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Chapter 8 addisional content Chapter 8 addisional content Document Transcript

  • 2013/05/101STATISTICSX-Kit TextbookChapter 8 & 9 (Learning more about Sample Data)Precalculus TextbookAppendix B: Concepts in StatisticsPar B.2 (Measures of Central Tendency & Dispersion)ORGANISE& SUMMARISERAW DATARaw DataDiscrete DataUngroupedFrequencyTableGrouped (lowfrequency)ContinuousDataGroupedFrequencyTableCall Centre Data: waiting times (in seconds)for 35 randomly selected customersC1 2 3 4 5 6 7 8 9 10 11 1275 37 13 90 45 23 104 135 30 73 34 12C13 14 15 16 17 18 19 20 21 22 23 2438 40 22 47 26 57 65 33 9 85 87 16C25 26 27 28 29 30 31 32 33 34 35102 115 68 29 142 5 15 10 25 41 49DISCRETE DATATERMINOLOGY EXPLANATIONVariableof Interest? Waiting times (in seconds).Continuous orDiscreteData?Continuous Data – workingwithmeasures of time.Raw Data? A list of different values. Data hasnotbeen processed in anyway.Numberof Observation? 35Frequency? The numberof times a data valueappears.FrequencyTable Grouped FrequencyTableFREQUENCY TABLEClass Intervals TallyMarks Frequency0 ≤ 𝑥 ≤ 25 //// //// 1025 < 𝑥 ≤ 50 //// //// / 1150 < 𝑥 ≤ 75 //// / 675 < 𝑥 ≤ 100 /// 3100 < 𝑥 ≤ 125 /// 3125 < 𝑥 ≤ 150 // 2HISTOGRAM: CONTINUOUS DATA024681012Intervals[0;25](25;50](50;75](75;100](100;125](125;150]
  • 2013/05/102FREQUENCY TABLEClass Intervals Frequency CumulativeFrequency0 ≤ 𝑥 ≤ 25 10 1025 < 𝑥 ≤ 50 11 10 + 11 = 2150 < 𝑥 ≤ 75 6 21 + 6 = 2775 < 𝑥 ≤ 100 3 27 + 3 = 30100 < 𝑥 ≤ 125 3 30 + 3 = 33125 < 𝑥 ≤ 150 2 33 + 2 = 35OGIVE: CUMULATIVE FREQUENCIES05101520253035400 25 50 75 100 125 150Cumulative FrequencyCumulative FrequencySTATISTICS IS …Collection of Data Analysis of DataInterpretation ofDataPresentation ofDataDESCRIPTIVE STATISTICSUse graphs, charts& tablesCalculation ofvarious statisticalmeasuresTo organise andsummariseinformationTo reduceinformation to amanageable sizeand place into focusINFERENTIAL STATISTICSPopulation The complete collectionofindividuals,items,or dataunder consideration in a studySample The portion ofthe population selected for analysisInferentialStatisticsConsists oftechniques for reachingconclusionsabout a populationbaseduponinformationcontainedin a sampleExample: Population–all registeredvotersSample – a telephone surveyof600registered votersVARIABLE,OBSERVATION AND DATA SET• A variable is a characteristic of interestconcerning the individual elements of apopulation or a sample.• Represent a variable by a letter such as x.• An observation is the value of a variable forone particular element from the sample orpopulation.• A data set consists of the observations of avariable for the elements of a sample.
  • 2013/05/103QUANTITATIVE VARIABLE:DISCRETE AND CONTINUOUS VARIABLE• A quantitative variable is determined whenthe description of the characteristic of interestresults in a numerical value.• A discrete variable is a quantitative variablewhose values are countable (results fromcounting).• A continuous variable is a quantitativevariable that can assume any numerical valueover an interval (results from making ameasurement).EXAMPLEDISCRETE VARIABLE POSSIBLE VALUESFOR THE VARIABLEThe number of individuals ingroups of 30 with a type Apersonality0, 1, 2, 3, ..., 30EXAMPLECONTINUOUS VARIABLE POSSIBLE VALUES FOR THEVARIABLEThe cholesterol reading forthose individuals havingcholesterol readings≥ 200mg/unitAll real numbers between200 and 𝑏 (largestcholesterol reading of allsuch individuals)QUALITATIVE VARIABLE:• A qualitative variable is determined when thedescription of the characteristic of interestresults in a nonnumeric value.• Classified into two or more categories.• The categories for qualitative variables areoften coded for purpose of performingcomputerised statistical analysis.EXAMPLEQualitativevariablePossible categoriesGender Male, femaleSUMMATION NOTATION𝒙 = 𝒕𝒉𝒆 𝒔𝒖𝒎𝒎𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝒙•Sigma notation (Greek symbol).•Operation of sums - 𝒙.•Operation of sums of squares -𝒙 𝟐; 𝒙 𝟐.•Operations of sums of cross products -𝒙𝒚.
  • 2013/05/104EXAMPLEX 0.1 0.2 0.3 0.4 0.5Y 2 4 6 8 10Calculate:1. 𝐱 𝟐2. 𝐱𝐲3. 𝐱 𝟐4. 𝐱 𝐲COMPUTER SOFTWARE AND STATISTICS•The techniques of descriptive andinferential statistics involve lengthyrepetitive computations as well as theconstruction of various graphicalconstructs.•Statistical packages: SAS, SPSS, MINITAB,EXCEL, STATISTIX