We can also determine how much variability exists in a set of scores. A measure of variability is a number that characterizes the amount of spread in a distribution of scores. One such measure is the standard deviation, symbolized as s, which indicates the average deviation of scores from the mean. Income is a good example. The Census Bureau reports that the median U.S. household income in 2012 was $53,046 (http://quickfacts.census.gov/qfd/states/00000.html). Suppose that you live in a community that matches the U.S median and there is very little variation around that median (i.e., every household earns something close to $53,046); your community would have a smaller standard deviation in household income compared to another community in which the median income is the same but there is a lot more variation (e.g., where many people earn $15,000 per year and many others $5 million per year). It is possible for measures of central tendency in two communities to be close with the variability differing substantially.
In scientific reports, the standard deviation is abbreviated as SD. It is derived by first calculating the variance, symbolized as s2 (the standard deviation is the square root of the variance). The standard deviation of a set of scores is small when most people have similar scores close to the mean. The standard deviation becomes larger as more people have scores that lie farther from the mean value. For the model group, the standard deviation is 1.14, which tells us that most scores in that condition lie 1.14 units above and below the mean—that is, between 4.06 and 6.34. Thus, the mean and the standard deviation provide a great deal of information about the distribution. Note that, as with the mean, the calculation of the standard deviation uses the actual values of the scores; thus, the standard deviation is appropriate only for interval and ratio scale variables.
Another measure of variability is the range, which is simply the difference between the highest score and the lowest score. The range for both the model and no-model groups is 4.