The normal curve (or bell-shaped curve) is a theoretical distribution in which the height of the curve indicates the percentage of cases under portions of the normal curve. As shown in the example in Figure 4.1, the test scores of the majority of individuals tend to cluster close to the mean. Fewer cases occur as we move farther from the mean. Specifically, about 68% of the sample will have scores within the range of plus or minus one standard deviation from the mean. Approximately 95% of the sample will have scores within the range of plus or minus two standard deviations from the mean. And more than 99% of the sample will have scores within the range of three standard deviations from the mean. Many variables (e.g., height, weight, IQ scores, achievement test scores) yield a curve, providing a large enough random sample is used.
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The Normal Curve