The ERF function in Google Sheets is a powerful tool used for statistical calculations involving the Gaussian error function. It is particularly useful in areas such as probability and statistics, where calculations involving integrals of error functions are necessary for data analysis.

Syntax

ERF(lower_limit, upper_limit)

• lower_limit: This parameter defines the lower bound of the integration.
• upper_limit: This parameter defines the upper bound of the integration.

Example #1

=ERF(0, 1)

This function call calculates the integral of the Gaussian error function from 0 to 1, which returns approximately 0.8427, indicating the probability of a standard normal variable being between those two limits.

Example #2

=ERF(-1, 1)

Here, the ERF function returns the integral from -1 to 1, yielding a result of around 0.6827, which represents the probability of a standard normal variable falling within that range.

Example #3

=ERF(0, 0)

In this instance, the function evaluates the integral from 0 to 0, resulting in 0, as the integral over a zero-width interval equals zero.

Error handling

• NUM!: This error occurs if the parameters provided are not numeric. Ensure that you are using numerical values for both the lower and upper limits.
• VALUE!: This error arises when non-numeric values are included in either parameter. Verify that only numbers are input as arguments.
• REF!: If the functional cell references an invalid cell or range, this error will appear. Check the linked cells for validity.

Conclusion

The ERF function in Google Sheets is an essential tool for anyone working with statistics and probability. By providing a simple and clear syntax along with robust error handling, users can seamlessly perform calculations involving the Gaussian error function. Mastery of the ERF function ensures accurate data analysis and enhances statistical insights.