Hockenbury Discovering Psychology 5th txtbk

Descriptive StatisticsA-3Frequency DistributionSuppose that at the start of the health-promotion study 30 people in the traditionalgroup reported getting the following number of hours of aerobic exercise each week:2, 5, 0, 1, 2, 2, 7, 0, 6, 2, 3, 1, 4, 5, 2,1, 1, 3, 2, 1, 0, 4, 2, 3, 0, 1, 2, 3, 4, 1Even with only 30 cases, it is difficult to make much sense of these data. Researchersneed a way to organize such raw scores so that the information makes sense ata glance. One way to organize the data is to determine how many participantsreported exercising zero hours per week, how many reported exercising one hour,and so on, until all the reported amounts are accounted for. If the data were putinto a table, the table would look like Table A.1.This table is one way of presenting a frequency distribution—a summary ofhow often various scores occur. Categories are set up (in this case, the number ofhours of aerobic exercise per week), and occurrences of each category are tallied togive the frequency of each one.What information can be gathered from this frequency distribution table? We knowimmediately that most of the participants did aerobic exercise less than three hours perweek. The number of hours per week peaked at two and declined steadily thereafter.According to the table, the most diligent exerciser worked out about an hour per day.Some frequency distribution tables include an extra column that shows the percentageof cases in each category. For example, what percentage of participantsreported two hours of aerobic exercise per week? The percentage is calculated bydividing the category frequency (8) by the total number of people (30), whichyields about 27 percent.While a table is good for summarizing data, it is often useful to present afrequency distribution visually, with graphs. One type of graph is the histogram(Figure A.1). A histogram is like a bar chart with two special features: The bars arealways vertical, and they always touch. Categories (in our example, the number ofhours of aerobic exercise per week) are placed on the x-axis (horizontal), and they-axis (vertical) shows the frequency of each category. The resulting graph lookssomething like a city skyline, with buildings of different heights.Table A.1A Frequency Distribution TableHours ofAerobic Exerciseper WeekFrequency0 41 72 83 44 35 26 17 130A table like this is one way of presentinga frequency distribution. It shows at aglance that most of the people in ourhypothetical group of 30 were not zealousexercisers before they began their traditionalhealth-promotion program. Nearlytwo-thirds of them (19 people) engagedin vigorous exercise for two hours or lesseach week.y-axis876Frequency5432100 1 2 3 4 5 6 7Hours of aerobic exercise per week x-axisat start of studyFigure A.1 A Histogram This histogram is another way of presentingthe data given in Table A.1. Like the table, the histogramshows that most people do, at best, only a moderate amount ofaerobic exercise (two hours or less each week). This is immediatelyclear from the fact that the highest bars on the chart are on theleft, where the hours of exercise are lowest.frequency distributionA summary of how often various scoresoccur in a sample of scores. Score values arearranged in order of magnitude, and thenumber of times each score occurs isrecorded.histogramA way of graphically representing afrequency distribution; a type of bar chartthat uses vertical bars that touch.