly strong negative relationship
 fairly strong positive relationship
 Perfect negative
 Perfect positive
Ques.21 The range of the correlation coefficient is?

1 to 0.
b. 0 to 1.
c. 1 to 1.
d. None of the above.
Ques.22 When looking at a sequence of monthly postal revenue data, we note that the revenue is consistently highest in December. The high December revenue is an illustration of:
 trend
 seasonal variation
 irregular fluctuations
 a cycle
Ques.23 Which of the following is NOT an assumption of the Binomial distribution?
 All trials must be identical.
 All trials must be independent.
 Each trial must be classified as a success or a failure.
 The probability of success is equal to .5 in all trials.
Ques.24.In Regression Analysis the independent variable is also known as
 Regressed variable
 Regressor variable
 Random variable
 All of the above
Ques.25.Given that we have collected pairs of observations on two variables X and Y , we would consider fitting a straight line with X as an explanatory variable if:
 the change in Y is an additive constant.
 the change in Y is a constant for each unit change in X
 the change in Y is a fixed percent of Y
 the change in Y is exponential
Ques.26 In Regression Analysis, a single regression line is obtained in case if
 r = +1
 r = 1
 r = +1
 r = 0
Ques.27 The regression Analysis Studies
 oneway causal effect
 twoway causal effect
 interdependence of the variables
 dependence of the variables
Ques.28 Correlation Coefficient is the —————between the regression coefficients
 arithmetic mean
 geometric mean
 harmonic mean
 median
Ques.29 Gradual shifting of a time series over a long period of time is called

periodicity.
b. cycle.
c. regression.
d. trend.
Ques.30 The trend component is easy to identify by using

moving averages
b. exponential smoothing
c. regression analysis
d. the Delphi approach
Ques.31 Seasonal components

cannot be predicted.
b. are regular repeated patterns.
c. are long runs of observations above or below the trend line.
d. reflect a shift in the series over time.
 32 What probability is shown on the Venn diagram by the shaded region below t probability is shown on the Venn diagram below
a. a. p(A) b. b. p(B) c. p(A and B) d. p(not B) 
Ques.33 At Sanjay Middle School, 3 out of 5 students make honor roll. What is the probability that a student does not make honor roll?
 65%
 40%
 60%
 None of the above
Ques.34 In a class of 30 students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a student is chosen at random, what is the probability of choosing a girl or an A student?
 19/30
 11/50
 12/30
 15/40
Ques.35  In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment, what is the probability that both are defective? a. 3/100 b. 1/330 c. 9/2500 d. 6/100 
Ques.36 Find the correlation coefficient r(X, Y) between X and Y,when
Cov(X,Y) = 2.45, Var (X) = 8.25 and Var (Y) = 21.49
 18
 – 0.18
 36
 – 0.36
Ques.37 A coin is tossed 5 times. What is the probability of getting atleast 3 heads?
 1/2
 1/3
 1/4
 1/5
Ques.38 Normal Distribution is symmetrical about its
 Harmonic mean
 Mean
 Range
 Standard deviation
Ques.39 In Normal Distribution 95% of the observations fall within 2 standard deviations of the mean, that is, between
 µ – σ and µ +σ
 µ – 2σ and µ +2σ
 µ – 3σ and µ +3σ
 Not defined
Ques.40 Condition for the Applicability of Binomial Distribution:
 There should be a finite number of trials.
 The trials do not depend on each other.
 Each trial should have only two possible outcomes, either a success or a failure.
 All of the above
_{ }
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