The ERFC function in Excel computes the complementary error function, a mathematical function widely used in statistics and probability theory. This function is particularly useful in calculating probabilities in normal distribution scenarios and is essential for various scientific computations.

Syntax

ERFC(x)

• x: A numeric value representing the input to the function. It can be any real number.

Example #1

ERFC(0)

This calculation determines the complementary error function for 0, resulting in a value of 1. This is because the complementary error function at 0 indicates that the probability of falling outside the area under the normal distribution curve is complete, hence 1.

Example #2

ERFC(1)

For an input of 1, this function calculates the complementary error function at that point, yielding approximately 0.1573. This value reflects the proportion of the distribution that lies beyond one standard deviation from the mean.

Example #3

ERFC(-1.5)

By using -1.5 as an input, the function yields about 0.9332. This indicates the high probability of the random variable falling below -1.5 standard deviations in a normal distribution context.

Error handling

• NUM! This error occurs if the input value is invalid or not a number.
• VALUE! This indicates that the input is of the wrong data type (for example, a string instead of a number).

Conclusion

In summary, the ERFC function is a valuable tool in Excel for statistical analysis. It provides insights into probability distributions, making it essential for decision-making processes across various fields, including finance, engineering, and scientific research.