# Central Tendency And Normal Distributions

A normal distribution can be used to describe how sample characteristics or events relate to each other. The distribution can be “used to 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” (“The use of normal distribution in finance”, 2011). Under the normal distribution curve (bell curve), data is distributed around the mean or expected value. A low standard deviation indicates that the data points tend to be close to the mean of the data set, while a high standard deviation indicates that the data points are spread out over a wider range of values. 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.

Normal distributions can be used in finance to:

· Determine probability of financial events

· Compare financial events and/or products

· Assist in risk assessment

· Forecast return on investment (ROI)

· Present data in an easy-to-understand format

· Measure accuracy of statistical information through statistical analysis of the distribution

Financial economists often track monthly stock returns and look to determine if they are normally distributed. We are going to return to the Dow Jones Industrial Average. Using the information, you have learned about the normal curve and Z score, make probability statements about future returns of the Dow Jones Industrial Average, and defend your projections. Go to The Wall Street Journal website https://www.wsj.com/market-data/quotes/index/DJIA/historical-prices and use the historical tool to calculate the mean and standard deviation for the month of August 2017 for your projections.

Steps to complete this assignment:

1. Scroll to the date boxes and enter 1/01/2020 in the first box and 12/31/2020 in the second box
2. Click the GO button
4. An Excel spreadsheet with all the daily values will need to be opened.
5. Please use the Close scores as the daily raw scores.
6. Please calculate the mean in Excel. You need to watch the videos if you do not know how to use Excel. In Excel the mean is called the average.
7. Please calculate the standard deviation in Excel. You need to watch the videos if you do not know how to use Excel. In Excel for ths assignment you are usind the standard deviation for a population. It is STDEV.P
8. Create a new column to the right of the close scores and calculate the Z or standard score.

Here is another video to assit you with this assignment.

1. Once you have all your Z scores you will need to create another column with the Area Under the Normal Distribution using the Z table . Identify any days that have a significant difference. Remember that a significant difference using a Z score means that Z< -2.0 or Z>+2.0.
2. Now conduct your analysis. Are there any days that are significantly different in the year? Did you create a graph of your data using a line graph, what does it look like? Can you make a prediction of how the DJIA is going to perform in 2021? How can you test your prediction to see if it is correct? Can you make a prediction how the DJIA is performing today compared to 2020?

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