 # GAUSS

In this comprehensive guide, we will explore the GAUSS function in Excel, which is used to calculate the cumulative distribution function of the standard normal distribution. The GAUSS function is particularly useful in statistical analysis, finance, and other fields where the normal distribution plays a significant role. We will cover the syntax, examples, tips and tricks, common mistakes, troubleshooting, and related formulae for the GAUSS function.

## GAUSS Syntax

The GAUSS function in Excel has a simple syntax with only one required argument:

=GAUSS(z)

Where:

• z is the value for which you want to calculate the cumulative distribution function. It represents the number of standard deviations from the mean.

## GAUSS Examples

Let’s look at some examples of how to use the GAUSS function in Excel:

Example 1: Calculate the cumulative distribution function for a z-value of 1.5.

=GAUSS(1.5)

This formula will return the value 0.4331928, which represents the probability that a value from the standard normal distribution is less than or equal to 1.5 standard deviations from the mean.

Example 2: Calculate the cumulative distribution function for a z-value of -2.

=GAUSS(-2)

This formula will return the value -0.47725, which represents the probability that a value from the standard normal distribution is less than or equal to -2 standard deviations from the mean.

Example 3: Calculate the cumulative distribution function for a z-value of 0.

=GAUSS(0)

This formula will return the value 0, which represents the probability that a value from the standard normal distribution is equal to the mean.

## GAUSS Tips & Tricks

Here are some tips and tricks to help you effectively use the GAUSS function in Excel:

1. Remember that the GAUSS function calculates the cumulative distribution function for the standard normal distribution, which has a mean of 0 and a standard deviation of 1. If you are working with a normal distribution with a different mean and standard deviation, you will need to standardize your values before using the GAUSS function.
2. The GAUSS function returns the probability that a value from the standard normal distribution is less than or equal to the specified z-value. To calculate the probability that a value is greater than the specified z-value, use the formula =1-GAUSS(z).
3. If you need more precision in your calculations, consider using the NORM.S.DIST function with the cumulative parameter set to TRUE. This function provides more accurate results than the GAUSS function, especially for extreme z-values.

## Common Mistakes When Using GAUSS

Here are some common mistakes to avoid when using the GAUSS function in Excel:

1. Using non-standardized values: The GAUSS function assumes that the input z-value is standardized, meaning it has a mean of 0 and a standard deviation of 1. If you are working with a normal distribution with a different mean and standard deviation, you will need to standardize your values before using the GAUSS function.
2. Forgetting to subtract the GAUSS result from 1 when calculating the probability of a value being greater than the specified z-value. Use the formula =1-GAUSS(z) to calculate this probability.

## Why Isn’t My GAUSS Function Working?

If you are having trouble with the GAUSS function in Excel, consider the following troubleshooting steps:

1. Ensure that you have entered the correct syntax for the GAUSS function, including the required z-value argument.
2. Check that your z-value is standardized, with a mean of 0 and a standard deviation of 1. If not, standardize your values before using the GAUSS function.
3. If you are still experiencing issues, consider using the NORM.S.DIST function with the cumulative parameter set to TRUE as an alternative to the GAUSS function. This function provides more accurate results, especially for extreme z-values.

## GAUSS: Related Formulae

Here are some related formulae that you may find useful when working with the GAUSS function in Excel:

1. NORM.S.DIST: This function calculates the standard normal distribution for a specified z-value. Use the syntax =NORM.S.DIST(z, cumulative), where cumulative is a logical value that determines whether to return the cumulative distribution function (TRUE) or the probability density function (FALSE).
2. NORM.S.INV: This function calculates the inverse of the standard normal cumulative distribution for a specified probability. Use the syntax =NORM.S.INV(probability).
3. NORM.DIST: This function calculates the normal distribution for a specified value, mean, and standard deviation. Use the syntax =NORM.DIST(x, mean, standard_dev, cumulative), where cumulative is a logical value that determines whether to return the cumulative distribution function (TRUE) or the probability density function (FALSE).
4. NORM.INV: This function calculates the inverse of the normal cumulative distribution for a specified probability, mean, and standard deviation. Use the syntax =NORM.INV(probability, mean, standard_dev).
5. STANDARDIZE: This function standardizes a value by subtracting the mean and dividing by the standard deviation. Use the syntax =STANDARDIZE(x, mean, standard_dev).

By understanding the GAUSS function and its related formulae, you can effectively analyze and work with normal distributions in Excel. Remember to standardize your values when necessary and consider using alternative functions like NORM.S.DIST for more accurate results.

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