Measures of Central Tendency

KNR 445Statisticst-testsSlide 1Measures of Central Tendency1

Study note using audio slidesAdvantagesRevisiting themNo attention lapsesNothing missed, everything available for comprehensive study guide come exam timesMore class time available for discussion/group work/explanation/SPSSDisadvantageNot real time lecture/no immediate interaction w/instructorCan result in wanting to ask questions, but not being able toRecommendation:Print slides before listening, make notes and write questions down as you goEmail question/s if needed in order to make progressListen to the slides early in the week so that theres plenty of time to allow for communication with the instructor

KNR 445CT/Spread & Z-scoresSlide 21234

KNR 445CT/Spread & Z-scoresSlide 3Measure of Central TendencyWhat SINGLE summary statistic or parameter best describes the central location of an entire distribution?Mode: which value occurs most (what is fashionable)Median: the middle value in the data, once its ranked (the 50th percentile)Mean: mathematical balance point; arithmetic mean; mathematical mean1234

General note on this early stuff

KNR 445CT/Spread & Z-scoresSlide 4ModeMost frequent occurrenceWhat if data were17, 19, 20, 20, 22, 23, 23, 28Problem: set of numbers can be bimodal, or trimodal, depending on the scoresNot a stable measure123

KNR 445CT/Spread & Z-scoresSlide 5MedianRank numbers, pick middle oneWhat if data were 17, 19, 20, 23, 23, 28Solution: add up two middle scores, divide by 2 (=21.5)Best measure in asymmetrical distribution (ie skewed), not sensitive to extreme scores12

KNR 445CT/Spread & Z-scoresSlide 6MeanAdd up the numbers and divide by the sample size (number of numbers!)Try this one5,3,2,6,9This is the best measure of the three after all, it uses more information than any of the others123

KNR 445CT/Spread & Z-scoresSlide 7Characteristics of the MeanBalance pointpoint around which deviations sum to zeroDeviation is difference between two numbersFor instance, if scores are 5,3,2,6,9Mean is 5Sum of deviations: 0+(-2)+(-3)+1+4= 0See?

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KNR 445CT/Spread & Z-scoresSlide 8Characteristics of the MeanBalance pointAffected by extreme scoresScores 7, 11, 11, 14, 17Mean = 12, Mode and Median = 11Scores 7, 11, 11, 14, 170Mean = 42.6, Mode & Median = 111

KNR 445CT/Spread & Z-scoresSlide 9Characteristics of the MeanBalance pointAffected by extreme scoresAppropriate for use with interval or ratio scales of measurement1

KNR 445CT/Spread & Z-scoresSlide 10Characteristics of the MeanBalance point Affected by extreme scoresAppropriate for use with interval or ratio scales of measurementMore stable than Median or Mode when multiple samples drawn from the same populationBasis for inferential stats1

KNR 445CT/Spread & Z-scoresSlide 11Guidelines to choose Measure of Central TendencyMean is preferred because it is the basis of inferential statisticsMedian may be better for skewed data?Distribution of wealth in the USMode to describe average of nominal data (Percentage - relative frequency)1

KNR 445CT/Spread & Z-scoresSlide 12MedianModeMeanScoresNormal Distribution1234

KNR 445CT/Spread & Z-scoresSlide 13Positively skewed distributionScoresMedianModeMean12

KNR 445CT/Spread & Z-scoresSlide 14Negatively skewed distributionMedianModeMeanScores12

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