Hockenbury Discovering Psychology 5th txtbk

Descriptive StatisticsA-5the two intervention groups in terms of compliance. Participants in the alternativegroup were more likely to be meditating at the end of the study than theirtraditional-group counterparts were to be practicing progressive relaxation.Measures of Central TendencyFrequency distributions can be used to organize a set of data and tell us how scoresare generally distributed. But researchers often want to put this information into amore compact form. They want to be able to summarize a distribution with a singlescore that is “typical.” To do this, they use a measure of central tendency.The ModeThe mode is the easiest measure of central tendency to calculate. The mode is simplythe score or category that occurs most frequently in a set of raw scores or in afrequency distribution. The mode in the frequency distribution shown in Table A.1is 2; more participants reported exercising two hours per week than any other category.In this example, the mode is an accurate representation of central tendency,but this is not always the case. In the distribution 1, 1, 1, 10, 20, 30, the mode is1, yet half the scores are 10 and above. This type of distortion is the reason measuresof central tendency other than the mode are needed.measure of central tendencyA single number that presents some informationabout the “center” of a frequencydistribution.modeThe most frequently occurring score in adistribution.medianThe score that divides a frequency distributionexactly in half so that the same numberof scores lie on each side of it.meanThe sum of a set of scores in a distributiondivided by the number of scores; the meanis usually the most representative measureof central tendency.The MedianAnother way of describing central tendency is to determine the median, or thescore that falls in the middle of a distribution. If the exercise scores were laid outfrom lowest to highest, they would look like this:0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7←What would the middle score be? Since there are 30 scores, look for the point thatdivides the distribution in half, with 15 scores on each side of this point. The mediancan be found between the 15th and 16th scores (indicated by the arrow). In this distribution,the answer is easy: A score of 2 is the median as well as the mode.The MeanA problem with the mode and the median is that both measures reflect only onescore in the distribution. For the mode, the score of importance is the most frequentone; for the median, it is the middle score. A better measure of central tendencyis usually one that reflects all scores. For this reason, the most commonlyused measure of central tendency is the mean, or arithmetic average. You have calculatedthe mean many times. It is computed by summing a set of scores and thendividing by the number of scores that went into the sum. In our example, addingtogether the exercise distribution scores gives a total of 70; the number of scores is30, so 70 divided by 30 gives a mean of 2.33.Formulas are used to express how a statistic is calculated. The formula for themean isX XNIn this formula, each letter and symbol has a specific meaning:X is the symbol for the mean. is sigma, the Greek letter for capital S, and it stands for “sum.” (Taking a coursein statistics is one way to learn the Greek alphabet!)X represents the scores in the distribution, so the numerator of the equation says,“Sum up all the scores.”N is the total number of scores in the distribution. Therefore, the formula says,“The mean equals the sum of all the scores divided by the total number of scores.”