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A bell curve represents a normal distribution of variables, with most values clustering around a mean and outliers above and below. It is used to determine if data is behaving predictably and to calculate standard deviation. A symmetrical bell curve indicates valid data.
A bell curve is a graph that represents a normal distribution of variables, where most values cluster around a mean, while outliers are above and below the mean. For example, human height often follows a bell-shaped curve, with outliers being unusually short and tall, and most people cluster around an average height, such as 70 inches (178 centimeters) for American men. When data that follows a normal distribution pattern is plotted, the graph often resembles a bell in cross section, explaining the term “bell curve.”
Normal or Gaussian distributions can be found in a wide variety of contexts, from graphs of financial market trends to test scores. When variables are graphed and a bell curve is displayed, it often means that the variables were within normal expectations and are behaving in a predictable manner. If the graph is distorted or erratic, it can indicate that there is a problem.
Ideally, a bell curve is symmetrical. In scoring, for example, a test should be written such that a small number of students fail on an F, and an equally small number score perfect on an A. Slightly more students should get Ds and Bs and the largest number should get Cs. If the bell curve is sloped and the curve peaks in the D’s, it suggests that the test was too hard, while a test peaking in the B’s is too easy.
Using a bell curve, it is also possible to arrive at the standard deviation for the data. The standard deviation shows how closely the variables are close to the mean. The standard deviations reflect the diversity of the variables being plotted and can be used to gather information about the validity of the data. A large standard deviation indicates that the variables are not tightly grouped and that there may be a problem with the data, while small standard deviations suggest that the data may be more valid.
For example, when surveys are conducted, the survey company releases the standard deviations. If the standard deviation is small, it means that if the survey were repeated, the data would be very close to that of the original survey, suggesting that the survey company used sound methods and that the information is accurate. If the standard deviation is large, however, it would indicate that repeated surveys may not return the same results, making the data less useful.
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