Central TendencySlide 2MeanProperties of Mean (cont.)MedianMedian (cont.)(cont.)ModeCT & Shape of DistributionLab 9Central TendencyMon. Feb 16th, 2004Central TendencyOne number that summarizes an entire distribution.3 measures of central tendency:–Mean – arithmetic average of scores–Median – score that divides distribution exactly in half (50% percentile)–Mode – most frequent scoreMeanBook notation: Ybar = Y / N–Where  (sigma) indicates ‘sum’–Labs often use “X bar” rather than “Y”, they are interchangeableProperties of the mean:–It is highly influenced by extreme scores (outliers)(3, 5, 9, 11, 15): Y bar = 43 / 5 = 8.6(3, 5, 9, 11, 54): Y bar = 82 / 5 = 16.4May not be very representative when outliersProperties of Mean (cont.)–Add/subtract a constant from each score, the mean changes by adding/subtracting that constant.(3, 5, 9, 11, 15): y bar = 8.6Add 2 to each..(5, 7, 11, 13, 17): y bar = 53 / 5 = 10.6 –Multiply/divide each score by constant, mean changes by mult/div that constant:(3, 5, 9, 11, 15) Y bar = 8.6Multiply each by 3 (9, 15, 27, 33, 45): y bar = 129 / 5 = 25.8Check (8.6 x 3) =25.8MedianDivides distribution in half, 50% scores above & 50% scores belowIf Odd # scores (N): find median position with (N+1) / 2(3, 4, 4, 5, 5, 5, 6, 6, 7), N=9, so (9+1)/2 = score in 5th position  5Median (cont.)If Even N: find median position with (N+1) / 2  (will give a ½ answer, so take average of scores in those 2 adjacent positions)N = 10: (8, 10, 12, 15, 15, 18, 18, 19, 25, 60), med position is (10+1) / 2 = 5.5, so take average of scores in 5th and 6th positions15 + 18 / 2 = 16.5 is median score(cont.)Median is unaffected by outliers (unlike mean), so a better choice for distributions w/outliersNote that in SPSS, easy way to find median in freq distribution tables…look for score/category that includes the 50% percentile (c%)ModeMost frequent scoreMay have bimodal distribution (2 modes)Not too informative, but best used when categorical/nominal data (median & mean don’t make sense there)CT & Shape of DistributionCan determine relative order of mean, median, mode based on skewness of distributionIn pos skew distribution, from L  R will find mode, median, mean (see example)In neg skew distribution, from LR will find mean, median, modeIf symmetrical distribution, mean, median, mode will all be equalLab 93 parts:–1. SPSS - Use students.sav data (used last week)…Do Q1 by hand–2. Use applet (click on button, opens window, then choose “Mean & Median”)–3. SPSS – use study.sav data, get histograms & examine for skewness, then predict position of mean, md,