Chapter 3 Descriptive Statistics: Numerical Measures Part A. Measures of Location Central Tendency Measures Percentiles and Quartiles. Mean. The mean of a data set is the average of all the data values. The sample mean is the point estimator of the population mean m. Sample Mean. - PowerPoint PPT Presentation
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Considerations in Using the MeanConsiderations in Using the Mean
Requires interval/ratio levelRequires interval/ratio level Influenced by extreme scoresInfluenced by extreme scores Balancing point of the distribution (+ Balancing point of the distribution (+
and -deviations cancel out)and -deviations cancel out) Minimizes the “sum of squares” (sum of Minimizes the “sum of squares” (sum of
squared deviations around mean is squared deviations around mean is smaller than around any other number)smaller than around any other number)
•Mean is our “best guess” or estimate Mean is our “best guess” or estimate – minimizes errors in prediction– minimizes errors in prediction
The The medianmedian is the is the middle score or midpoint middle score or midpoint of ofa set of scores when scores are arranged in order.a set of scores when scores are arranged in order.
For an For an odd numberodd number of observations: of observations:
The The modemode of a data set is the value that occurs of a data set is the value that occurs with greatest frequency.with greatest frequency. The greatest frequency can occur at two or moreThe greatest frequency can occur at two or more different values.different values. If the data have exactly two modes, the data areIf the data have exactly two modes, the data are bimodalbimodal.. If the data have more than two modes, they areIf the data have more than two modes, they are multimodalmultimodal..
Admission test scores for colleges and universitiesAdmission test scores for colleges and universities are frequently reported in terms of percentiles.are frequently reported in terms of percentiles.
The The ppth percentileth percentile of a data set is a value such of a data set is a value such that at least that at least pp percent of the items take on this percent of the items take on this value or less and at least (100 - value or less and at least (100 - pp) percent of ) percent of the items take on this value or more.the items take on this value or more.
Arrange the data in ascending order.Arrange the data in ascending order.
Compute index Compute index ii, the, the position position of the of the ppth percentile.th percentile.
ii = ( = (pp/100)/100)nn
If If ii is is not an integernot an integer, round , round upup. The . The pp th percentileth percentile is the is the value in the value in the ii th positionth position..
If If ii is an is an integerinteger, the , the pp th percentile is the th percentile is the averageaverage of the values in positionsof the values in positions i i and and ii +1.+1.