Where would one find approximately 95% of the scores in the following example if scores are normally distributed? Scores ranged from 30 to 68, M = 45, SD = 7
a. Between 37 and 61
b. Between 38 and 52
c. Between 31 and 59
d. Between 30 and 68
ANS: C
The range, standard deviation, and variance are statistics that describe the extent to which the values in the sample vary from one another. The most common of these statistics to be reported in the literature is the standard deviation, because of its direct association with the normal curve. If the frequency distribution of any given variable is approximately normal, knowing the standard deviation of that variable allows us to know what percentages of subjects' values on that variable fall between +1 and –1 standard deviation. Referring back to the hypothetical frequency distribution of pain in Figure 21-1, when we calculate a standard deviation, we know that 34.13% of the subjects' pain scores were between the mean pain score and 1 standard deviation above the mean pain score. We also know that 34.13% of the subjects' pain scores were between the mean pain score and 1 standard deviation below the mean. The middle 95.44% of the subjects' scores were between –2 standard deviation and +2 standard deviations.
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