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StatisticsMath 314

Game PlanIntroductionPresentation Line graphPie graphPictographBar graphHistogram Raw Stats Frequency Stats Missing Values

Stats IntroThere are lies, there are damn lies and then there are statistics - Mark TwainThe gist of statistics is that you are trying to convey an idea by use of numbers. It is not always honest!

Stats IntroHypothesis: Student A has a school average of 10%Conclusion: Student A is a bad person. The statistic does not measure the persons goodness or badness.What does that statistic mean?This means on average student As mark is 10%

Presentation A picture is worth a thousand words - AnonymousLine Graph- time is always x Data t value 0 5 1 4 2 2 3 4

Line Graph

Pie or CircleYou need to addto your dataData Type # Bass 6 Salmon 12 Perch 2

Pie Charts 1st step draw a circle 2nd step measure the angle3rd step label36108BassPerchSalmonDo Stencil #1 & 2

PictographBe creativeBe artisticDataType # Bass 6Salmon 12Perch 2 Legend = 2 fishPBS

Bar Graph VerticalDataType # Bass Salmon Perch6122

Bar Graph HorizontalDataType # Bass Salmon Perch6122This bar graph will be tilted 90 clockwise

Compound Vertical GraphDataType # Bass Salmon Perch6122What is the same / difference here?Do #4; you have 10 minutes

HistogramA bar graph is where the bars touchUsually interested in intervals of numbersExample: Given the data below, draw a histogram with an intervals of 50(3,8,9,22,46,47,80,85,87,99)We are thankful that they are in order; otherwise, put them in order!

HistogramIntervalTally f (frequency)[0,50[64[50,100]50100

Raw Statistics (mean, median,mode & Range)Download / review slides on this topicAnalysis Rule #1: Put them in order 1st Example: Calculate the mean, mode, median and range of the following(2,7,9,12,15)Notice that they are in order!

Raw Stats SolutionRecall #s are (2,7,9,12,15)Mean = 45/9 = 9Mode = 0Median 2, 7], 9, [12, 15 = 9 Range = 15-2 = 13

Frequency StatsData is not always simply listed out. It may be presented as a frequency tableValue xi f 2 3 7 2 10 1 15 6If we wanted to see it listed out2,2,2,7,7,10,15,15,15,15,15,15This is not always practical!What is the mean, mode, median and range of this?

Example Xi f xi x f Interval 2 3 6 1st 3rd 7 2 14 4th 5th 10 1 10 6th 15 6 90 7th 12th Total 12 120

nsum

Solutionx = 120/12x = 10M We need the (6th and 7th interval) / 2 X6 = 10X7 = 15M = 10 + 15 2M = 12.5

SolutionMode is the value with the biggest frequencyMode = 15Range is the highest lowestRange = 15-2 = 13Another example (optional)

Missing DataThese questions are given to see if you UNDERSTAND what the statistics meanTricks x = SUM nSum = x x n Median: Odd / Even amount of #?Consider it a game you must think!

Missing DataExample #1: Given the following distributions, determine the missing value(s)16, 23, 34, 15 n = 5 x = 32Order 1st! 15, 16, 23, 34Missing 1 = ASum = n x x5 x 32 = 160 Sum (now) = 15 + 16, + 23 + 34 = 88 160 = 88Thus A = 160 - 88 = 72 (missing)

Missing DataExample #2: Consider 12, 18, 24, 30 n = 5 and median is 20Missing 1 = An is odd, median must be in the set!A = 20

Missing DataEx#3: 10,12,15,19,21 n=7, x=15, Median=15, Mode=0 R = 16Missing 2: A & BSum = n x x7 x 15 = 105Sum (now) = 10 + 12 + 15 + 19 + 21 = 77Thus A + B = 105 77 = 28Median = 15 means that there is one more than 15 and one less than 15. However, the range is wrong!Try A B = 16 Thus, A + B = 28 (respecting sum rule) A B = 16 (respecting range)2A = 44A = 22 (missing)B = 6