A financial normal distribution is a statistical term used to describe how particular population sample characteristics or event(s) results are placed in relation to each other. The normal distribution is used to help predict and adjust for a wide range of financial goals by optimizing financial decision-making by applying and graphically mapping financial data into a distribution set of variables.

In other words, data such as prices can be plotted on a normal distribution graph with dots. The dots are then connected with a line that reveals the data’s distribution in terms of two axis continuums known as the X and Y axis on a graph. An example of a normal distribution is the amount of money spent on obtaining the calories consumed by individuals over time. If the X axis represents calories consumed, and the Y axis represents cost per calorie, the data set will produce a statistical and graphical distribution when plotted on graph.

This article will illustrate how the normal distribution is used in finance in addition to providing tips and techniques for applying the normal distribution to financial practices such as investing. It is important to note the normal distribution is not the only type of statistical distribution, and thus the mathematical benefits arising from use of normal distributions in finance may not be realized for non-normally distributed data.

## How normal distribution is used in finance

The normal distribution is used to make quantitative and qualitative financial decisions based on the mathematical nature of normal distributions. This is to say, normal distributions tend to follow certain similarities such as conglomeration of distribution toward the mean among other things such as standard deviation from the mean. Due to this and other trends, numerical forecasting is more justified by the statistical patterns underlying the data. Thus, determining if certain financial events are normally distributed can be useful because those events may be more likely to follow probabilistic patterns in the future.

To illustrate further, the normal distribution helps financial analysts and/or investors make better financial decisions based on the statistical information provided by the normal distribution. Using the example above, if a sample of 20,000 people reveals that the average daily calorie consumption of Americans is 2,100 calories per day, and the majority of food consumers are near this range, with others calorie levels tapering off evenly above and below this point, the distribution is normal. This can then lead to a mathematical connection between calories consumed and dollars spent on calories. The data can be further analyzed if two normal distributions exist at different price levels all other variables such as population held constant.

If investors want to determine how caloric intake affects consumption trends at fast food chains, it is probable a maximum revenue for the chain can be assumed based on the normal distribution of the population samples caloric intake. Furthermore, if price per calorie rises at the fast food chain, a new normal distribution may be formed creating what is known as correlation or the statistical measurement of a change in one set of variables influencing another set of variables. For example, if the price of burgers at a burger food chain rise by 20 percent and the caloric intake of the population declines but is still normally distributed, a correlation may be present. The degree of these correlations can be used to determine if price rises may be profitable and therefore a good or bad investment. A few more ways normal distributions can be used in finance are listed below.

- To determine probability of financial events occurring
- Can be used in comparing financial events and/or products
- Statistically assists in assessing risk
- Helps in forecasting return on investment (ROI)
- Presents data in an easier to understand format
- Allows an investor to measure accuracy of the statistical information through statistical analysis of the distribution

## Tips and techniques for applying normal distributions

When using normal distributions to make financial decisions, there are techniques and rules that can be utilized to make the abstract nature of statistics more down to earth and ‘realistic’ in terms of common financial concerns such as profit, cost, accuracy of information, competitiveness etc. A few of these rules and principles are listed below and may convey a more helpful way to make sense of and apply normal distributions in finance.

Determine the line of best fit: When multiple data sets are obtained from the same sample group over time, an average distribution can be obtained. This is known as the line of best fit, which if a group of normal distributions without a change in variables, has the effect of averaging the normal distribution. Thus, a normal distribution that is averaged in this way may be more accurate.

Find the beta value: The beta value is the correlation i.e. relationship between a depending variable such as a company stock price with an independent variable such as industry raw materials costs. If the beta value is above 1, the correlation of movements in prices between the two variables is higher.

Look at the P-Value: When comparing two hypotheses represented by normal distributions the P-value illustrates the quality and strength of the statistical analysis. Small P-values under .05 or lower are good.

Use computer software: A good statistical software program will make the tough statistical calculations easy with a sound understanding of the statistical principles and their application in finance. This saves time and energy on calculations.

Make sure the distributions are relevant: Normal distributions may not be financially helpful if they don’t have a strong bearing and implication on a financial decision being made. For this reason, making sure the information is relevant can help optimize decision-making.

Plot the distribution on a graph: Graphical illustrations of statistical data can help make it more understandable and complement statistical values and probabilities.

Normal distributions help determine financial trends and relationships. These trends and relationships can then be used for comparing financial products, forecasting financial outcomes, assessing risk, and predicting return on investment, estimating cost and demand among other things.

Certain statistical data may be more useful than other statistical data so it is important to know what to look for when applying the statistical values of normal distributions to financial evaluations and choices. Also, since not all distributions are normal, it is important to determine whether or not a distribution is in fact normal, for the mathematical characteristics of normal distributions to apply. When utilizing normal distributions correctly applying the data derived from the distribution to the financial application is key.