What Is A Bell Curve? (With Uses, Examples And Limitations)

Updated 28 September 2022

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Bell curves describe the mathematical concept of normal distribution. Bell-shaped or symmetric, this graph describes the relationship between variables in a data set and the average of the data. Knowing more about this distribution can help you understand how an organisation may analyse large amounts of data and interpret it to make strategic decisions. In this article, we define a bell curve, examine its many uses, provide some examples to comprehend the distribution and share its limitations.

What Is A Bell Curve?

A bell curve, or a normal distribution or Gaussian distribution, is a normal probability distribution, which is a reference for various probability problems. The curve of this graph has a raised centre and falls on both sides. This shape shows that data are symmetrical. The highest point on the graph represents a probable event, selected from a large data set. There are other occurrences as well that exist around the mean. This continuous probability distribution has another parameter apart from the mean, referred to as standard deviation (SD).

Stock market analysts and other professionals who conduct statistical research may often utilise a normal distribution. The principles of the central limit theorem (CLT) guide a normal distribution. According to this theory, there are multiple unrelated factors that affect a single trait or a variable. The result of these factors devises a sum that may often create a Gaussian or normal distribution. There are 68% of values in a single distribution curve. This percentage of values is within plus-minus one SD from the mean, along with 95% of the values being within plus-minus two SD from the mean.

What Is A Standard Deviation?

Data may often have a standard deviation, which signifies a quantity or a value. These two components together show how different the members of the data are from the data of the mean value. This average value of the data is the mean value. A quantity that represents SD shows there is a deviation in data entries from the average. If the standard deviation quantity is high or low, it means that other data entries are near the data set's mean. Standard deviation also controls how the normal distribution spreads.

Uses

A company may use a normal distribution to plan employee benefits, design an office space that is comfortable for every age group or identify recruitment requirements. An individual may utilise this tool to recognise career growth opportunities. Apart from these, here are some other uses of this graph:

Biologists may use this distribution to measure characteristics in biology.
A school may use this tool to measure students' heights at a grade level.
After teachers take a class test to measure the test scores, they may use this statistical tool to calculate the average.
Financial analysts use this graph when determining the nature of stocks or their patterns and volatility.
If an engineer or a construction worker is to take measurements of equipment repeatedly, they may utilise this distribution.
Professionals in statistics use it to model real-world data, like performance assessments of employees.
Its ability to solve probability problems may be crucial to numerous pricing models that make forecasts regarding returns.

Characteristics Of Normal Distribution

Here are some characteristics to help you identify normal distribution:

There is just one peak, and the curve has the shape of a bell.
The centre of this distribution is the mean of the curve.
The two tails of the distribution never meet at the horizontal axis, but they extend perpetually.
Given there is one maximum point, a normal distribution possesses unimodality.
In a normal curve, the value of the mode, median and mean is the same.

Gaussian Distribution And Decision-Making

Below is the role of Gaussian distribution in decision-making:

Negotiations: With the help of a Gaussian distribution, companies create profitable contracts. With this curve, they are better able to evaluate prices and determine if they are above the average range or below.
Product prices: With a Gaussian distribution, deciding the cost of products may become easy. With this graph, companies may compare similar products and determine reasonable prices.
Financial trading: A trader may conduct a price compilation to develop a Gaussian distribution over a particular period. With the help of SD from this distribution, the trader may choose trades requiring a short time, as it is easier to find out entry or exit point than over a longer period.

Limitations

If an organisation evaluates performance using a normal distribution, then it may categorise its employees. These categories may be poor, average or good. For groups that are small, putting a specific number of individuals in each category to suit a normal distribution may not be beneficial. This is because sometimes, these people may be average or even talented students or professionals.

Giving people ratings or grades to make them fit a normal distribution may often put them in the poor group, but an organisation may also acknowledge that data may not be perfectly normal all the time. While sometimes there is skewness, often there is no symmetry between what is above or below the mean. Sometimes, tail events are more probable than the Gaussian distribution may predict.

Examples

Here are some examples to understand this statistical tool better:

Height

Height is a suitable example of normal distribution. For instance, an individual uses this tool to evaluate the height of a random population of 2,000 other individuals. Many of these people have average height. There is a smaller group of people who are taller or shorter than the people who have average height. Here, there are more values that are near the mean and some values that are occurring at the tail ends. There are many factors, like genetic and environmental, that may affect this outcome, so height remains an independent variable.

Stock market

A stock market may prove to be volatile, as share values may often rise and fall. If the distribution of returns is typical, then 90% may fall within the mean's SD. The dynamic stock values and price indexes may result in a bell-shaped curve. This specific characteristic of the normal distribution allows investors to predict conclusions regarding the risks and returns associated with those stocks.

Intelligence quotient

Intelligence quotient or IQ is another appropriate example of normal distribution. For instance, an individual intends to assess the IQ levels of a specific population. This population may be students in a classroom or teachers in a school. After this assessment, the individual finds that most people have an IQ that is within the normal range. There are only a few persons who are within the deviate region, possessing an IQ level that is above the average or below.

A newborn's weight

A healthy newborn has a weight that typically ranges from two to four kilograms. This average may develop a normal curve. The weight of most newborns is within the range and there are only some newborns whose weights may deviate or even occur below or above the average. Examining a population of newborns may help an individual determine the average weight of the sample population.

Distribution of income

Income ranges largely depend on the economy of a country or its government's financial policies. The middle class makes up a larger population, compared with the rich and poor. The income of the middle class forms the mean on a normal distribution curve. An economy's income distribution may produce a bell-shaped graph, as this class has a dense population that is occurring towards the expected value.

Clothing size

Clothing manufacturers may conduct a survey to determine which sizes of clothing are most in demand. The size of shoes and clothes has a normal curve. This happens because there are more people who are within the average range of size and fewer people who are below or above this average. This factor may have an influence on the number of clothes that the manufacturer is making for a particular size range. It may also get challenging for people to find clothes in their sizes when these people are outside the range.

Average student performance

To promote academic excellence, a school may present its students' average results. They may do this using social media or other mass communication platforms. The objective of this exercise is to convince parents to enrol their children. According to the school management, it has found that student performance follows a normal curve. The number of students who possess average performance is higher than other groups of students.