Bell Curve

What Is a Bell Curve?

A bell curve is a common type of distribution for a variable, otherwise called the normal distribution. The term "bell curve" begins from the way that the graph used to portray a normal distribution comprises of a symmetrical bell-formed curve.

The highest point on the curve, or the highest point of the bell, addresses the most probable event in a series of data (its mean, mode, and median in this case), while any remaining potential events are symmetrically distributed around the mean, making a descending slanting curve on each side of the pinnacle. The width of the bell curve is portrayed by its standard deviation.

Understanding a Bell Curve

The term "bell curve" is utilized to portray a graphical portrayal of a normal likelihood distribution, whose underlying standard deviations from the mean make the curved bell shape. A standard deviation is a measurement used to evaluate the variability of data dispersion, in a set of given values around the mean. The mean, thusly, alludes to the average of all data points in the data set or sequence and will be found at the highest point on the bell curve.

Financial analysts and investors frequently utilize a normal likelihood distribution while breaking down the returns of a security or of overall market sensitivity. In finance, standard deviations that portray the returns of a security are known as volatility.

For instance, stocks that display a bell curve typically are blue-chip stocks and ones that have lower volatility and more unsurprising behavioral examples. Investors utilize the normal likelihood distribution of a stock's past returns to make assumptions with respect to expected future returns.

Notwithstanding teachers who utilize a bell curve while contrasting grades, the bell curve is in many cases likewise utilized in the world of statistics where it tends to be widely applied. Bell curves are additionally sometimes employed in performance management, putting employees who perform their job in an average fashion in the normal distribution of the graph. The high performers and the least performers are addressed on one or the other side with the dropping slant. It tends to be helpful to bigger companies while doing performance audits or while going with managerial choices.

Illustration of a Bell Curve

A bell curve's width is defined by its standard deviation, which is calculated as the level of variation of data in a sample around the mean. Utilizing the empirical rule, for instance, in the event that 100 grades are collected and utilized in a normal likelihood distribution, 68% of those grades ought to fall inside one standard deviation above or below the mean. Moving two standard deviations from the mean ought to incorporate 95% of the 100 grades collected. Moving three standard deviations from the mean ought to address 99.7% of the scores (see the figure above).

Test scores that are extreme exceptions, for example, a score of 100 or 0, would be viewed as long-tail data points that subsequently lie squarely outside of the three standard deviation range.

Bell Curve versus Non-Normal Distributions

The normal likelihood distribution assumption doesn't necessarily hold true in the financial world, in any case. It is possible for stocks and different securities to sometimes display non-normal distributions that fail to look like a bell curve.

Non-normal distributions have fatter tails than a bell curve (normal likelihood) distribution. A fatter tail slants negative signs to investors that there is a greater likelihood of negative returns.

Limitations of a Bell Curve

Evaluating or surveying performance utilizing a bell curve powers groups of individuals to be classified as poor, average, or great. For more modest groups, sorting a set number of people in every category to fit a bell curve will give a raw deal to the people. As sometimes, they may be in every way just average or even great workers or understudies, however given the need to accommodate their rating or grades to a bell curve, a few people are forced into the poor group. In reality, data are not entirely normal. Sometimes there is skewness, or a lack of evenness, between what falls above and below the mean. Different times there are fat tails (excess kurtosis), making tail events more probable than the normal distribution would foresee.

Highlights

• A bell curve is a graph portraying the normal distribution, which has a shape suggestive of a bell.
• Its standard deviation portrays the bell curve's relative width around the mean.
• Bell curves (normal distributions) are utilized commonly in statistics, remembering for breaking down economic and financial data.
• The highest point of the curve shows the mean, mode, and median of the data collected.

FAQ

How Is the Bell Curve Used in Finance?

Analysts will frequently utilize bell curves and other statistical distributions while modeling different potential results that are significant for investing. Contingent upon the analysis being performed, these could comprise of future stock prices, rates of future earnings growth, potential default rates, or other important peculiarities. Before utilizing the bell curve in their analysis, investors ought to carefully consider whether the results being examined are as a matter of fact normally distributed. Failing to do so could genuinely sabotage the precision of the subsequent model.

What Are the Characteristics of a Bell Curve?

A bell curve is a symmetric curve based on the mean, or average, of the multitude of data points being estimated. The width of a bell curve is determined by the standard deviation — 68% of the data points are inside one standard deviation of the mean, 95% of the data are inside two standard deviations, and 99.7% of the data points are inside three standard deviations of the mean.

What Are the Limitations of the Bell Curve?

Albeit the bell curve is an extremely valuable statistical concept, its applications in finance can be limited in light of the fact that financial peculiarities —, for example, expected stock-market returns — don't fall flawlessly inside a normal distribution. Thusly, depending too vigorously on a bell curve while creating forecasts about these events can lead to inconsistent outcomes. Albeit most analysts are very much aware of this limitation, it is relatively hard to defeat this weakness since it is many times muddled which statistical distribution to use as an alternative.