Normal Distribution

The probabability that the value of something (say, an exam grade) would lie between two extreme numbers (high and low extremes) is obtained from an equation depicting the so-called "Normal Distribution". As an example, consider someone dropping a handful of sand onto a point on the ground (fall spot). Most of the sand grains would fall close to the centerpoint of the fall spot, but some would fall in all directions outward from that fall spot. Consider an x-axis through the fall spot...the furthermost distance in the positive x-direction that a grain of sand is found would be one extreme value and the furthermost distance in the negative x-direction would be the other extreme value.

If the distances of each of the sand grains from the fall spot are logged, it would be found that most at the fall spot, with decreasing numbers on either side. The equation that is fit to the distribution of these distances, when graphed, resembles a "bell curve." The bell curve has some interesting characteristics that allows us to estimate how many grains of sand would be found at various distances (assuming no outside influences). Statisticians define quantities like mean, mode, standard deviation etc. on the bases of this equation.