In addition to examining the distribution of scores, you can calculate descriptive statistics. Descriptive statistics allow researchers to make precise statements about the data. Two statistics are needed to describe the data. A single number can be used to describe the central tendency, or how participants scored overall. Another number describes the variability, or how widely the distribution of scores is spread. These two numbers summarize the information contained in a frequency distribution.
A central tendency statistic tells us what the sample as a whole, or on the average, is like. There are three measures of central tendency—the mean, the median, and the mode. The mean of a set of scores is obtained by adding all the scores and dividing by the number of scores. It is symbolized as ; in scientific reports, it is abbreviated as M. The mean is an appropriate indicator of central tendency only when scores are measured on an interval or ratio scale, because the actual values of the numbers are used in calculating the statistic. In Table 12.1, the mean score for the no-model group is 3.10 and for the model group is 5.20. Note that the Greek letter Σ (sigma) in Table 12.1 is statistical notation for summing a set of numbers. Thus, ΣX is shorthand for “sum of the values in a set of scores.”
The median is the score that divides the group in half (with 50% scoring below and 50% scoring above the median). In scientific reports, the median is abbreviated as Mdn. The median is appropriate when scores are on an ordinal Page 249scale because it takes into account only the rank order of the scores. It is also useful with interval and ratio scale variables, however. The median for the nomodel group is 3 and for the model group is 5.
The mode is the most frequent score. The mode is the only measure of central tendency that is appropriate if a nominal scale is used. The mode does not use the actual values on the scale, but simply indicates the most frequently occurring value. There are two modal values for the no-model group—3 and 4 occur equally frequently. The mode for the model group is 5.
The median or mode can be a better indicator of central tendency than the mean if a few unusual scores bias the mean. For example, the median family income of a county or state is usually a better measure of central tendency than the mean family income. Because a relatively small number of individuals have extremely high incomes, using the mean would make it appear that the “average” person makes more money than is actually the case.