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# Amity dbm assignments solution

Section A

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.
2. a. Show for the following function f(x) = x + 1/x has its Mi value greater that its ax value.
3. An enquiry into the faculty budgets of middle class families gave the following information given below.
4. 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

1. Also calculate
2. Coefficient of correlation
3. Interquartile Range (Q3-Q1)
4. Skewness

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

Life (in thousands of Kms) Brand A Brand B
20-25 8 6
25-30 15 20
30-35 12 32
35-40 18 30
40-45 13 12
45-50 9 0
Which brand of tyre would you use on the fleet of trucks and why?

1. Answser the following guestions.
2. The income of a person in a particular week is Rs.5o per day. Find mean deviation of his income for the week.
3. The median and variance of a distrthution are 35 & 2.56 per day. Find median and variance if each observation is multiplied by 3.
4. 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.
5. The mean and standard deviation of a distribution are 15 & w respectively. Find meamn and standard distribution if each observation is multiplied by 5.

1. a. Define the following Matrix with an example of each.
2. Row Matrix b. Column Matrix c. Zero or Null Matnx
3. square Matrix e. Diagonal Matrix f. Scalar Matrix
4. unit or dentity Matrix h. Upper Triangular Matrix i. Lower Triangular Matrix
5. Comparable Matrix k. Equal Matrix
6. b. Solve the following equations using MATRIx method.

-2x ÷ y + 3z = 9
x.+.y.+.x =-6.
xo-.y.+.z =-2.
Section B

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(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
1. Calculate the Rank Correlation and Coefficient.
2. Is the relationship significant?

1. 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

1. Estimate the likely production for the year 2o0o.
2. 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)

1. Given the form of the scattered diagram, does it appear that a straight line provides an accurate

model for the data?

1. Find the correlation coefficient between Age(X) and Blood Pressure(Y) and discuss its nature.
• Find the two lines of regression.
1. 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.

1. dynamic decisions
2. static decisions
3. Both
4. None

Ques.2 Stocking of an item for sale in a certain trade fair, illustrates a

1. Static decision
2. Where uncertainly exists
3.  Nature is opponent.
4. All of above

Ques.3 Quantitative analysis is also called

1. Operations research
2. Management science
3. Quantitative techniques
4. All the above

Ques.4 Quantitative research provides the fundamental connection between

1. empirical observation and mathematical expression
2. empirical observation and qualitative expression
3. empirical observation and social expression
4. empirical observation and all expression

Ques.5  Most of the business decisions can be made on the basic of

1. Rule of thumb
2. Commonsense
3. Snap judgment.
4. Quantitative Techniques

Ques.6 Statistics is a branch of

1. applied physics
2. applied mathematics
3. applied commerce
4. Dramatics

Ques.7 The mean of 7, 12, 24, 20, 19 is

1. 14
2. 16
3. 15.4
4. 16.4

Ques.8 ∑ (X/c) =

1. ∑ ( X)/n c
2. ∑ ( X)/∑ c
3. ∑ ( X)/c
4.  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

1. 75
2. 87
3. 88
4. 94

Ques.10 Which measure of Central tendency is most efficient

1. Mean
2. Median
3. Mode
4. All are equal

Ques.11 Mean Deviation can be calculated from

1. Mean
2. Median
3. All the three

Ques.12 Qualitative data are

1. Non-numeric
2. Numeric
3. Can be both
4. None

Ques.13 The numeric data that have a finite number of possible values is called

1. Continuous data
2. Discrete data
3. Datum
4. None

Ques.14 The Coefficient of Variance is expressed as

1. CV   =     .S .   X   100

Xmean

1. CV   =     .S .

Xmean

1. CV   =     . Xmean .  X   100

S

1. CV = (X – Xmean )

Ques.15 Which one is unaffected by extreme scores

1. Mean
2. Median
3. Mode
4. 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?

1. Mean
2. Median
3. Mode
4. None

Ques.17 The correlation coefficient, r = -1, implies

1. Perfect negative
2. Perfect positive
3. No correlation
4. Limited correlation

Ques.18 If two variables changes in the opposite direction and in the same proportion, the correlation between the two is

1. Perfect positive
2. Limited positive
3. Limited Negative
4. Perfect negative

Ques.19 The value of ‘r’ gives the magnitude of correlation and its sign denotes its

1. Value
2. Direction
3. Both
4. None

Ques.20 By the Rank method the  value of R is -0.73  it suggests a

1. fairly strong negative relationship
2. fairly strong positive relationship
3. Perfect negative
4. Perfect positive

Ques.21 The range of the correlation coefficient is?

1. -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:

1. trend
2. seasonal variation
3. irregular fluctuations
4. a cycle

Ques.23 Which of the following is NOT an assumption of the Binomial distribution?

1. All trials must be identical.
2. All trials must be independent.
3. Each trial must be classified as a success or a failure.
4. The probability of success is equal to .5 in all trials.

Ques.24.In Regression Analysis the independent variable is also known as

1. Regressed variable
2. Regressor variable
3. Random variable
4. 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:

1. the change in Y is an additive constant.
2. the change in Y is a constant for each unit change in X
3. the change in Y is a fixed percent of Y
4. the change in Y is exponential

Ques.26 In Regression Analysis, a single regression line is obtained in case if

1. r =  +1
2. r =   -1
3. r =  +1
4. r =   0

Ques.27 The regression Analysis Studies

1. one-way causal effect
2. two-way causal effect
3. interdependence of the variables
4. dependence of the variables

Ques.28 Correlation Coefficient is the —————between the regression coefficients

1. arithmetic mean
2. geometric mean
3. harmonic mean
4. median

Ques.29 Gradual shifting of a time series over a long period of time is called

1. periodicity.
b. cycle.
c. regression.
d. trend.

Ques.30 The trend component is easy to identify by using

1. moving averages
b. exponential smoothing
c. regression analysis
d. the Delphi approach

Ques.31 Seasonal components

1. 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.

1. 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?

1. 65%
2. 40%
3. 60%
4. 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?

1. 19/30
2. 11/50
3. 12/30
4. 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

1. 18
2. – 0.18
3. 36
4. – 0.36

Ques.37 A coin is tossed 5 times. What is the probability of getting atleast 3 heads?

1. 1/2
2. 1/3
3. 1/4
4. 1/5

Ques.38 Normal Distribution is symmetrical about its

1. Harmonic mean
2. Mean
3. Range
4. Standard deviation

Ques.39 In Normal Distribution 95% of the observations fall within 2 standard deviations of the mean, that is, between

1. µ – σ and µ +σ
2. µ – 2σ and µ +2σ
3. µ – 3σ and µ +3σ
4. Not defined

Ques.40 Condition for the Applicability of Binomial Distribution:

1. There should be a finite number of trials.
2. The trials do not depend on each other.
3. Each trial should have only two possible outcomes, either a success or a failure.
4. All of the above