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.
What Does a Bell Curve Tell You?
The term bell curve is used to describe a graphical depiction of a normal probability distribution, whose underlying standard deviations from the mean 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.
Example of How to Use a Bell Curve
A bell curve uses standard deviations, which are calculated after the mean is calculated, and represent a percentage of the total data collected. On a bell curve, 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.
The Difference Between a Bell Curve and Non-Normal Distributions
The normal probability distribution assumption doesn’t always hold true in the financial world, however. 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 bell curve (normal probability) distribution. A fatter tail that skews negative signals to investors that there is a greater probability of negative returns.
Key Takeaways
- A bell curve is a graph that is considered to be a normal distribution.
- It gains its name (Bell) from the overall shape/profile
- Also called the “Gaussian Curve” after Friedrich Gauss
- The top of the curve shows the most likely event out of the data collected.
- After the mean is calculated, standard deviations are figured.
- Standard deviations that depict the returns of security are known as volatility.
- When making assumptions about a stock’s potential future returns, investors look at the normal probability distribution of its past returns.
- The Bell Curve represents what statisticians call a "normal distribution." A normal distribution is a sample with an arithmetic average and an equal distribution above and below average like the curve below.
Course Overview
Our Lean Six Sigma courses provide in-depth training on FTY calculations and its importance in production processes, measuring the quality and efficiency of a process by evaluating the proportion of defect-free units produced. Our Lean Six Sigma courses equip professionals with the knowledge and tools needed to master FTY and drive continuous improvement in their organisations. Join us to learn from industry experts and take your career to the next level.
Membership, Stay Connected. Stay Relevant.
Completing a program is a point-in-time exercise that delivers huge value, but there is a next step to maintaining the currency of your skills in the ever-evolving professional world.
Membership is the next step.
A unique platform, membership is designed to ensure that you are in tune and up-to-date with the latest tools, trends and developments. Being a member provides just-in-time training and continuous professional development, and an exclusive and evolving content library informed by subject matter experts and industry leaders.
Lean Six Sigma | Standard Deviation - What it is and why is used
Lean • Lean Six Sigma • Lean Six Sigma Training
_165x115_fc3.jpg)
Lean Six Sigma | Applying Standard Deviation to make decisions
Lean • Lean Six Sigma • Lean Six Sigma Training
_165x115_fc3.jpg)
Lean Six Sigma | Unplanned Variation vs. Planned Variety
Lean • Lean Six Sigma • Lean Six Sigma Training
