Management Programme

SOLVED ASSIGNMENT2010

QUANTITATIVE TECHNIQUES IN MANAGEMENT

Amity University

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QUANTITATIVE TECHNIQUES IN MANAGEMENT

Assignment A

Question 1: How has quantitative analysis changed the current scenario inthe management world today?

Answer:

Quantitative analysis requires the representation of the problem using amathematical model. Mathematical modeling is a critical part of thequantitative approach to decision making. Quantitative factors can bemeasured in terms of money or quantitative units. Examples areincremental revenue, added cost, and initial outlay.

Qualitative factors in decision making are the factors relevant to adecision that are difficult to measure in terms of money. Qualitativefactors may include: (1) effect on employee morale, schedule and otherinternal elements; (2) relationship with and commitments to suppliers;(3) effect on present and future customers; and (4) long-term futureeffect on profitability. In some decision-making situations, qualitativeaspects are more important than immediate financial benefit from adecision.

Different Statistical TechniquesMeasures of Central Tendency: For proper understanding ofquantitative data, they should be classified and converted into afrequency distribution. This type of condensation of data reduces their

bulk and gives a clear picture of their structure. If you want to know anyspecific characteristics, of the given data or if frequency distribution ofone set of data to be compared with another, then it is necessary that thefrequency distribution itself must be summarized and condensed in such amanner that it must help us to make useful inferences about the data andalso provide yardstick for comparing different sets of data.

Measures of Dispersion: Measures of dispersion would tell you thenumber of values, which are substantially different from the mean,median or mode. The commonly used measures of dispersion are range,mean deviation and standard deviation.

Correlation: Correlation coefficient measures the degree to which thechange in one variable (the dependent variable) is associated with changein the other variable (Independent one). For example, as a marketingmanager, you would like to know if there is any relation between theamounts of money you spend on advertising and the sales you achieve.Here, sales are the dependent variable and advertising budget is theindependent variable. Correlation coefficient, in this case, would tell youthe extent of relationship between these two variables, whether therelationship is directly proportional (i.e. increase or decrease inadvertising is associated with increase or decrease in sales) or it is aninverse relationship (i.e. increasing advertising is associated withdecrease in sales and vice-versa) or there is no relationship between thetwo variables.

Regression Analysis: Regression analysis includes any techniques formodeling and analyzing several variables, when the focus is on therelationship between a dependent variable and one or more independentvariables. Using this technique you can predict the dependent variables onthe basis of the independent variables. In 1970, NCAER (National Councilof Applied and Economic Research) predicted the annual stock of scootersusing a regression model in which real personal disposable income andrelative weighted price index of scooters were used as independentvariable.

Time Series Analysis: With time series analysis, you can isolate andmeasure the separate effects of these forces on the variables. Examplesof these changes can be seen, if you start measuring increase in cost ofliving, increase of population over a period of time, growth of agriculturalfood production in India over the last fifteen years, seasonal requirementof items, impact of floods, strikes, and wars so on.

Index Numbers: An index number is an economic data figure reflectingprice or quantity compared with a standard or base value. The baseusually equals 100 and the index number is usually expressed as 100times the ratio to the base value. For example, if a commodity costs twice

as much in 1970 as it did in 1960, its index number would be 200 relativeto 1960. Index numbers are used especially to compare business activity,the cost of living, and employment. They enable economists to reduceunwieldy business data into easily understood terms.

Sampling and Statistical Inference: In many cases due to shortage oftime, cost or non availability of data, only limited part or section of theuniverse (or population) is examined to (a) get information about theuniverse as clearly and precisely as possible, and (b) determine thereliability of the estimates. This small part or section selected from theuniverse is called the sample, and the process of selections such a section(or past) is called sampling.

Example: Site selection process (quantitative and qualitativefactors)While quantitative factors have been and will continue to be veryimportant in the site selection process, qualitative factors are also criticalin order to ensure that the company makes the best decision. What arethe most important quantitative and qualitative factors evaluated by siteselection advisors and companies when making a decision regarding thelocation of a new or expanded operation? The list will vary depending ontype of facility (i.e. manufacturing, logistics, research & technology,office), but most factors apply to all forms of projects. Below is asummary of the most important quantitative and qualitative factorsconsidered by companies.

Quantitative Factors1. Property Tax Rates2. Corporate Income Tax Rates3. Sales Tax Rates4. Real Estate Costs5. Utility Rates6. Average Wage/Salary Levels7. Construction Costs8. Worker’s Compensation Rates9. Unemployment Compensation Rates10. Personal Income Tax Rates11. Industry Sector Labor Pool Size12. Infrastructure Development Costs13. Education Achievement Levels14. Crime Statistics15. Frequency of Natural Disasters16. Cost of Living Index17. Number of Commercial Flights to Key Markets18. Proximity to Major Key Geographic Markets19. Unionization Rate/Right to Work versus Non-Right to Work State20. Population of Geographic Area

Qualitative Factors1. Level of Collaboration with Government, Educational and Utility Officials2. Sports, Recreational and Cultural Amenities3. Confidence in Ability of All Parties to Meet Company’s Deadlines4. Political Stability of Location5. Climate6. Availability of Quality Healthcare7. Chemistry of Project Team with Local and State Officials8. Perception of Quality of Professional Services Firms to Meet theCompany’s Needs9. Predictability of Long-term Operational Costs10. Ability to Complete Real Estate Due Diligence Process Quickly

Another important part of the site selection evaluation process relates tothe weighting of the key quantitative and qualitative factors. Dependingon the type of project, factors will be weighted differently. As an example,for a new manufacturing facility project, issues such as utility rates, realestate costs, property tax rates, collaboration with governmental entities,and average hourly wage rates may be weighted more heavily. Bycontract, for a new office facility factors such as real estate costs, numberof commercial flights, crime statistics, climate and industry sector laborpool size may be more important.

Every project is unique and must be evaluated based upon its ownindividual set of circumstances.

Question 2: What are sampling techniques? Briefly explain the clustersampling technique.

Answer:A sample is a group of units selected from a larger group (the population). Bystudying the sample, one hopes to draw valid conclusions about the larger group.

A sample is generally selected for study because the population is too largeto study in its entirety. The sample should be representative of the generalpopulation. This is often best achieved by random sampling. Also, beforecollecting the sample, it is important that one carefully and completelydefines the population, including a description of the members to beincluded.

A common problem in business statistical decision-making arises when weneed information about a collection called a population but find that the costof obtaining the information is prohibitive. For instance, suppose we need toknow the average shelf life of current inventory. If the inventory is large,the cost of checking records for each item might be high enough to cancelthe benefit of having the information. On the other hand, a hunch about the

average shelf life might not be good enough for decision-making purposes.This means we must arrive at a compromise that involves selecting a smallnumber of items and calculating an average shelf life as an estimate of theaverage shelf life of all items in inventory. This is a compromise, since themeasurements for a sample from the inventory will produce only anestimate of the value we want, but at substantial savings. What we wouldlike to know is how "good" the estimate is and how much more will it costto make it "better". Information of this type is intimately related to samplingtechniques.

Cluster sampling can be used whenever the population is homogeneous butcan be partitioned. In many applications the partitioning is a result ofphysical distance. For instance, in the insurance industry, there are small"clusters" of employees in field offices scattered about the country. In such acase, a random sampling of employee work habits might not required travelto many of the" clusters" or field offices in order to get the data. Totallysampling each one of a small number of clusters chosen at random caneliminate much of the cost associated with the data requirements ofmanagement.

Question 3: What is the significance of Regression Analysis? How does ithelp a manager in the decision making process?

Answer:Regression analysis is a powerful technique for studying relationship betweendependent variables (i.e., output, performance measure) and independent variables(i.e., inputs, factors, decision variables). Summarizing relationships among thevariables by the most appropriate equation (i.e., modeling) allows us to predict oridentify the most influential factors and study their impacts on the output for anychanges in their current values.

Unlike the deterministic decision-making process, such as linear optimization bysolving systems of equations, Parametric systems of equations and in decisionmaking under pure uncertainty, the variables are often more numerous and moredifficult to measure and control. However, the steps are the same. They are:

1. Simplification2. Building a decision model3. Testing the model4. Using the model to find the solution:

Ø It is a simplified representation of the actual situationØ It need not be complete or exact in all respectsØ It concentrates on the most essential relationships and ignores the less

essential ones.Ø It is more easily understood than the empirical (i.e., observed)

situation, and hence permits the problem to be solved more readilywith minimum time and effort.

5. It can be used again and again for similar problems or can be modified.

Fortunately the probabilistic and statistical methods for analysis and decision makingunder uncertainty are more numerous and powerful today than ever before. Thecomputer makes possible many practical applications. A few examples of businessapplications are the following:

Ø An auditor can use random sampling techniques to audit the accountsreceivable for clients.

Ø A plant manager can use statistical quality control techniques to assure thequality of his production with a minimum of testing or inspection.

Ø A financial analyst may use regression and correlation to help understand therelationship of a financial ratio to a set of other variables in business.

Ø A market researcher may use test of significace to accept or reject thehypotheses about a group of buyers to which the firm wishes to sell aparticular product.

Ø A sales manager may use statistical techniques to forecast sales for thecoming year.

Question 4 Explain the following terms in detail (give examples wherenecessary): -

(a.) Arithmetic mean(b.) Harmonic mean(c.) Geometric mean(d.) Median(e.) Mode

Answer:(a.) Arithmetic Mean:The arithmetic mean (or the average, simple mean) is computed by summingall numbers in an array of numbers (xi) and then dividing by the number ofobservations (n) in the array.

Mean = = Xi /n, the sum is over all i's.

The mean uses all of the observations, and each observation affects themean. Even though the mean is sensitive to extreme values; i.e., extremelylarge or small data can cause the mean to be pulled toward the extremedata; it is still the most widely used measure of location. This is due to thefact that the mean has valuable mathematical properties that make itconvenient for use with inferential statistical analysis. For example, the sumof the deviations of the numbers in a set of data from the mean is zero, andthe sum of the squared deviations of the numbers in a set of data from themean is the minimum value.

(b) Harmonic Mean:

The harmonic mean (H) is another specialized average, which is useful inaveraging variables expressed as rate per unit of time, such as mileage perhour, number of units produced per day. The harmonic mean (H) of n non-zero numerical values x(i) is: H = n/[ (1/x(i)].

An Application: Suppose 4 machines in a machine shop are used to producethe same part. However, each of the four machines takes 2.5, 2.0, 1.5, and6.0 minutes to make one part, respectively. What is the average rate ofspeed?

The harmonic means is: H = 4/[(1/2.5) + (1/2.0) + 1/(1.5) + (1/6.0)] =2.31 minutes.

If all machines working for one hour, how many parts will be produced?Since four machines running for one hour represent 240 minutes of operatingtime, then: 240 / 2.31 = 104 parts will be produced.

(C.) The Geometric Mean:The geometric mean (G) of n non-negative numerical values is the nth root ofthe product of the n values.

If some values are very large in magnitude and others are small, then thegeometric mean is a better representative of the data than the simple average. Ina "geometric series", the most meaningful average is the geometric mean (G).The arithmetic mean is very biased toward the larger numbers in the series.

An Application: Suppose sales of a certain item increase to 110% in the firstyear and to 150% of that in the second year. For simplicity, assume you sold100 items initially. Then the number sold in the first year is 110 and the numbersold in the second is 150% x 110 = 165. The arithmetic average of 110% and150% is 130% so that we would incorrectly estimate that the number sold in thefirst year is 130 and the number in the second year is 169. The geometric meanof 110% and 150% is G = (1.65)1/2 so that we would correctly estimate that wewould sell 100 (G)2 = 165 items in the second year.

(D.) Median:Median: The median is the middle value in an ordered array of observations.If there is an even number of observations in the array, the median is theaverage of the two middle numbers. If there is an odd number of data in thearray, the median is the middle number.

The median is often used to summarize the distribution of an outcome. If thedistribution is skewed, the median and the interquartile range (IQR) may be

better than other measures to indicate where the observed data areconcentrated.

Generally, the median provides a better measure of location than the meanwhen there are some extremely large or small observations; i.e., when thedata are skewed to the right or to the left. For this reason, median income isused as the measure of location for the U.S. household income. Note that ifthe median is less than the mean, the data set is skewed to the right. If themedian is greater than the mean, the data set is skewed to the left. Fornormal population, the sample median is distributed normally with m = themean, and standard error of the median (p/2) times standard error of themean.

The mean has two distinct advantages over the median. It is more stable,and one can compute the mean based of two samples by combining the twomeans.

(D.) Mode:The mode is the most frequently occurring value in a set of observations.Why use the mode? The classic example is the shirt/shoe manufacturer whowants to decide what sizes to introduce. Data may have two modes. In thiscase, we say the data are bimodal, and sets of observations with more thantwo modes are referred to as multimodal. Note that the mode is not a helpfulmeasure of location, because there can be more than one mode or even nomode.

When the mean and the median are known, it is possible to estimate themode for the unimodal distribution using the other two averages as follows:

Mode » 3(median) - 2(mean)

This estimate is applicable to both grouped and ungrouped data sets.

Question 5: Explain the classical approach to the probability theory. Alsoexplain the limitation of classical definition of probability.

Answer:The classical approach to probability is to count the number of favorableoutcomes, the number of total outcomes (outcomes are assumed to bemutually exclusive and equiprobable), and express the probability as a ratioof these two numbers. Here, "favorable" refers not to any subjective valuegiven to the outcomes, but is rather the classical terminology used toindicate that an outcome belongs to a given event of interest. What is meantby this will be made clear by an example, and formalized with theintroduction of axiomatic probability theory.

Classical definition of probabilityIf the number of outcomes belonging to an event E is NE, and the totalnumber of outcomes is N, then the probability of event E is defined as.

Limitation of classical definition of probabilityThere are basically four types of probabilities, each with its limitations. None of theseapproaches to probability is wrong, per se, but some are more useful or moregeneral than others.

In everyday speech, we express our beliefs about likelihoods of events using thesame terminology as in probability theory. Often, this has nothing to do with anyformal definition of probability, rather it is an intuitive idea guided by our experience,and in some cases statistics.

Probability can also be expressed in vague terms. For example, someone might say itwill probably rain tomorrow. This is subjective, but implies that the speaker believesthe probability is greater than 50%.

Subjective probabilities have been extensively studied, especially with regards togambling and securities markets. While this type of probability is important, it is notthe subject of this book. A good reference is "Degrees of Belief" By Steven Vick(2002).

There are two standard approaches to conceptually interpreting probabilities. Thefirst is known as the long run (or the relative frequency approach) and the subjectivebelief (or confidence approach). In the Frequency Theory of Probability, probability isthe limit of the relative frequency with which an event occurs in repeated trials (notethat trials must be independent).

Frequentists talk about probabilities only when dealing with experiments that arerandom and well-defined. The probability of a random event denotes the relativefrequency of occurrence of an experiment's outcome, when repeating theexperiment. Frequentists consider probability to be the relative frequency "in thelong run" of outcomes.

Physical probabilities, which are also called objective or frequency probabilities, areassociated with random physical systems such as roulette wheels, rolling dice andradioactive atoms. In such systems, a given type of event (such as the dice yieldinga six) tends to occur at a persistent rate, or 'relative frequency', in a long run oftrials. Physical probabilities either explain, or are invoked to explain, these stablefrequencies. Thus talk about physical probability makes sense only when dealing withwell defined random experiments. The two main kinds of theory of physicalprobability are frequentist accounts (such as Venn) and propensity accounts.

Relative frequencies are always between 0% (the event essentially never happens)and 100% (the event essentially always happens), so in this theory as well,probabilities are between 0% and 100%. According to the Frequency Theory ofProbability, what it means to say that "the probability that A occurs is p%" is that if

you repeat the experiment over and over again, independently and under essentiallyidentical conditions, the percentage of the time that A occurs will converge to p. Forexample, under the Frequency Theory, to say that the chance that a coin landsheads is 50% means that if you toss the coin over and over again, independently,the ratio of the number of times the coin lands heads to the total number of tossesapproaches a limiting value of 50% as the number of tosses grows. Because the ratioof heads to tosses is always between 0% and 100%, when the probability exists itmust be between 0% and 100%.

In the Subjective Theory of Probability, probability measures the speaker's "degreeof belief" that the event will occur, on a scale of 0% (complete disbelief that theevent will happen) to 100% (certainty that the event will happen). According to theSubjective Theory, what it means for me to say that "the probability that A occurs is2/3" is that I believe that A will happen twice as strongly as I believe that A will nothappen. The Subjective Theory is particularly useful in assigning meaning to theprobability of events that in principle can occur only once. For example, how mightone assign meaning to a statement like "there is a 25% chance of an earthquake onthe San Andreas fault with magnitude 8 or larger before 2050?" (See Freedman andStark, 2003, for more discussion of theories of probability and their application toearthquakes.) It is very hard to use either the Theory of Equally Likely Outcomes orthe Frequency Theory to make sense of the assertion.

QUANTITATIVE TECHNIQUES IN MANAGEMENT

Assignment B

Question 1: Write a note on decision making in management. How one willtake decision under risk and uncertainty.

Answer:Decision-making is a crucial part of good business. The question then is ‘howis a good decision made?

One part of the answer is good information, and experience in interpretinginformation. Consultation ie seeking the views and expertise of other peoplealso helps, as does the ability to admit one was wrong and change one’smind. There are also aids to decision-making, various techniques which helpto make information clearer and better analysed, and to add numerical andobjective precision to decision-making (where appropriate) to reduce theamount of subjectivity.

Managers can be trained to make better decisions. They also need asupportive environment where they won’t be unfairly criticised for makingwrong decisions (as we all do sometimes) and will receive proper supportfrom their colleague and superiors. A climate of criticism and fear stifles risk-taking and creativity; managers will respond by ‘playing it safe’ to minimisethe risk of criticism which diminishes the business’ effectiveness inresponding to market changes. It may also mean managers spend too muchtime trying to pass the blame around rather than getting on with running thebusiness.

Decision-making increasingly happens at all levels of a business. The Boardof Directors may make the grand strategic decisions about investment anddirection of future growth, and managers may make the more tacticaldecisions about how their own department may contribute most effectively tothe overall business objectives. But quite ordinary employees areincreasingly expected to make decisions about the conduct of their owntasks, responses to customers and improvements to business practice. Thisneeds careful recruitment and selection, good training, and enlightenedmanagement.

Types of Business Decisions

1. Programmed Decisions These are standard decisions which alwaysfollow the same routine. As such, they can be written down into a series offixed steps which anyone can follow. They could even be written as computerprogram

2. Non-Programmed Decisions. These are non-standard and non-routine.Each decision is not quite the same as any previous decision.

3. Strategic Decisions. These affect the long-term direction of the businesseg whether to take over Company A or Company B

4. Tactical Decisions. These are medium-term decisions about how toimplement strategy eg what kind of marketing to have, or how many extrastaff to recruit

5. Operational Decisions. These are short-term decisions (also calledadministrative decisions) about how to implement the tactics eg which firmto use to make deliveries.

Figure 1: Levels of Decision-Making

Figure 2: The Decision-Making Process

The model in Figure 2 above is a normative model, because it illustrateshow a good decision ought to be made. Business Studies also uses positivemodels which simply aim to illustrate how decisions are, in fact, made inbusinesses without commenting on whether they are good or bad.

Linear programming models help to explore maximising or minimisingconstraints eg one can program a computer with information that establishesparameters for minimising costs subject to certain situations and informationabout those situations.

Spread-sheets are widely used for ‘what if’ simulations. A very largespread-sheet can be used to hold all the known information about, say,pricing and the effects of pricing on profits. The different pricing assumptionscan be fed into the spread-sheet ‘modelling’ different pricing strategies. Thisis a lot quicker and an awful lot cheaper than actually changing prices to seewhat happens. On the other hand, a spread-sheet is only as good as theinformation put into it and no spread-sheet can fully reflect the real world.But it is very useful management information to know what might happen toprofits ‘what if’ a skimming strategy, or a penetration strategy were used forpricing.

The computer does not take decisions; managers do. But it helps managersto have quick and reliable quantitative information about the business as it isand the business as it might be in different sets of circumstances. There is,however, a lot of research into ‘expert systems’ which aim to replicate theway real people (doctors, lawyers, managers, and the like) take decisions.The aim is that computers can, one day, take decisions, or at leastprogrammed decisions (see above). For example, an expedition could carryan expert medical system on a lap-top to deal with any medical emergencieseven though the nearest doctor is thousands of miles away. Already it is

possible, in the US, to put a credit card into a ‘hole-in-the-wall’ machine andget basic legal advice about basic and standard legal problems.

Constraints on Decision-Making

Internal Constraints

These are constraints that come from within the business itself.

- Availability of finance. Certain decisions will be rejected because theycost too much

- Existing Business Policy. It is not always practical to re-write businesspolicy to accommodate one decision

- People’s abilities and feelings. A decision cannot be taken if it assumeshigher skills than employees actually have, or if the decision is so unpopularno-one will work properly on it.

External Constraints

These come from the business environment outside the business.

- National & EU legislation

- Competitors’ behaviour, and their likely response to decisions yourbusiness makes

- Lack of technology

- Economic climate

Quality of Decision-Making

Some managers and businesses make better decisions than others. Gooddecision-making comes from:-

1. Training of managers in decision-making skills. See DevelopingManagers

2. Good information in the first place.

3. Management skills in analysing information and handling itsshortcomings.

4. Experience and natural ability in decision-making.

5. Risk and attitudes to risk.

6. Human factors. People are people. Emotional responses comebefore rational responses, and it is very difficult to get people to makerational decisions about things they feel very strongly about. Rivalriesand vested interests also come into it. People simply take differentviews on the same facts, and people also simply make mistakes.

Question 2: The Mumbai Cricket Club, a professional club for the cricketers, has the player wholed the league in batting average for many years. Over the past ten years, Amod Kambali hasachieved a mean batting average of 54.50 runs with a standard deviation of 5.5 runs. This yearAmod played 25 matches and achieved an average of 48.80 runs only. Amod is negotiating hiscontract with the club for the next year, and the salary he will be able to obtain is highlydependent upon his ability to convince the team’s owner that his batting average this year wasnot significantly worse than in the previous years. The selection committee of the club is willing touse a 0.01 significance level.You are required to find out whether Amod’s salary will be cut next year.

Answer:Null Hyopothesis -Ho: Amod’s batting average this year (48.80)is not significantly different from his all-time batting average of54.50

Alternative Hypothesis -Ha: Amod’s batting average this year(48.80) is significantly lower than his all-time batting average of54.50

α = 0.01

t =48.80 - 54.50

= -5.18185.5 / 25

The critical value of t is -2.492 at df = 24

Conclusion: Reject Ho and accept Ha (Amod’s batting averagethis year is significantly lower than his all-time batting average.Amod’s salary will most likely be cut next year.

3 The salaries paid to the managers of a company had a mean of Rs. 20,000 with a standarddeviation of Rs 3,000, What will be the mean and standard deviation if all the salaries areincreased by1) 10%2) 10% of existing mean3) Which policy would you recommend if the management does not want to have increaseddisparities of wages?

Answer1) 10%

Both the mean and standard deviation will simply increase by 10% toRs 22,000 and Rs 3,300, respectively.

2) 10% of existing mean

Only the mean will increase by 10% to Rs 22,000 and the standarddeviation will remain the same at Rs 3,000.

3) Which policy would you recommend if the management does notwant to have increased disparities of wages?

Increasing the salaries by 10% of existing mean does not increasedisparities of wages, therefore, is recommended.

Case studyPlease read the case study given below and answer questions given at the end.

Kushal Arora, a second year MBA student, is doing a study of companies going public for the firsttime. He is curious to see whether or not there is a significant relationship between the sizes ofthe offering (in crores of rupees) and the price per share after the issue. The data are givenbelow:Size (incrore ofrupees)

108 39 68.40 51 10.40 4.40

Price ( inrupees)

12 13 19 12 6.50 4

QuestionYou are required to calculate the coefficient of correlation for the above data set and commentwhat conclusion Kushal should draw from the sample.

Answer:

N X Y XY X2 Y2

1 12 108 1296 144 116642 13 39 507 169 15213 19 68.4 1299.6 361 4678.564 12 51 612 144 26015 6.5 10.4 67.6 42.25 108.166 4 4.4 17.6 16 19.36

TOTALS 66.5 281.2 3799.8 876.25 20592.08

r =[

6(3799.8) - (66.5)(281.2)2 ][

= 0.6726(876.25) - (66.5) 6(20592.08) - (281.2)

Conclusion: There is a positive correlation for the above set of data

Assignment C(Objective Questions)

Answer all questions.Tick Mark (√) the most appropriate answer.

1. Which of the following is not correct about construction of bar charts?a. All bars should rise from the same base lineb. Width of the bar should be proportional to the data representedc. The bars should be arranged from the left to rightd. Length of the bars should be proportional to the data represented

2. Which of the following is not true about mean absolute deviation :-a. Mean deviation is obtained by calculating the absolute deviations ofeach observation from meanb. Mean deviation is a more comprehensive measure compared to rangec. It is conducive to further algebraic treatmentd. It cannot be computed for distributions with open end classes.

3. The value index number measures the--a. Changes in prices of a basket of commodities from one period to anotherb. Changes in quantities consumed of a basket of commodities over a period of timec. Change in the total monetary value of a basket of commodities over aperiod of timed. Change in the retail prices of various commodities

4. A market researcher wants to find out the buying behavior of the typical household during theweekends. He divides the city into various localities such that each locality represents the citypopulation in terms of age group, gender and social status. Then he randomly selects fivelocalities and surveys each household. Which of the following sampling techniques bestdescribes the method used by the researcher:-

a. Cluster samplingb. Systematic samplingc. Stratified samplingd. Convenience sampling.

5. If every item in the data set is increased by the same quantity then the standard deviation ofthe data set--

(a) Remains the same(b) Increases by the same quantity by which every data item is increased(c) Decreases by the same quantity by which every data item is increased(d) Increases by the square root of the same quantity by which every data item isincreased

6. Which of the following is true with regard to a linear equation Y – a – bX = 0, where X is theindependent variable and Y is the dependent variable:-

(a) The slope of the straight line is ‘a’(b) The Y-intercept of the straight line is 0(c) The Y-intercept of the straight line is ‘b’(d) The slope and the Y-intercept remain constant for all combinations of Xand Y values which satisfy the equation

7. Which of the following quantitative method is not used by managers to take decision:-(a) Linear programming

b) Time seriesc) Regression analysisd) Hypothesis testing

8. In the graphical method of solving linear programming problems the feasible region is the set ofall points--

a) Which does not satisfy any of the constraints?b) Which satisfy exactly one of the constraints?c) Which satisfy all the constraints?d) At which the objective function has the same value?

9. Which of the following is false in regard to histogram :-a) The class intervals are represented by the base of the rectanglesb) The frequencies are represented by the heights of the rectanglec) If the class intervals are of equal width then the bases of the rectangles will be equal inlengthd) The tallest rectangle in a histogram represents the class interval with thelowest frequency

10. Which of the following measures in not affected by the presence of extreme values in adataset :-

a) Rangeb) Arithmetic meanc) Standard deviationd) Median

11. 1\2x + 1/3y – 1/3z = -11/3x – 1/2y -1/6z = 41/6x – 5/6y + 1/2z = 3

The values of x in the above simultaneous equations would be--a) 3b) 6c) 9d) 12

12. The following details are available with regard to a data set: Sx = 33, Sx2 = 199,

n = 6. If each observation in the data set is multiplied by 2 then the standard deviation of the

resulting values will be equal to:

a) (35/3)1/2b) 35/3c) 3d) 25

13. The following data pertains to three commodities:-

Commodity Price in 2004 (Rs. /kg) Price in 1994 (Rs. /kg)RiceWheatPulses

11.5013.5026

9.508.5020

The base year is 1994. The unweighted aggregates price index for the year 2004 isapproximately--

14. If the regression equation is the perfect estimator of the dependent variable then which of thefollowing is false?

a) The standard error of estimate is zerob) The coefficient of correlation is zeroc) The coefficient of determination is 1.00d) All the data points fall on the regression line

15. If the regression equation is a perfect estimator of the dependent variable then which of thefollowing is false :-

a) The standard error of estimate is zerob) The coefficient of correlation is zeroc) The coefficient of determination is 1.00d) All the data points fall on the regression line

16. Which of the following represents the proportion of variation in the dependent variable that isexplained by the regression line :-

a) Coefficient of determinationb) Coefficient of correlationc) Coefficient of variationd) Standard error of estimate

17. If the coefficient of correlation between the two variables lies between -1 and 0, then thecovariance between them is--

a) Positiveb) Negativec) Zerod) Equal in magnitude to the variances of both the variables

18. If bYX is the slope of coefficient of regression line of Y on X, and bXY is the slope coefficient ofregression line of X on Y then which of the following is true :-

a) bYX is positive implies that bXY is positiveb) bYX is positive implies that bXY is negativec) bYX and bXY are reciprocalsd) The product of bYX and bXY is zero

19. A graphical method of representing states of nature and courses of action involved in decisionmaking is referred to as--

a) Decision treeb) Histogramc) Scatter diagramd) Frequency distribution

20. If the probability of occurrence of one event is not affected by the occurrence of another eventand vice versa then the two events are said to be--

a) Collectively exhaustiveb) Independentc) Dependentd) Mutually exclusive

21. Bayes’ theorem helps the statistician to calculate---a) Dispersionb) Subjective probabilityc) Posterior probabilityd) Classical probability

22. In a binomial distribution the probability of getting zero or more numbers of successes isequal to--

a) 0b) 1c) The probability of getting zero successd) The probability of getting successes in all trials

23. Which of the following measures represent the scatter of the values in a data set :-a) Arithmetic meanb) Geometric meanc) Standard deviationd) Median

24. As the sample size increases--a) The variation of the sample mean from the population mean becomes largerb) The variation of the sample mean from the population mean becomessmallerc) The variance of the sample becomes less than the variance of the populationd) The standard deviation of the sample becomes more than the standard deviation ofthe population.

25. In the graphical method of solving linear programming problems if there is a unique optimalsolution, then the optimal solution--

a) Is always found at the center of the feasible regionb) Is always at the originc) Lies outside the feasible regiond) Is located at one of the corner points of the feasible region

26. A multiple regression equation has--a) Multiple dependent variablesb) One independent variablec) One dependent variabled) A standard error of estimate equal to zero

27. Which of the following conditions indicate the existence of multiple optimal solutions when alinear programming problem is solved by the graphical method :-

a) One of the constraints is parallel to the horizontal axisb) The objective function is parallel to the vertical axisc) The objective function is parallel to one of the edges of the feasibleregion which is in the direction of optimal movement of the objectivefunctiond) If two or more constraints are parallel to each other

28. Three persons enter into a railway carriage and there are 8 seats available. In how manyways they can seat themselves?

a) 24b) 336c) 40d) 56

29. In which of the following the simple harmonics mean is appropriate:a) A set of ratios using the numerators of the ratio data as weightsb) A set of ratios using the denominators of the ratio data as weightsc) A set of ratios which have been calculated with the same numeratorsd) A set of ratios which have been calculated with the same denominators

30. Which of the following statements is not true about standard deviation?a) Combined standard deviation of two or more groups can be calculatedb) The sum of the squares of the deviations of items of any series from avalue other than the arithmetic mean would always be smallerc) Standard deviation is independent of any change of origind) Standard deviation is dependent on the change of scale

31. Which of the following is/are true with respect to geometric mean :-(a) Geometric mean cannot be calculated if any of the value in the set is zero.(b) Geometric mean is appropriate for averaging the ratios of change, for average ofproportions, etc.(c) Geometric mean is considered most suitable average for index numbers.

Only (I) above(i) Only (II) above(ii) All (I), (II) and (III) above(iii) Only (II) above

32. The probability of getting two heads from three tosses of a fair coin is--a) 1/8b) 1/4c) 3/8d) 1/2

33. If A and B are two mutually exclusive events and P(A) = 2/3, then the probability of events Aand B happening together is--

a) 0b) 1/3c) 2/3d) 1/2

34. Which of the following can be directly used as the test statistic in hypothesis tests on thebasis of non standardized scale :-

(a) The sample mean, when the test involves the population mean.(b) The difference between two sample means, when the tests involve the differencebetween two population means.(c) The sample proportion when the test is about the population proportion

(i) Only (a) above(ii) Only (b) above(iii) Only (c) above(iv) All (a), (b), (c) above

35. A box contains 60 ball point pens out of which 10 pens are defective. 8 pens are randomlypicked up from the box. The probability distribution of the number of pens which are randomlypicked, will be--

a) A discrete uniform distribution

b) A binomial distributionc) A hyper geometric distributiond) A Chi- square distribution

36. If we consider the process of selecting a simple random sample as an experiment then whichof the following can be treated as random variable(s)?

(a) Sample mean(b) Sample standard deviation(c) Sample range(d) Sample median

(i) Only (a) above(ii) Only (b) above(iii) All (a), (b), (c), (d) above(iv) Only (d) above

37. The covariance of random variable with itself is always--a) A positive quantityb) A negative quantityc) 0d) Less than its expected value

38. A man has 6 friends. In how many ways he can invite one or more of them to a party?a) 63b) 64c) 119d) 120

39. Find x; if logx/log2 = log36/log4a) 0b) 2c) 4d) 6

40. The empirical relationship between range (R) and mean deviation (M.D) is--a) 2R=15M.Db) 3R=17M.Dc) R=17M.Dd) 3R=M.D