Bell Curve Definition: 3 Bell Curve Examples

Bell curves are common, but they aren’t universal. These are some of the limitations of relying on these graphs to depict all forms of data:

• Inability to apply universally: Although bell curves represent normal distributions, always remember there are plenty of non-normal distributions as well. These might feature extra-long tails, asymmetrical sloping, multiple peaks, and other statistical idiosyncrasies. Refrain from disregarding data just because it computes in an atypical fashion.
• Need for completely accurate inputs: For your bell curve to be accurate, you need to provide accurate data points in the first place. The illegitimacy of a poorly planned or badly biased bell curve graph will, in turn, invalidate your research. The book The Bell Curve by Richard J. Herrnstein and Charles Murray received a great amount of criticism for making sweeping public policy suggestions (with racist undertones) despite using data in a statistically haphazard fashion.
• Occasionally unreliable results: Even the best data falls through sometimes. Try to be as thorough as possible when pulling in information for your probability distributions. Your bell curve might prove unreliable if you approach your research from the wrong angle or leave out important factors.

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The term “bell curve” refers to the standard normal distribution curve of statistical data. Also called Gauss or Gaussian distributions, these histograms keep track of probability density and follow the central limit theorem—an empirical rule stating statistical distributions are likely to tend toward a bell-shaped appearance as you bring in more sample data.

The top of a bell curve represents the mean of all statistical data you’ve gathered for the specific distribution. These graphs also include a number of standard deviations to highlight individual differences along the tails of the curve. These represent outliers where data points are less than or more than the average. In other words, the majority of data points exist in the center of the curve, whereas a minority of anomalies appear on either side.

Bell curves help make sense of previously random variables. Consider these common characteristics of normal distributions:

• Mean, median, and mode: The mean (or average) sits at the highest point of any given bell curve graph. This part of the bell curve is also simultaneously the median (or middle value) and mode (or most commonly used value). Any bell curve must satisfy all three of these criteria to serve as a normal distribution.
• Standard deviations: Standard deviations of the mean stretch out from both sides of the top of a bell curve. These include data points that are outside the average because they are either lower or higher than the mean. These help make up the total area of the bell curve graph, sloping downward from either side. Over ninety-nine percent of all data points are within three standard deviations of the mean on any bell curve.
• Symmetric curvature: A bell curve increases and decreases on the x-axis at the same rate. This symmetrical bell curvature has an elegant, sloping appearance. It’s also the primary reason statisticians refer to normal distributions by the name “bell curve” in the first place.

People take sample sizes for all sorts of reasons and a high number of these datasets turn out to be bell curves. Here are a few examples of bell curves you’ll see in the world:

1. 1. IQ scores: Intelligence testing has its critics—plenty of psychologists and social scientists believe it’s impossible to trace the cognitive ability to excel with an IQ test alone. Still, IQ scores often present a bell-shaped curve across all sorts of different populations. Most people score as average and fewer stand out with exceptionally low or high scores.
2. 2. Stock values: Financial analysts utilize bell curves to determine potential stock pricing and risk. Stocks known for volatility often do not follow the bell-shaped continuum, instead presenting as full of skew and kurtosis (both of which are factors indicating a tendency for less probable events to occur). If they can find a stock with a true bell curve, they can rest easier as it indicates future returns will, on average, occur at the same rate and in the same fashion as past returns.
3. 3. Test results: High school students who take the SAT or ACT provide a large sample size for statisticians. These test scores almost always appear as bell curves—most students obtain the same standard score while a few exceptions test at a higher or lower percentile. The same trend occurs among students’ grades across all years of study, as well as for scores on higher education entrance exams like the GRE, LSAT, and MCAT.