Assessment, Statistics, and Research: Normal Distribution or Bell Curve

Monday, March 29, 2021

Normal Distribution or Bell Curve

The bell curve is also known as the normal curve or normal distribution. This curve has mathematical properties that allow researchers to draw conclusions about where scores are located relative to other scores.

The three measures ofcentral tendency (mode, median, mean) are at the same middle point in a normal curve. The numbers representing the middle of the curve divide the curve in half.

The x-axis in the normal curve indicates the mean at zero and the standard deviation units above and below the mean.

The height of the curve indicates the percentage of scores in that area. You can see that a large percentage of the scores are between 1 and -1 standard deviations.

The ends of the distribution are called tails. Extreme scores are in the tails. Consider the height of the distribution at - 2.5 or +2.5 standard deviations. At these points, the curve almost touches the x-axis.

Only a small percentage of scores is beyond 2.5 standard deviations in either direction. Theoretically, the tails of the curve never touch the baseline. Only a small fraction of a percent of scores is beyond 3 standard deviations.

The picture below illustrates the percentage of scores (or data) within different areas of the curve. For example, on a normally distributed test, 34.1% of scores will fall between the mean and 1 standard deviation above the mean. Because the curve is symmetrical, the same percentage will be between the mean and 1 standard deviation below the mean.