chapter 5.2 - central tendency

mode

most commonly occurring score in a distribution, highest point on curve

median

middle score in an ordered data set corresponding to 50th percentile

median location

location of median in ordered series, (n+1)/2

mean

average of all observations, sample mean (x̄) and population mean (μ) have same formula: ΣX/n

greek letters

population parameters (every person in group of interest)

english letters

sample statistics (smaller groups to make inferences about group of interest)

mean=median

indicates distribution is symmetrical

mean=median=mode

indicates distribution is symmetrical and unimodal

mode advantages

represents largest # with same score, not affected by extreme scores, great with nominal data, ie. favorite ice cream flavor

mode disadvantages

may not be representative of all numbers and misrepresent “center” of distribution with skewed data, ie. # cigarettes smoked in a day where mode of 0 would be misleading

median advantages

minimally affected by extreme scores, ie. when extreme scores are present it better measures central tendency than mean like salary, also useful with ordinal data, ie. cu’s median ranking among midwestern universities is 3 which means 50% said 3 or higher and 50% said 3 or lower

median disadvantages

difficult to use in statistical procedures, inferential analysis, median isn’t tied to variability

mean advantages

could be used in algebraic equations because standard equations can’t be written for median and mode, estimating pop. mean and inferential procedures

mean disadvantages

largely influenced by extreme scores, sometimes doesn’t exist as a score which can be odd to interpret, has to be on at least an interval scale, ie. can’t be nominal