The graph of a normal or Gaussian distribution is often referred to as the bell curve due to its resemblance to a bell. While there are other types of distribution that look like a bell when graphed, such as Cauchy or logistic distributions, the bell curve usually refers to a normal or Gaussian curve. This curve is an extremely useful statistical tool, as it allows you to calculate the probability of events or values for a real-valued random variable. For this reason, this tool is sometimes used to make predictions regarding financial investments. However, you should tread carefully, as normally distributed variables are not common in this area.
In this guide, you will learn what a bell curve is and what it represents. You will learn how a bell curve works through the example of the standard normal distribution, and you will also learn how to graph this distribution using Google Sheets. Finally, you will learn about common uses of the normal distribution in finance and the precautions you should take if you want to use it.
What is a Bell Curve?
The bell curve is the informal name given to the graph of a normal or Gaussian distribution, which is a continuous probability distribution for a real-valued random variable. It is perfectly symmetrical on either side of the mean, represented by the peak of the bell. The width is determined based on standard deviations from the mean.
Below, you have the graph of the standard normal distribution.
However, it’s important to note that the normal or Gaussian distribution is not the only one shaped like a bell: Cauchy, logistic, and Student’s t distributions are also bell-shaped. The unique characteristics of normal distributions make them valuable analytic tools, but only if you’re dealing with variables that are normally distributed. This is not always the case in finance, so be careful how you use it.
How Does a Bell Curve Work?
The area under the curve represents the probability, adding up to a total of 1. The further from the mean along the x-axis, the lower the probability. However, note that the tails of the graph are asymptotic, which means they approach the x-axis, but never actually meet it.
Below, you can see how the values are distributed in a standard normal distribution. Values within one standard deviation of the mean (-1 to 1) account for 68.2% of the total, while values within two standard deviations account for 95.4%. Values within three standard deviations account for 99.7% of the total. Remember that the tails are asymptotic, which is why it’s not 100%.
In the next section, you will learn how to create the standard normal distribution curve using Google Sheets.
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How to Create a Bell Curve in Google Sheets?
Below, you have step-by-step instructions on how to create a bell curve of the standard normal distribution, which has a mean of 0 and a standard deviation of 1. However, the data will be set up so you can easily change the mean or standard deviation as needed.
- 1. Open Google Sheets.
- 2. In separate cells, type in the mean and standard deviation for a standard normal distribution: 0 and 1, respectively.
- 3. First, define the percentiles that will make up the x-axis, which shows standard deviations from the mean. I’ll use values between -3 and 3 in intervals of 0.1.
- 4. Next, calculate the x values by adding the mean to the product of the percentile and the standard deviation. Use absolute referencing for the mean and standard deviation.
- 5. Press ‘Enter’. In this case, the x-values will equal the percentiles.
- 6. Grab the fill handle and drag it down to the last row to get the rest of the values.
- 7. Next, you need to calculate the y values. Use the probability density function for the normal distribution, NORM.DIST.
- 8. For the first parameter, select the cell with the first x value. For the second and third parameters, use absolute referencing to select the mean and the standard deviation, respectively.
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- 9. The third parameter is “FALSE”, as the result should not be cumulative. Close the parenthesis and press ‘Enter’.
- 10. Grab the fill handle and drag it down to the last row.
- 11. Select the x and y values and go to Insert > Chart.
- 12. That’s it. You have a bell curve.
- 13. You can easily change the values of the mean and standard deviation, and the rest will update automatically.
When is the Bell Curve Used in Finance?
Financial analysts often use the bell curve and other types of distributions to model potential outcomes in different investment scenarios. Depending on the type of analysis, the purpose is to predict future stock prices, default rates, or earnings. However, this can be very problematic, as many financial variables don’t have a normal distribution. If that is the case, the results will not be very helpful and could be highly misleading. For this reason, it’s important to check that you’re dealing with a normally distributed variable before using the normal distribution or bell curve in your analysis.
As you have seen, the bell curve or normal distribution is a very useful statistical tool. However, it should only be used to analyze variables that are normally distributed. Unfortunately, many of the variables of interest to financial investors have non-normal distributions, which makes using the bell curve very risky.
You now know what a bell curve is and how it works. You know that 68.2% of the observations fall within one standard deviation of the mean and 95.4% within two standard deviations. You also know that the standard normal distribution has a mean of 0 and a standard deviation of 1, and you know how to graph it using Google Sheets. You also know about its use in finance, as well as the associated dangers when used with non-normal distributions.