A normal distribution in finance is a statistical tool used to find out how a particular population, sample characteristics, or event(s) are placed in relation to each other.

It is a continuous distribution of probabilities. The normal distribution is used in forecasting and adapting for a broad range of financial goals through optimization of the financial decision-making process by factual application and graphical mapping of financial data into a set of variables.

In other words, data like prices can be plotted on a normal distribution graph with dots. The dots are then joined through a line that represents the distribution of the data. It is done on a graph in terms of two axes, known as the X and Y-axis. As an example of the normal distribution, consider the amount of money spent on obtaining the calories consumed by individuals over time. If the X-axis depicts the calories consumed, and the Y-axis depicts the cost per calorie, the set of data will form a statistical and graphical distribution when plotted on the graph.

## The Use Of Normal Distribution In Finance

This article will exemplify how the normal distribution is used in the field of finance, along with giving tips and techniques in respect of the application of the normal distribution to financial practices such as investing. There is a noteworthy fact that normal distribution is not the sole type of statistical distribution, and thus the mathematical benefits emerging from the use of normal distributions in finance may not be perceived for unusually distributed data.

### How normal distribution is used in the finance

The normal distribution is utilized to devise quantitative and qualitative financial decisions based on the mathematical nature of normal distributions. This implies that normal distributions tend to follow certain similarities, such as the combination of distribution toward the mean, among other things like the standard deviation from the mean.

Due to this and various other trends, by the statistical patterns underlying the data, numerical forecasting is a bit more validated. Thus, ascertaining whether certain financial events are normally distributed can prove to be useful because those events may be more likely to follow probabilistic patterns in the future.

For further illustration, the normal distribution also helps financial analysts and/or investors make better financial decisions on the basis of the statistical information rendered by the normal distribution. Referring to the above example, if a sample of 10,000 people shows that the average daily consumption of calorie of the Americans is 2100 calories per day, and the most of the consumers fall in this range, with other calorie levels pointing evenly above and below this point, the distribution is normal.

This can then extended to a mathematical association between calories consumed and money spent on those calories. The data can be analyzed to further extent if two normal distributions exist at different price levels being all other variables such as population held to be constant.

If investors want to identify that how caloric intake affects consumption trends at fast food outlet chains, it is possible that maximum revenue for the chain can be assumed based on the normal distribution of the samples of the caloric intake. Moreover, if at the fast-food chain, the price per calorie expands, a new normal distribution may be formulated according to what is known as correlation or the statistical measurement of a modification in one set of variables affecting another set of variables.

Let’s take an example, if, at a burger food chain, the price of burgers rise by 15% and the calorie consumption of the population reduces but is still normally distributed, there may exist a correlation. To identify whether the price rise may be profitable and, therefore, a good or bad investment, the degree of these correlations can be utilized. Some more ways to make use of normal distributions in finance are mentioned as follows:

• To ascertain the probability of the occurrence of the financial events
• Statistical assistance with respect to risk assessment.
• Can be utilized for comparison of financial events and/or products
• Facilitates forecasts of return on investment (ROI)
• Presents data in a simple and intelligible format
• Enables an investor to estimate the statistical accuracy

### Tips and techniques for the application of normal distributions

While making use of normal distributions for financial decisions, there are some rules and techniques that can be used to make the statistics of abstract nature a bit more down to earth and ‘practical’ as common financial aspects such as profit, costs, the accuracy of the information, competitiveness, etc. Few rules and principles are mentioned below, and it may promote a more improved way to apply normal distributions in finance to reap benefits.

Determine the best fit segment: When several sets of data are extracted from the same sample over time, an average distribution can be obtained. It is called the best fit segment in which, if a group of normal distributions, has the effect of averaging the normal distribution without a change in variables. Thus, a normal distribution that is averaged in such a way may prove to be more precise in terms of accuracy.

Find the Beta value: The beta value is the correlation, i.e., the relationship between a dependent variable such as the share price of a company with an independent variable such as raw materials costs of the industry. If the calculated beta value is above 1, then the correlation of movements in prices among both of these variables is higher.

Look at the P-Value: Normal distributions describe a comparison of two hypotheses, the P-value shows the strength and quality of the statistical analysis. Small P-values, i.e., under .05 or lower, are accepted as a good one.

Use computer software: A competent statistical software program with a fair understanding of the statistical principles and their application in finance will transform daunting statistical calculations into easy ones. It renders economies of time and operations on calculations.

Ensure that the distributions are relevant: Normal distributions may not prove to be financially helpful if they don’t have a strong bearing and involvement in the financial decision being taken. Due to this reason, ensure that the information is relevant can facilitate the optimization of the decision-making process.

Plot the distribution on a graph: Graphical presentations of statistical data help out to make it more intelligible and complement statistical values and possibilities.

Normal distributions help to figure out the financial trends and relationships. For comparison of financial products, assessing risks involved, forecasting financial outcomes, predicting a return on investment, estimating the cost, and demand of other things, these trends and relationships can be utilized.

Some statistical data prove to be more useful than other statistical data. Therefore, it is important to have a know-how of what to look for when applying the statistical values of normal distributions to financial estimations and conditions. Also, Since not all the distributions are normal distribution, so for the mathematical features of normal distributions to apply, it is significant to determine whether a distribution is normal or not. While utilizing the normal distributions, the key is to correctly apply the data sourced from the distribution to the financial conditions.

### Sushma Singh

Sushma is a full-time blogger and financial expert. Join Sushma and 10,000 monthly readers here to learn how to save and invest your money wisely.