"COLLEGE OFBUSINESSUnit Reader BookUnit Code: BEO1106Unit Name: Business StatisticsWeek 1 – 6Seminar NotesSeminar ExercisesPractice ProblemsAssignment Questions and Model Answer Tables and FormulaeYear 2017Sidney Lung, Christabel Zhang vu.edu.auVictoria University CRICOS Provider No. 00124K (Melbourne), 02475D (Sydney), RTO Code 3113 BUSINESS STATISTICSBEO1106WEEK 1 EXAMINING DISTRIBUTION:• DATA• DISPLAYING DISTRIBUTION WITHGRAPHS 1INTRODUCTION TO THE UNIT Please read the Unit of Study Guide for all essential information.All learning resources required to study this unit can be downloaded from the unit VU Collaborate web-site:vu.edu.au/student-tools/myvu-student-portalVU Collaborate login details are the same as for your VU email account: User name: Student ID number preceded by “s”eg. s3456789Default password:Your date of birth (ddmmyyyy). Please check the unit web-site regularly (at least twice a week) for messages from the unit coordinator. 2 Assessment:Test(in Week 4)15 marksAssignment35 marksExamination50 marks Total 100 marks Students who cannot sit the test in week 4, and have an application forspecial consideration approved, will have the test component removed fromtheir assessment regime.For these students, the exam will be worth 65marks.The assignment will be completed progressively and submitted in class inWeek 8.Late assignment will be penalised by 1 mark per day for a maximumof 5 working days. Students who obtain a total mark between 45 and 49, inclusive, will be offereda supplementary assessment. Students who pass the supplementaryassessment will be awarded a mark of 50. 3Software: Microsoft Excel is used in this unit to perform statistical procedures.Students will be given instructions on how to use Excel for the relevantstatistical analyses and are required to practice regularly. ReferenceText: Basic Business Statistics: Concepts and Applicationsby Berenson, M.L., Levine, D.M., Szabat, K.A., O’Brien, M., Jayne, N.,and Watson, J. th Publisher: Pearson Australia, 4 ed. 2015. The Practice of Statistics for Business and Economics. by Moore, D.S., McCabe, G.P., Alwan, L.C. & Craig, B. A. th Publisher: Macmillan, USA, 4 ed. 2016.Calculator: A basic calculator is essential for this unit but a statistical calculator isnot essential. You are permitted to take to the exam any hand heldcalculator (scientific, statistical, financial or graphics). 4 Learning method Students must attend 2 X 90 minutes seminars each week.Students should devote of the order of 9 hours a week on thestudy of the unit (i.e. six hours of independent study in addition toclass attendance).This should include revising seminar notes,working through the recommended weekly practice problems andcompleting assignment tasks. The aim of the unitTo introduce students to the basic statistical techniques necessaryto describe and analyze business and economic data for rationalmanagerial decision making. After completing the unit, we would like students to be able to thinkobjectively about conclusion drawn from data and use statisticalmethods in their own way. 5Major topics:1. Examining Distributions with Graphs and with Numbers2. Probability: The Study of Randomness3. Introduction to Inference 4. Inference for Population Means and Proportions5. Inference for Regression 6. Time Series Forecasting7. Index Numbers 6 Session 1 DataWhat is Statistics?Statistics is an area of applied mathematics, concerned with collecting,presenting, analyzing and interpreting numerical facts, which we call data.Statistics is the science of data. We are bombarded by data in our everyday lives. To assist in the makingof rational decisions (about a variable or variables of interest), a knowledgeof statistics helps separate sense or non-sense in this flood of data. The study and collection of data are also important in the work of manyprofessions, so training in the science of statistics is valuable preparationfor a variety of careers.Most areas of academic study make use of numbers and therefore alsomake use of the methods of statistics.It means that it is extremely likelythat your undergraduate studies will involve at some level of statistics.7Learning from DataThe goal of statistics is to learn from data. We often perform calculations andmake graphs based on a set of numbers.However, to learn from data, wemust do more than calculate and plot because data are not just numbers.Theyare numbers with context.The numbers have meanings and stories.• When you do statistical problems, don’t just graph and calculate. Thinkabout the context, and state your conclusion in the specific setting of theproblem.• The goal of statistics is not calculation for its own sake, but gainingunderstanding from numbers.The calculation and graphs can be automatedmachine but you must apply the understanding. A fancy computer analysiscarried out without attention to basic principles will often produce elaboratenonsense.• As you read, seek to understand the principles as well as the necessarydetails of methods and recipes.A statistical analysis requires a set of data. A set of data can be constructed bydeciding what cases are under study and then collect or record the informationobservations about the characteristics of the cases.A set of data forms a 8variable which different observations have different values for the variable.Key Definitions• Casesare objects described by a set of data.Cases may be Customers, subjects in a study, companies, or other objects.• VariableA variable is a characteristic ofcases.Different cases or quantities canvary or take on different values for the variable. For example, eye colour is is a characteristic. This characteristic forms variable because, for example,John, one of the case, has blue colour eyes while Mary, another case, has brown colour eyes – vary from case to case.Sometimes we come across the term Variable of interest, which is the set of cases or quantities weseek to measure (of our interest). We adopt the simple term Variable.• PopulationThe entire set of items /objects /members of a group that is the focus of astatistical investigation.• SampleA small subset /portion of the population selected for analysis.A key aspectof much of the statistics we do is that this subset is representative of the 9population.Key Definitions (cont.)• ParameterA numerical summary measure describing a particular characteristic ofa population.• StatisticA numerical summary measure describing a particular characteristic ofa sample. Note the dual (but related) meaning of the word “statistics” – a branchof applied mathematics, numerical summary measures of a sample. There is actually a third one that you may encounter referring toobservations of a variable of interest (i.e. data) – e.g. VicRoads sign - “Don’t become a road statistic”. • Census A census is a study that obtains data from the entire population. 10 Population vs. SampleVariable of interest#1Population#2Commuting time#3of all VUstudentsSample#4e.g. commuting timesof 36 randomly#...selected VU students#...Numerical summary Numerical summarymeasures of a population measures of a sample are called parameters are called statistics 11Example 1A sample of size 36 students surveyed to determine the principal methodof commuting to campus and the time taken (one-way) in minutes. Commuting methodVariable nametrain, tram, train, train, walk, tram, tram, train, car,bike, walk, tram, train, bike, car, train, train, train,Observationstram, train, bus, scooter, train, train, tram, train, train,tram, train, train, tram, train, tram, train, train, tramVariable name (include units if appropriate)Commuting time (minutes)50, 30, 15, 25, 5, 10, 35, 70, 25, 20, 5, 5, 25, 5, 15,Observations55, 50, 20, 25, 50, 30, 15, 28, 70, 40, 60, 60, 15, 40,25, 40, 20, 30, 45, 45, 15 Note:Raw (as collected) data 12 In practice, any set of data is accompanied by background informationthat helps us understand the data.When you plan to collect a set ofprimary data or conduct statistics on a set of secondary data, ask yourselfthe following questions:• Who? What cases do the data describe?How many cases appearsin the data.• What? How many variables do the data contains?What are theexact definition of these variables? In what unit of measurement iseach variable recorded? • Why? What purpose do the data have?Do we hope to answer somespecific questions? Do we want to draw conclusions about cases otherthan the one we actually have data for? Are the variable that arerecorded suitable for the intended purpose?13Applied your knowledgeFigure 1.A sample of principle methods of commuting (X) and commutingtime (Y)in minutes to City Flinders Campus by VU students ID X Y ID X Y ID X Y 1 train 50 13 train 25 25 tram 40 2 tram 30 14 bike 5 26 train 60 3 train 15 15 car 15 27 train 60 4 train 25 16 train 55 28 tram 15 5 walk 5 17 train 50 29 train 40 6 tram 10 18 train 20 30 train 25 7 tram 35 19 tram 25 31 tram 40 8 train 70 20 train 50 32 train 20 9 car 25 21 bus 30 33 tram 30 10 bike 20 22 scooter 15 34 train 45 11 walk 5 23 train 28 35 train 45 12 tram 5 24 train 70 36 tram 15 Refer to the data above,answer: What cases do the data describe?Howmany cases are there?How many variables are there? What are their definition 14and unit of measurement? What purpose do the data have?• Some variables, like Commuting Method, simply place theobservations into categories without much arithmetic we can do.Now,take a moment to interpret the “average commuting method”. Does itmake sense?• Other variables, like Commuting Time have numerical values for whichwe can do arithmetic.It makes sense to find out the average time forcommuting to campus.Types of DataDataCategorical QuantitativeNominal Ordinal Discrete Continuous 15Types of Data (cont.)Categorical A categorical variable places a case into one or the other groups.• NominalData representing the name or label of a category/group e.g. marital status, hair colour, gender, commuting method• OrdinalData that assumes a natural ordere.g. exam grades (HD, D, C, P, N), survey responses (stronglyagree, agree, no opinion, disagree, strongly disagree) 16 Types of Data (cont.)QuantitativeA quantitative variable take numerical values which arithmetic can beperformed and the results of the arithmetic make sense.• Discrete Data with the characteristic that there are a finite number of valuesin a given interval e.g. number of students in a sample of 36 who might commute bytram … how many possible values are there between 1 and 3?0123 …Only three possible values 17Types of Data (cont.)• Continuous Data with the characteristic that there is (theoretically) an infinitepossible number of values in a given interval.e.g. commuting time – how many possible time values are therebetween 40 and 60 minutes?Unlimited number of values between40 min 60 min e.g. 45 mins, 45.1 mins, 45.06 mins, 45.059 mins – theoretically aninfinite number of possible values between 40 and 60 minutes. Note that theoretically continuous data is most often discretised once themeasurement is made (due to the accuracy restriction on the measuring device). What degree of accuracy appears to be the case for the commuting timemeasurements (see Slide 12)?18 Levels/Scales of MeasurementCategorical data is said to be “measured” on a nominal or ordinalscale depending on whether the data is nominal or ordinal.For data measured on a nominal scale about all wecan do iscount the frequencies of repetition of the observations.For datameasured on an ordinal scale not only can frequency counts beperformed but also the data can be ordered/ranked.Quantitative data is said to be measured on a ratio or intervalscale depending on whether the scale contains an absolute zeroor not.For data measured on an interval scale not only can frequencycounts and ordering be performed but the arithmetical operationsof addition and subtraction are meaningful.For data measuredon a ratio scale all of the previously mentioned numericaloperations (frequency counts, ordering, + and –) are possibletogether with the operations of multiplication and division. 19Levels/Scales of Measurement - examplesNote that higher level scales incorporate the mathematicalattributes of all scales beneath them. True zero existsHighest Height, weight, age,(multiplication and Ratio DataLevelweekly food expensesdivision are possible)No true zero (only Temperature in degreesaddition and subtraction Interval DataCelsius, % changearepossible)Rankings in a tennisWe can rank andtournament, student letterOrdinal Dataorder the data grades, Likert scalesLowestMarital status, type of carWe can performLevel Nominal Datafrequency countsowned, gender, hair colourHomework -Practice Problems:Week 1, Q1.1, 1.2, 1.3 20 In-class Statistic Problems Solving by Students Group discussions with assistance from instructor and academic support staffA recently released report suggests that mobile phone addiction iscosting Australians $560 million a year in bill “blow outs”.The followingdata represents the “bill shocks” (correct to the nearest dollar) over a 12month period of a random sample of 45 mobile phone users whoseannual charges exceeded what they expected. 482 608 428 619 328695 368 594 299 547137 311 222 447 88533 692 101 358 23958 114 561 265 16619691 99 264 468526 347 98 193 544253 333 276 406 659575 23 287 218 661 211. Describe as precisely as possible the variable represented by the data.2. What cases do the data describe?3. How many variables are there? 4. How many cases are there? 5. What is the unit of measurement? 6. What purpose do the data have? 7. What type of datathe variable represent, categorical or quantitative? 8. Out of the four scales of measurement, which level the data can beclassified.9. What arithmetic this data can be applied? 22 BUSINESS STATISTICS BEO1106 WEEK 1EXAMINING DISTRIBUTION: • DATA • DISPLAYING DISTRIBUTION WITHGRAPHS 1 Session 2 Displaying Distribution withGraphs To understand a set of data, we can first explore the main features bydescribing what we see using a graph or graphs.• For categorical variables, we can use Bar (Column) Charts and PieCharts.The values of a categorical variable are labels for the categories, such as“train”, “bus” and “scooter”. The distribution of a categorical variable liststhe categories and gives either the count (Frequency (f)) or the percent(Relative Frequency (rf)) of cases that falls in each category. • For quantitative variable, we can use Histogram and Time Plot. Quantitative variables often take many values. A graph of the distributioncan be clearer if nearby values are grouped together to form classes.Themost common graph of the distribution for grouped quantitative variable isa histogram.2Categorical Data- Tables and Graphs/Charts Categorical Data Graphs Summary Tables (Frequency andRelative Frequency) Column Charts Pie Charts (Frequency andRelative Frequency) 3 Summary Table Frequency and Relative Frequency Tables for the Commuting Method(categorical) DataTable 1. Frequency (f) and relative frequency (rf)table for thecommuting method dataFrequency values obtainedVariable of by tallying repetitions of eachinterest commuting method. C Method f rf (%) Bike 2 5.6 Clustering/concentration Bus 1 2.8 18 students travelled by train. (18/36)X100=50.0%of students travelledCar 2 5.6 by trainCategories Scooter 1 2.8 Train 18 50.0 Tram 10 27.8 Variability Walk 2 5.6 Commuting method data exhibitsconsiderable variability (7 categoriesTotal 36 100.2 (rather than 1 or 2)). Sample size Theoretically 100%(round-off error) 4Graphs • Graphical alternative to a frequency or relativeColumn Charts frequency table. Example - Commuting method data• Height of column proportional to frequency (orrelative frequency). • Columns of equal widths with equal spacesC Method f rf (%) between. Bike 2 5.6 • Variable of interest along horizontal axis. Bus 1 2.8 • Frequency or Relative Frequency (usually %)along vertical axis. Car 2 5.6 • Clustering/concentration – tallest column(s). Scooter 1 2.8 • Variability – number of columns. Train 18 50.0 Frequency Tram 10 27.8 20 Walk 2 5.6 18 16 Total 36 100.2 14 12 10 8 6 4 2 0 Bike Bus Car Scooter Train Tram Walk Commuting method 5 Graphs (cont.) Pie Charts Example - Commuting method data • Graphical alternative to a relative frequency(%) table. C Method f rf (%) • Area of sector (slice) proportional to relativefrequency. Bike 2 5.6 • Clustering/concentration – largest slice(s). Bus 1 2.8 • Variability – number of slices. Car 2 5.6 Walk Bike Scooter 1 2.8 Bus 6% 6% 3% Car Train 18 50.0 6% Tram Scooter Tram 10 27.8 28% 3% Walk 2 5.6 Total 36 100.2 Train 50% Commuting method Practice Problems:Week 1, Q1.4 6"