What Is a Bell Curve?
A bell curve is the most common type of distribution for a variable and is thus considered to be a normal distribution. The term "bell curve" originates from the fact that the graph used to depict a normal distribution consists of a bell-shaped line.
The highest point on the curve, or the top of the bell, represents the most probable event in a series of data, while all other possible occurrences are equally distributed around the most probable event, creating a downward-sloping line on each side of the peak.
Understanding Bell Curves
The term bell curve is used to describe a graphical depiction of a normal probability distribution, whose underlying standard deviations from the median create the curved bell shape. A standard deviation is a measurement used to quantify the variability of data dispersion, in a set of given values. The "mean" refers to the average of all data points, in the data set or sequence.
Standard deviations, which are calculated after the mean is calculated, represent a percentage of the total data collected. For example, if 100 test scores are collected and used in a normal probability distribution, 68% of those test scores should fall within one standard deviation above or below the mean. Moving two standard deviations away from the mean should include 95% of the 100 test scores collected. Moving three standard deviations away from the mean should represent 99.7% of the scores.
Test scores that are extreme outliers, such as a score of 100 or 0, would be considered long-tail data points that consequently lie squarely outside of the three standard deviation range.
[Important: Standard deviations that depict the returns of a security are known as volatility.]
Special Considerations: Bell Curves in Finance
Financial analysts and investors often use a normal probability distribution when analyzing the returns of a security or of overall market sensitivity. In finance, standard deviations that depict the returns of a security are known as volatility. For example, stocks that display a bell curve are normally blue-chip stocks and that have lower volatility and more predictable behavioral patterns. Investors use the normal probability distribution of a stock's past returns to make assumptions regarding expected future returns.
It is feasible for stocks and other securities to sometimes display non-normal distributions, that fail to resemble a bell curve. Non-normal distributions have fatter tails than a normal probability distribution. A fatter tail that skews negative, signals to investors that there is a greater probability of negative returns.