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104774013 mb0040-mb0040-–-statistics-for-management-november-2012

1. 1. May 2012Master of Business Administration- MBA Semester 1MB0040 – Statistics for Management - 4 Credits(Book ID: B1129)Assignment Set - 1 (60 Marks)Note: Each question carries 10 Marks. Answer all the questions.Q1. Define “Statistics”. What are the functions of Statistics? Distinguish between Primarydata and Secondary data.An : Statistics is a mathematical science pertaining to the collection, analysis, interpretationor explanation, and presentation of data. It also provides tools for prediction and forecastingbased on data. It is applicable to a wide variety of academic disciplines, from the natural andsocial sciences to the humanities, government and business.Statistical methods can be used to summarize or describe a collection of data; this is calleddescriptive statistics. In addition, patterns in the data may be modeled in a way that accountsfor randomness and uncertainty in the observations, and are then used to draw inferencesabout the process or population being studied; this is called inferential statistics. Descriptive,predictive, and inferential statistics comprise applied statistics.There is also a discipline called mathematical statistics, which is concerned with thetheoretical basis of the subject. Moreover, there is a branch of statistics called exact statisticsthat is based on exact probability statements.The word statistics can either be singular or plural. In its singular form, statistics refers to themathematical science discussed in this article. In its plural form, statistics is the plural of theword statistic, which refers to a quantity (such as a mean) calculated from a set of data.Management
2. 2. in all business and organizational activities is the act of getting people together to accomplishdesired goals andobjectivesusing available resources efficiently and effectively.Management comprisesplanning,organizing,staffing,leadingor directing,andcontrollinganorganization(a group of one or more people or entities) or effort for thepurpose of accomplishing a goal.Resourcingencompasses the deployment and manipulationof human resources,financialresources,technologicalresources, and natural resources.Since organizations can be viewed assystems,management can also be defined as humanaction, including design, to facilitate the production of useful outcomes from a system. Thisview opens the opportunity to manage oneself, a pre-requisite to attempting to manageothers. Management operates through various functions, often classified as planning,organizing, staffing, leading/directing, controlling/monitoring and motivation.Planning: Deciding what needs to happen in the future (today, next week, next month, nextyear, over the next five years, etc.) and generating plans for action.Organizing : (Implementation) making optimum use of the resources required to enable thesuccessful carrying out of plans.Staffing: Job analysis, recruitment, and hiring for appropriate jobs.Leading/directing : Determining what needs to be done in a situation and getting people todot.Controlling/monitoring: Checking progress against plans.Motivation: Motivation is also a kind of basic function of management, because withoutmotivation, employees cannot work effectively. If motivation does not take place in an
3. 3. organization, then employees may not contribute to the other functions (which are usually setby top-level management).Basic rolesInterpersonal: roles that involve coordination and interaction with employees.Difference between primary and secondary data :Primary Data1. Primary data are always original as it is collected by the investigator.2. Suitability of the primary data will be positive because it has been systematically collected.3. Primary data are expensive and time consuming.4. Extra precautions are not required.5. Primary data are in the shape of raw material.6. Possibility of personal prejudice.Secondary Data
4. 4. 1. Secondary data lacks originality. The investigator makes use of the data collected by otheragencies.2. Secondary data may or may not suit the objects of enquiry.3. Secondary data are relatively cheaper.4. It is used with great care and caution.5. Secondary data are usually in the shape of readymade products.6. Possibility of lesser degree of personal prejudice.Q2. Draw a histogram for the following distribution:AgeAge 0-10 10-20 20-30 30-40 40-50No. Of 2 5 10 8 4People Age No of People 0-10 2 10-20 5 20-30 10 30-40 8 40-50 4
5. 5. histogram diagram 12 10 8 people 6 4 2 0 10 20 30 40 50Q3. Find the (i) arithmeticmean and (ii) the Age median valueof the following set of values:40, 32, 24, 36, 42, 18, 10. x =Σ fixi/ Σfi(40+32+24+36+42+18+10)/7=28.85Median value10,18,24,32,36,40,42N=7Median =(N+1)/2 th =(7+1)/2 =4M=32Q4. Calculate the standard deviation of the following data:Marks 78-80 80-82 82-84 84-86 86-88 88-90No. Of 3 15 26 23 9 4Students
6. 6. Class interval Mead valueX Frequency „f‟ d=X-83/2 fd fd²78-80 79 3 -2 -6 1280-82 81 15 -1 -15 1582-84 83 26 0 0 084-86 85 23 1 23 2386-88 87 9 2 18 3688-90 89 4 3 12 36 80 32 122σ²=[Σfd²/n-[Σfd/Σf]²]x(C.I)²σ²=[122/80-[32/80]²]x4=5.46standard deviation=σ=2.336Q5. Explain the following terms with respect to Statistics: (i) Sample, (ii) Variable, (iii)Population.Instatistics,a sample is asubsetof apopulation.Typically, the population is verylarge, making acensusor acompleteenumerationof all the values in the population impracticalor impossible. The sample represents asubset of manageable size. Samples are collected andstatistics are calculated from the samples so that onecan makeinferencesorextrapolationsfromthe sample to the population. This process of collectinginformation from a sample is referred toassampling. A complete sample is a set of objects from a parentpopulation that includes ALL such objectsthat satisfy a set of well-defined selection criteria. For example, acomplete sample of Australianmen taller than 2m would consist of a list of every Australian male taller than2m. But it wouldntinclude German males, or tall Australian females, or people shorter than 2m. So tocompile sucha complete sample requires a complete list of the parent population, including data onheight,gender, and nationality for each member of that parent population. In the case of humanpopulations,such a complete list is unlikely to exist, but such complete samples are oftenavailable in other disciplines,such as complete magnitude-limited samples of astronomicalobjects.An unbiased sample is a set of objectschosen from a complete sample using a selection processthat does not depend on the properties of theobjects. For example, an unbiased sample of Australian men taller than 2m might consist of a randomlysampled subset of 1% of Australianmales taller than 2m. But one chosen from the electoral register mightnot be unbiased since, forexample, males aged under 18 will not be on the electoral register. In anastronomical context, anunbiased sample might consist of that fraction of a complete sample for which dataare available,provided the data availability is not biased by individual source properties.The best way toavoid a biased or unrepresentative sample is to select arandom sample,alsoknown as a probability sample. Arandom sample is defined as a sample where each individualmember of the population has a known, non-zero chance of being selected as part of the sample.
7. 7. MB0040-STATISTICS FOR MANAGEMENTMB0040 Page 13Several types of random samples aresimple random samples, systematic samples, stratifiedrandomsamples,andcluster random samples.(ii)VariableA variable is a characteristic that may assume more than one set of values to which anumerical measure canbe assigned.Height, age, amount of income, province or country of birth, grades obtained at school andtypeof housing are all examples of variables. Variables may be classified into various categories,some ofwhich are outlined in this section.Categorical variables:A categorical variable (also called qualitative variable) is one for whicheach response can be put into aspecific category. These categories must be mutually exclusiveand exhaustive. Mutually exclusive meansthat each possible survey response should belong toonly one category, whereas, exhaustive requires that thecategories should cover the entire set of possibilities. Categorical variables can be either nominal or ordinal.Nominal variables:Anominal variableis one that describes a name or category. Contrary toordinal variables, there is no naturalordering of the set of possible names or categories.Ordinal variables: Anordinal variableis a categoricalvariable for which the possible categoriescan be placed in a specific order or in some natural way.Numericvariables: Anumeric variable,also known as a quantitative variable, is one that canassume a number of realvalues —such as age or number of people in a household. However, notall variables described by numbers areconsidered numeric. For example, when you are asked toassign a value from 1 to 5 to express your level ofsatisfaction, you use numbers, but the variable(satisfaction) is really an ordinal variable. Numeric variablesmay be either continuous ordiscrete.Continuous variables: A variable is said to be continuous if it canassume an infinite number of real values. Examples of acontinuous variable are distance, age and temperature.The measurement of a continuous variable is restricted by the methodsused, or by the accuracyof the measuring instruments. For example, the height of a student is a continuousvariablebecause a student may be 1.6321748755... metres tall.Discrete variables: As opposed to acontinuous variable, adiscrete variablecan only take a finitenumber of real values. An example of a discrete variable would be the score given by ajudge toa gymnast in competition: the range is 0 to 10 and the score is always given to one decimal (e.g.,aPopulationA statistical population is a set of entities concerning whichstatistical inferencesare tobe drawn, often based on arandomsampletaken from the population. For example, if wewere interested in generalizations aboutcrows,then we woulddescribe the set of crowsthat is of interest. Notice that if we choose a population like all crows, we will be limitedtoobserving crows that ulatixist now or will exist in the future. Probably,geographywillalso constitute a limitation in thatour resources for studying crows are also limited.Population is also used to refer to a set of potentialmeasurementsorvalues, including notonly cases actually observed but those that are potentiallyobservable.Suppose, forexample, we areinterested in the set of all adult crows now alive in the county of Cambridge shire,and we want to know the meanweight of these birds. For each bird inthe population of crows there is a weight, and the set of these weights is calledthepopulation of weights.Asubsetof a population is called a subpopulation. If different subpopulations havedifferent properties, the properties andresponse of the overall population can often bebetter understood if it is first separated into distinct subpopulations.
8. 8. For instance, a particular medicine may have different effects on differentsubpopulations, and these effects may beobscured or dismissed if such specialsubpopulations are not identified and examined in isolation.Similarly, one can often estimate parameters more accurately if one separates outsubpopulations: distribution of heightsamong people is better modeled by consideringmen and women as separate subpopulations, for instance.Populations consisting of subpopulations can be modeled bymixture models,whichcombine the distributions withinsubpopulations into an overall population distribution.6) An unbiased coin is tossed six times. What is the probability that the tosses will result in: (i) atleast four heads, and (ii) exactly two headsLet „A‟ be the event of getting head. Given that:(iI) The probability that the tosses will result in exactly two heads is given by:herefore, the probability that the tosses will result in exactly two heads is 15/64.(I)probability of at least four headsP(X>=4) =P(X=4)+P(X=5)+P(X=6)= 22/64=11/32May 2012Master of Business Administration- MBA Semester 1MB0040 – Statistics for Management - 4 Credits(Book ID: B1129)Assignment Set - 2 (60 Marks)Note: Each question carries 10 Marks. Answer all the questions.Q1. Find Karl Pearson‟s correlation co-efficient for the data given in the below table:X 18 16 12 8 4
9. 9. Y 22 14 12 10 8 X Y X² Y² XY 18 22 324 484 396 16 14 256 196 224 12 12 144 144 144 8 10 64 100 80 4 8 16 64 32 ΣX=58 ΣY=66 ΣX²=804 ΣY²=988 ΣXY=876 R=NΣXY- ΣX ΣY/(N ΣX²-( ΣX)²)½X(N ΣY²-(ΣY)²)½R= 0.89Q2. Find the (i) arithmetic mean (ii) range and (iii) median of the following data: 15, 17, 22,21, 19, 26, 20.(I) Arithmatic mean We have n=7 X=Σxi/nX=(15+17+22+21+19+26+20)/7=140/7=20(II)rangeR=H-L =26-15 =11(iii) median15,17,19,20,21,22,26 M=(n+1)/2 =8/2th =4thQ3. What is the importance of classification of data? What are the types of classification ofdata?Classification of Data perform many function 1) It condenses the bulk data 2) It simplifies data and makes the datamore comprehensible 3) It faciliates comparison of charactristic
10. 10. 4) It renderthe dataready for any statistical analysis.Types of classification. 1) Geo graphical classification 2) Charonological classification 3) Conditional classification 4) Qualatative 5) Quantative classificaation 6) Statstical seriesQ4. The data given in the below table shows the production in three shifts and the number ofdefective goods that turned out in three weeks. Test at 5% level of significance whether theweeks and shifts are independent.Shift 1st Week 2nd Week 3rd Week TotalI 15 5 20 40II 20 10 20 50III 25 15 20 60Total 60 30 60 150Q5. What is sampling? Explain briefly the types of samplingThe sampling techniques may be broadly classified into1. Probability sampling2. Non-probability samplingProbability Sampling:Probability sampling provides a scientific technique of drawing samples from the population. The technique of drawing samples isaccording to the law in which each unit has a probability of being included in the sample. Simple random samplingUnder this technique, sample units are drawn in such a way each and every unit in the population has an equal and independentchance of being included in the sample. If a sample unit is replaced before drawing the next unit, then it is known as simple RandomSampling with Replacement. If the sample unit is not replaced before drawing the next unit, then it is case, probability of drawing a unitis 1/N, where N is the population size. In the case probability of drawing a unit is 1/Nn. Stratified random samplingThis sampling design is most appropriate if the population is heterogeneous with respect to characteristic under study or the populationdistribution is highly skewed. Table: Merits and demerits of stratified random sampling Merits Demerits1. Sample is more representative 1. Many times the stratification is not effective2. Provides more efficient estimate 2. Appropriate sample sizes are not drawn from each of the stratum3. Administratively more convenient4. Can be applied in situation where different degrees of accuracy isdesired for different segments of population Systematic samplingThis design is recommended if we have a complete list of sampling units arranged in some systematic order such as geographical,chronological or alphabetical order.
11. 11. Table: Merits and demerits of systematic sampling Merits Demerits1. Very easy to operate and easy to check. 1. Many case we do not get up-to-date list.2. It saves time and labour. 2. It gives biased results if periodic feature exist in the data.3. More efficient than simple random sampling if we have up-to-dateframe. Cluster samplingThe total population is divided into recognizable sub-divisions, known as clusters such that within each cluster they are homogenous.The units are selected from each cluster by suitable sampling techniques. Multi-stage samplingThe total population is divided into several stages. The sampling process is carried out through several stagesNon-probability sampling:Depending upon the object of inquiry and other considerations a predetermined number of sampling units is selected purposely so thatthey represent the true characteristics of the population. Judgment samplingThe choice of sampling items depends exclusively on the judgment of the investigator. The investigator‟s experience and knowledgeabout the population will help to select the sample units. It is the most suitable method if the population size is less. Table: Merits and demerits of judgment sampling Merits Demerits1. Most useful for small population 1. It is not a scientific method.2. Most useful to study some unknown traits of a population some ofwhose characteristics are known. 2. It has a risk of investigator‟s bias being introduced.3. Helpful in solving day-to-day problems. Convenience samplingThe sampling units are selected according to convenience of the investigator. It is also called “chunk” which refer to the fraction of thepopulation being investigated which is selected neither by probability nor by judgment. Quota samplingIt is a type of judgment sampling. Under this design, quotas are set up according to some specified characteristic such as age groups orincome groups. From each group a specified number of units are sampled according to the quota allotted to the group. Within the groupthe selection of sampling units depends on personal judgment. It has a risk of personal prejudice and bias entering the process. Thismethod is often used in public opinion studies.Q6. Suppose two houses in a thousand catch fire in a year and there are 2000 houses in avillage. What is the probability that: (i) none of the houses catch fire and (ii) At least onehouse catch fire?An : Given the probability of a house catching fire isP=2/1000=0.002 and n=2000.‟.m=nap=2000*0.002=4Therefore the required probabilities are calculated as follows.‟ 1) The probabilities that none catches fire is given by P(x=0)=
12. 12. 2)the proababilities that at least one catches fire is given byP(x>=1)=1-(x=0)=1-0.01832=0.98168