The PHI function in Excel is a valuable tool for statisticians and analysts, as it computes the probability density function of the standard normal distribution. It returns the value at a specified point, providing insights into the behavior of normally distributed data.

Syntax

PHI(z)

• z: A numeric value representing the point at which the function is evaluated within the standard normal distribution.

Example #1

PHI(0)

This function call returns the probability density function value at z = 0, resulting in approximately 0.3989422804014337, which is the peak of the standard normal distribution.

Example #2

PHI(1)

This function retrieves the density function value at z = 1. The output will be around 0.24197072451914337, indicating the likelihood of observing a value in the standard normal distribution at that point.

Example #3

PHI(-1)

In this case, evaluating PHI at z = -1 provides a density function value of roughly 0.24197072451914337, which is symmetrical to the result at z = 1 due to the properties of the normal distribution.

Error handling

• VALUE!: This error occurs if a non-numeric value is used as the argument for z, as the function requires a numeric input.
• NUM!: This error may appear if z is too large or too small; however, valid numerical inputs for standard normal variables typically do not trigger this error.

Conclusion

The PHI function is a crucial element within Excel for those dealing with statistics and probability. By understanding how to use it, analysts can effectively assess the density of observations in a normal distribution, facilitating more informed decision-making and analysis.