Statisticians work with large masses of data. Before any conclusions can be drawn from such data, it must be condensed and arranged in a usable form. One of the most common ways to summarize and describe a mass of data is to arrange a frequency distribution table. These tables can then be graphed with the frequency scale on the y-axis and the interval being graphed on the x-axis. Above each interval a horizontal line is drawn which corresponds to the frequency of the interval, resulting in a stair-step histogram pattern. Connecting the midpoints of these class intervals produces a frequency polygon and an interval curve. Distribution curves which can be "folded" vertically so that the two halves of the curve are essentially the same are said to be bilaterally symmetrical. Perfectly symmetrical curves which have a bell shape are said to be normal curves, or Gaussian curves (after the German mathematician Frederic Gauss). Normal curves occur frequently both in nature and in human events, and, as such, form the basis for much statistical analysis. This research examines the nature of the normal curve, when it occurs, how it is developed, and its characteristics and significant limitations and abnormalities.
In human events, normal distributions can be found in coin tosses, heights of sample populations, and scores on human intelligence tests. The bulk of the frequencies occur in the middle of the range, with the frequencies decreasing as the measures approach either extreme. The normal distribution is also found in nonhuman events, such as the length of cockroaches in a house, the weights of carrots in a field or the velocities of molecules in a gas.
Normal distributions have many applications, and are used in a wide variety of fields. In business, a manufacturer may use normal distributions to establish an acceptable failure rate for his product. For example, a light bulb manufacturer may claim that his light bulbs h...