Define Bell Curve

What Is a Bell Curve and How Does It Work?

A bell curve, commonly known as the normal distribution, is a typical form of distribution for a variable. The phrase "bell curve" refers to the symmetrical bell-shaped curve that is used to show a normal distribution on a graph.

The most likely event in a series of data (its mean, mode, and median in this case) is represented by the highest point on the curve, or the top of the bell, while all other possible occurrences are symmetrically distributed around the mean, creating a downward-sloping curve on each side of the peak. The standard deviation describes the breadth of the bell curve.

TAKEAWAYS IMPORTANT

• A bell curve is a graph that depicts the normal distribution and has a bell-like shape.

• The mean, mode, and median of the data gathered are shown at the top of the curve.

• The standard deviation shows how wide the bell curve is around the mean.

• Bell curves (normal distributions) are widely utilised in statistics, particularly in the analysis of economic and financial data.

The Bell Curve: What It Is and What It Isn't

The phrase "bell curve" refers to a graphical representation of a normal probability distribution with a curved bell shape created by the underlying standard deviations from the mean. A standard deviation is a metric for quantifying the variability of data dispersion in a collection of values centred on the mean. The mean, on the other hand, is the average of all data points in a data set or sequence, and it can be found at the top of the bell curve.

When examining the returns of a securities or general market sensitivity, financial analysts and investors frequently utilize a normal probability distribution. Volatility is a term used in finance to describe the standard deviations of a security's returns.

Blue-chip companies, for example, are more likely to have a bell curve because they have lower volatility and more predictable behavioural tendencies. The normal probability distribution of a stock's previous returns is used by investors to form assumptions about projected future returns.

A bell curve is frequently used in the realm of statistics, where it may be broadly used, in addition to instructors who utilise it while comparing exam scores. In performance management, bell curves are occasionally used to place workers who do their jobs well in the normal distribution of the graph. On either side of the descending slope, the highest and lowest achievers are depicted. Larger firms may find it valuable when conducting performance evaluations or making managerial choices.

A Bell Curve in Action

The standard deviation, which is measured as the degree of variation of data in a sample around the mean, determines the breadth of a bell curve. If 100 test scores are gathered and utilised in a normal probability distribution, 68 percent of those test scores should lie within one standard deviation above or below the mean, according to the empirical rule. 95 percent of the 100 test scores should be included when moving two standard deviations away from the mean. Three standard deviations out from the mean should account for 99.7% of the results (see the figure above).

Extreme outliers, such as a score of 100 or 0, are termed long-tail data values, which fall outside the three standard deviation range.

Non-Normal vs. Bell Curve Distributions

However, in the financial sector, the normal probability distribution assumption does not always hold true. Stocks and other assets can occasionally have non-normal distributions that do not match a bell curve.

The tails of non-normal distributions are larger than those of a bell curve (normal probability). A larger tail sends out negative signals to investors, signalling a higher likelihood of negative returns.

The Bell Curve's Limitations

When utilising a bell curve to grade or measure performance, groups of people are forced to be classified as bad, average, or good. Persons in smaller groups will be harmed by having to classify a specific number of individuals in each category to suit a bell curve. Because they may all be merely ordinary or even good employees at times.

Some pupils are put into the poor category due to the necessity to conform their rating or grades to a bell curve. Data isn't totally normal in reality. Between what falls above and below the mean, there might be skewness, or a lack of symmetry. Fat tails (excess kurtosis) can also occur, making tail occurrences more likely than the normal distribution would imply.

What Is a Bell Curve and What Are Its Characteristics?

A bell curve is a symmetric curve that is centred on the mean, or average, of all data points being measured. The standard deviation determines the breadth of a bell curve: 68 percent of data points are within one standard deviation of the mean, 95 percent of data points are within two standard deviations, and 99.7% of data points are within three standard deviations of the mean.

What Is the Function of the Bell Curve in Finance?

When modelling diverse potential outcomes that are important to investment, analysts frequently employ bell curves and other statistical distributions. Future stock prices, rates of future profits growth, probable default rates, and other significant phenomena may be included, depending on the investigation. Investors should carefully assess whether the outcomes being analysed are normally distributed before employing the bell curve in their study. Failure to do so might jeopardise the accuracy of the model that results.

What Are the Bell Curve's Limitations?

Although the bell curve is a valuable statistical concept, its applicability in finance is restricted since financial events, such as predicted stock-market returns, do not fit cleanly into a normal distribution. As a result, when generating predictions regarding these occurrences, leaning too much on a bell curve might lead to incorrect findings. Despite the fact that most analysts are aware of this constraint, it is frequently difficult to overcome it since it is unclear which statistical distribution to employ as a substitute.