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1. Descriptive statistics
1.1 Accounting & StatisticsAccountingis an information system that:1. Identifies economic dataof a company.2. Measures accurately andreliably theimpactof economic data.3. Communicatesthis datathroughinternalmanagement reports and externalfinancial reports, so that it can be used fortimelydecision--‐making.
Accountingdata iscriticalfor:? Allocationof humanresourcesand natural resources (biotic &abiotic)? Facilitating decision--‐making? Discharging accountability to thosewho manage resources
How does statisticshelp?? For Internal Users(managementteam) à? management accounting:very detailed tailored confidential dataà? Statisticalmethodshelp themanagement estimate trends, seasonalelements…? For External Users(investors, suppliers…)à? Financialaccounting provides periodic summarised financial datathatis disclosed in‘general purpose financial reports’ to external usersà? statistics help to evaluate risk and returnand answer their concerns…? For Auditors(internal auditors for internal regulations; external auditors for guidelines and regulations) à? statistical methods help to assessthe validity and accuracy of the reported accounting data in order to evaluatebusinessrisk(e.g. 抽样看数据差错的比例)
Data Type:? Qualitative data? Quantitative data:Discrete or Continuous
1.2 Population,sample and statistical methodsA statistical population contains thecomplete selectionof all items of interest,e.g. all companies inAustralia…
A statistical sample is a randomly drawnsubsetof thepopulation withrepresentative characteristics. Randomly drawnsamplesabide to threeprinciples:1) Everysampleitemcomes fromthe same population2) Everyitemhasthe same chance ofbeing selected3) Each item isselected independentlyfrom any other
A parameter describesa feature of the population (e.g.population mean), andastatistic describes a feature of thesample(e.g. sample mean).
à? as the sample increasesthe statistic becomesmore representative ofits parameter
Statistical MethodsDescriptivestatistics aims to understand the key characteristics of the sampleddataInferentialstatistics use sample information to make probabilisticstatements about likelypopulation characteristics, with statisticaltestingofhypotheses to assess the degree of likelihood that the probabilistic statement is true or false.
1.3 Measures of central tendencyCentral tendencydescribes the processof how the data tendsto cluster arounda specific value
file:///C:/Users/MONKEY~1/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif(1) Arithmetic mean (or arithmetic average)
Population mean (parameter):Sample mean (statistic):
Mean is most widely--‐used measureof central tendencybut it has a serious drawback – itissensitivetoextremevalues (outliers)
(2) MedianThe mediandescribes the value that lies halfway in anorderedsample. If n or N is odd, the medianis the middle number.If n or N is even, the median is the averageof the two middle numbers
The medianis unaffected by extreme values,hence we say that it is arobust statistic of central tendency
(3) ModeThe mode is the value that appearsmostfrequently in acollection of data.E.g.For sampleXi = 1,1,2,3,4,6,7,7,7,8,9 the mode is7
The mode is unaffected by extreme values:it is also a robust statistic of centraltendency
The mode is bestfordiscretedata.e.g. estimate the central tendency of maleshoessizes soldin Brisbane to know whatto ship next. A random sampleof shoe sizesgives the following values: Xi=39,40,41,42,43,44,44,44,44.Shouldship44.
Acollection of data with asinglemost frequent value is called unimodal, e.g. 1, 2, 3,4, 4, 4Withtwo mostfrequent values is called bimodal, e.g. 11123444
With more than two most frequent values is called multimodal, e.g. 112344566
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