Hockenbury Discovering Psychology 5th txtbk

Descriptive StatisticsA-7Table A.2Calculating the Standard DeviationWeight Mean Weight Mean (Weight Mean) SquaredX XX X(X X ) 2155 124 31 961149 124 25 625142 124 18 324138 124 14 196134 124 10 100131 124 7 49127 124 3 9125 124 1 1120 124 4 16115 124 9 81112 124 12 144110 124 14 196105 124 19 361102 124 22 48495 124 29 841Sum ( g ) 1,860 g 0 g 4,388Mean ( X ) 124To calculate the standard deviation, yousimply add all the scores in a distribution(the left-hand column in this example) anddivide by the total number of scores to getthe mean. Then you subtract the meanfrom each score to get a list of deviationsfrom the mean (third column). Next yousquare each deviation (fourth column),add the squared deviations together,divide by the total number of cases, andtake the square root.SD Bg 1X X 2 2N B4,38815 17.10listed in the third column of the table. The next step is to square each of the deviations(done in the fourth column), then add the squared deviations (S 4,388)and divide that total by the number of participants (N 15). Finally, we take thesquare root to obtain the standard deviation (SD 17.10). The formula for thestandard deviation (SD) incorporates these instructions:g 1 X X 2 2SD B NNotice that when scores have large deviations from the mean, the standard deviationis also large.z Scores and the Normal CurveThe mean and the standard deviation provide useful descriptive information aboutan entire set of scores. But researchers can also describe the relative position of anyindividual score in a distribution. This is done by locating how far away from themean the score is in terms of standard deviation units. A statistic called a z scoregives us this information:z X XSDThis equation says that to compute a z score, we subtract the mean from the scorewe are interested in (that is, we calculate its deviation from the mean) and dividethis quantity by the standard deviation. A positive z score indicates that the score isabove the mean, and a negative z score shows that the score is below the mean. Thelarger the z score, the farther away from the mean the score is.standard deviationA measure of variability; expressed as thesquare root of the sum of the squareddeviations around the mean divided by thenumber of scores in the distribution.z scoreA number, expressed in standard deviationunits, that shows a score’s deviation fromthe mean.