A normal distribution is a distribution that is bell-shaped and symmetrical. The mean, median, and mode are all the same and coincide with the peak of the curve. The frequencies then gradually decrease at both ends of the curve. The normal distribution is also often called the bell-shaped curve because of its shape.
Properties Of The Normal Distribution
One of the most noticeable characteristics of the normal distribution is its shape and perfect symmetry. Notice that if you fold the picture of the normal distribution exactly in the middle, you have two equal halves, each a mirror image of the other. This also means that one half of the observations in the data fall on each side of the middle of the distribution.
The midpoint of the normal distribution is the point that has the maximum frequency. That is, it is the number or response category with the most observations for that variable. The midpoint of the normal distribution is also the point at which three measures fall: the mean, median, and mode. In a perfect normal distribution, these three measures are all the same number.
In all normal or nearly normal distributions, there is a constant proportion of the area under the curve lying between the mean and any given distance from the mean when measured in standard deviation units. For instance, in all normal curves, 99.73 percent of all cases will fall within 3 standard deviations from the mean. 95.45 percent of all cases will fall within 2 standard deviations from the mean, and 68.27 percent of cases will fall within 1 standard deviation from the mean.
Normal distributions are often represented in standard scores (Z scores). Z scores are numbers that tell us the distance between an actual score and the mean in terms of standard deviations. The standard normal distribution has a mean of 0.0 and a standard deviation of 1.0.
Even though the normal distribution is theoretical, there are several variables that researchers study that closely resemble a normal curve. For example, standardized test scores such as the SAT, ACT, and GRE typically resemble a normal distribution. Height, athletic ability, and numerous social and political attitudes of a given population also typically resemble a bell-shaped curve.
Frankfort-Nachmias, C. & Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand Oaks, CA: Pine Forge Press.