The bell curve is one of the possible kinds of distribution, namely a normal one. It is called after its graphical representation, which shows a curved bell-shaped line, with its top standing for the most common result from a data set, and the rest of possible outcomes being distributed along two symmetrical downward lines from both sides of the top.
A standard deviation of a data set serves as a width determinant for that data set’s bell curve. The very middle of a bell curve (its highest point) represents a single number, which actually reflects several important figures of said data set, being its mean, median and mode at the same time.
Use of Bell Curves
Bell curves are widely used in statistics and analytics, being applied in various fields, including finance and economics. In the financial sphere, bell curves are frequently employed to assess previous results of a security’s performance and predict possible future returns, as well as for other reasons. Depicting volatility is one more common way of using bell curves in finance.
It’s worth noting, though, that bell curves are better applicable to when assessing stable and well-established securities, as a bell curve represents a normal distribution, and in finance other types of distributions are highly likely to take place. Distributions of non-normal types usually have fatter tails than a typical bell curve and might cause incorrect forecasting if being assessed as normal ones.
Additional inconvenience ensues when a bell curve is used to estimate performance of a group of people, as it indicates that some employees fall into the below average group. Even if their performance in general doesn’t significantly differ in productivity or results, the very nature of a bell curve implies such a division into average, below average and above average, which might have unfortunate implications for some people.
Bell Curve main features
An important concept that needed to be understood to analyze a bell curve correctly is a standard deviation. It determines the width of a bell curve for a given data set and holds the information crucial for statistic purposes. A standard deviation measures how dispersed the possible meanings are from the most average meaning of the data set (which is the top point in the graph), and it’s calculated by finding the variance’s square root.
A standard deviation then determines and forms the side lines of the graph. When moving one standard deviation from the most average point of a bell curve (which is on its top), 68% of all possible meanings fall into that interval. When moving two standard deviations from it, 95% of possible figures in a given data set are believed to be included in the interval. And finally, more than 99% of possible meanings should be represented on the graph if we move three standard deviations away. The most infrequent numbers of a data set usually fall outside a typical bell curve, as they don’t fit into three standard deviations away from the mean normally used when depicting such distributions.