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Making Sense of Sample Data

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Understanding financial mathematics

Understanding financial mathematics

Published in: Economy & Finance, Technology

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  • 1. 2013/05/071STATISTICSX-Kit TextbookChapter 8 (Making sense of Sample Data)Precalculus TextbookAppendix B: Concepts in StatisticsPar B.1 (Representing Data)ORGANISE& SUMMARISERAW DATARaw DataDiscrete DataUngroupedFrequencyTableGrouped (lowfrequency)ContinuousDataGroupedFrequencyTableNumber of fraudulent cheques receivedat abank each week for 30 weeksWeek12 3 4 5 6 7 8 9 105 3 8 3 3 1 10 4 6 8Week1112 13 14 15 16 17 18 19 203 5 4 7 6 6 9 3 4 5Week2122 23 24 25 26 27 28 29 307 9 4 5 8 6 4 4 10 4DISCRETEDATATERMINOLOGY EXPLANATIONVariable of Interest? It is the number of fraudulent chequesin a week.Continuous or DiscreteData?Discrete Data because cheques can onlyexist in whole numbers.Raw Data? A list of different values. Data has notbeen processed in any way.Data Point or Observation? Each of the values in the raw data.Frequency? The number of times a data valueappears.Frequency Table Table to organise and summarise data.FREQUENCYTABLEDistinct Values Tally Marks Frequency1 / 12 03 //// 54 //// // 75 //// 46 //// 47 // 28 /// 39 // 210 // 2GRAPH0123456781 2 3 4 5 6 7 8 9 10FrequencyFrequency
  • 2. 2013/05/072Truck Data: weights(in tonnes) of 20 fullyloaded trucksTruck12 3 4 5 6 7 8 9 10Weight4.543.81 4.29 5.16 2.51 4.63 4.75 3.98 5.04 2.80Truck1112 13 14 15 16 17 18 19 20Weight2.525.88 2.95 3.59 3.87 4.17 3.30 5.48 4.26 3.53CONTINUOUSDATATERMINOLOGY EXPLANATIONVariable of Interest? The weight of a loaded truck.Continuous or DiscreteData?Continuous Data, you can get anynumber of values between twogiven values.Frequency Table Table to organise and summarisedata.Grouped Frequency TableFREQUENCYTABLEClass Intervals Tally Marks Frequency𝟐. 𝟓 ≤ 𝒙 ≤ 𝟑. 𝟎 //// 4𝟑. 𝟎 ≤ 𝒙 ≤ 𝟑. 𝟓 / 1𝟑. 𝟓 ≤ 𝒙 ≤ 𝟒. 𝟎 //// 5𝟒. 𝟎 ≤ 𝒙 ≤ 𝟒. 𝟓 /// 3𝟒. 𝟓 ≤ 𝒙 ≤ 𝟓. 𝟎 /// 3𝟓. 𝟎 ≤ 𝒙 ≤ 𝟓. 𝟓 // 2𝟓. 𝟓 ≤ 𝒙 ≤ 𝟔. 𝟎 // 2GRAPH01234560 - 2.5 2.5 - 3.0 3.0 - 3.5 3.5 - 4.0 4.0 - 4.5 4.5 - 5.0 5.0 - 5.5 5.5 - 6.0FrequencyFrequencyPRESENTATIONOF DATAFrequencyTablePictogramBarGraphsHistogramPieChartLineGraphsStem-and-LeafOgiveFREQUENCYTABLEClass Intervals Frequency CumulativeFrequency𝟐. 𝟓 ≤ 𝒙 ≤ 𝟑. 𝟎 4 4𝟑. 𝟎 ≤ 𝒙 ≤ 𝟑. 𝟓 1 5𝟑. 𝟓 ≤ 𝒙 ≤ 𝟒. 𝟎 5 10𝟒. 𝟎 ≤ 𝒙 ≤ 𝟒. 𝟓 3 13𝟒. 𝟓 ≤ 𝒙 ≤ 𝟓. 𝟎 3 16𝟓. 𝟎 ≤ 𝒙 ≤ 𝟓. 𝟓 3 19𝟓. 𝟓 ≤ 𝒙 ≤ 𝟔. 𝟎 1 20
  • 3. 2013/05/073OGIVE05101520252.5 3 3.5 4 4.5 5 5.5 6Cumulative FrequencyCumulative FrequencyPictogram: Net Worthof AmericasRichest BillionairesPie Chart: Average Annual Expenses in a U.S. HouseholdEXAMPLEIn a class with 30 pupils there are 12 withblue eyes; 9 with brown eyes; 4 with darkbrown eyes and 5 with green eyes.1. Draw a pie chart showing thisinformation.2. Calculate the fraction and percentagerepresented by each eye colour.EXAMPLE: SOLUTIONColour ofEyesFrequency Angle at Centre PercentageBlue 12 𝟏𝟐𝟑𝟎× 𝟑𝟔𝟎°= 𝟏𝟒𝟒°𝟏𝟐𝟑𝟎× 𝟏𝟎𝟎 = 𝟒𝟎%Brown 9 𝟗𝟑𝟎× 𝟑𝟔𝟎°= 𝟏𝟎𝟖°𝟗𝟑𝟎× 𝟏𝟎𝟎 = 𝟑𝟎%Dark Brown 4 𝟒𝟑𝟎× 𝟑𝟔𝟎°= 𝟒𝟖°𝟒𝟑𝟎× 𝟏𝟎𝟎 = 𝟏𝟑, 𝟑%Green 5 𝟓𝟑𝟎× 𝟑𝟔𝟎°= 𝟔𝟎°𝟓𝟑𝟎× 𝟏𝟎𝟎 = 𝟏𝟔, 𝟕%Total 30 𝟑𝟔𝟎° 𝟏𝟎𝟎%PIE CHARTBlueBrownDark BrownGreen
  • 4. 2013/05/074Bar Graph: Expected U.S. PopulationAged 100 and Over DoubleBar Graph: Fuel EfficiencyLineGraph: Effectof Inflationon the Valueof a $100,000LifeInsurance PolicyDoubleLineGraph: Populationsof Californiaand TexasStem-and-Leaf PlotRepresent the data below in a stem-and-leaf plot:152; 165; 143; 139; 138;144; 150; 158; 161; 157;143; 156; 162; 165; 139;158; 151; 167; 166; 160;170; 132; 145; 151; 148;147; 171; 155; 146; 141.Stem-and-Leaf PlotSTEM LEAVES13 9; 8; 9; 214 3; 4; 3; 5; 8; 7; 6; 115 2; 0; 8; 7; 6; 8; 1; 1; 516 5; 1; 2; 5; 7; 6; 017 0; 1