Bell curve
A bell curve, or normal distribution, is a graph that illustrates how a set of values is distributed, featuring a peak at the center that represents the mean, with values tapering off symmetrically on either side. This shape emerges from the statistical principle that, in a normal distribution, values closer to the mean are more frequent than those far from it, resulting in a characteristic bell-like appearance. The concept of the bell curve dates back to the 18th century, credited to mathematician Abraham De Moivre, who explored probability theory and random occurrences. In statistics, normal distributions are vital as they represent random variables, with both the mean and standard deviation defining their boundaries. While bell curves are often discussed in the context of grading in education—where they can generate controversy regarding fairness—they also play a significant role in business and finance, particularly in stock market analysis. Overall, the bell curve is a fundamental concept in understanding patterns of data across various fields.
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Bell curve
A bell curve is a type of graph that shows the normal distribution of a set of values. It has a central value that peaks in the center with other values that taper off on either side. The side values follow a symmetrical pattern, creating the illusion of a bell. Values should follow a normal distribution pattern, with an equal number of measurements occurring above and below the mean value. The number of potential bell curves is unlimited, as there are an infinite number of normal distributions.
Overview
The bell curve traces its roots to 1733 to Abraham De Moivre, a French mathematician known for his work with probability theory and normal distribution. He expanded on the work of Dutch scientist Christiaan Huygens and authored a textbook on probability. Much of his work explored probability and gambling. De Moivre was particularly interested in the probability of random occurrences. The bell curve is a normal distribution. When graphically depicted, bell curve distributions have a peak in the center that represent the mean. The mean is the average of all values involved. The mean stands in contrast to the median, or center point of the distribution, and the mode, which is the value that is most frequently appearing. Values that are close to the mean appear more frequently than values that are farther away from the mean. Although all normal distributions are symmetrical, not all symmetrical distributions are normal. If a distribution is perfectly normal, the mean, median, and mode will all be at the peak of the curve. Normal distribution contains two boundaries: the standard deviation and the mean.
Bell curves, or normal distributions, are important in statistics because they represent random variables whose distributions are unknown. Although normal distributions are frequently referred to as bell curves, there are other statistical distributions that form a bell shape when plotted graphically.
Although bell curves are tied directly to statistics, the term is often mentioned by students who ask their teachers or professors if they are grading on a curve. Grading on a curve has become a controversial topic in education. When grading on a bell curve, only a small percentage of students will earn an A, while most will earn B’s and C’s. There will also be D’s and F’s. Proponents of using the bell curve to grade argue that the bell curve helps maintain the excellence or status of the A grade. Opponents argue that bell curves take away from students who performed at a high level but were not among the absolute highest in their class/group. In addition to education, bell curves are found in other areas, including business. Normal distribution is considered the most common type of distribution in stock market and other statistical analyses.
Bibliography
Bloomenthal, Andrew. “Bell Curve Definition: Normal Distribution Meaning Example in Finance.” Investopedia, 15 Aug. 2024, www.investopedia.com/terms/b/bell-curve.asp. Accessed 3 Feb. 2025.
Goldberg, Shelley R. “Bell Curve Definition.” U.S. News & World Report, 8 Dec. 2023, money.usnews.com/investing/term/bell-curve. Accessed 12 July 2023.
Gore, Adrian. “We Need to Let Go of the Bell Curve.” Harvard Business Review, 14 Jan. 2022, hbr.org/2022/01/we-need-to-let-go-of-the-bell-curve. Accessed 3 Feb. 2025.
Mcleod, Saul. “Introduction to the Normal Distribution (Bell Curve).” Simply Psychology, 11 Oct. 2023, www.simplypsychology.org/normal-distribution.html. Accessed 3 Feb. 2025.