What is LOGNORM.INV?
The LOGNORM.INV function in Google Sheets is a statistical function used to calculate the inverse of the lognormal distribution. This function is particularly useful in scenarios where you need to find a value that corresponds to a given probability in a lognormally distributed dataset. The lognormal distribution is often used in fields such as finance, environmental studies, and reliability engineering, where the data is positively skewed.
In simpler terms, LOGNORM.INV allows you to determine the value of a variable that has a lognormal distribution based on a specified probability.
A Practical Example
Imagine you are analyzing the distribution of incomes in a certain region, and you want to find out what income level corresponds to a specific percentile.
Income Distribution Table:
| Percentile | Probability |
|---|---|
| 10% | 0.10 |
| 50% | 0.50 |
| 90% | 0.90 |
Assume the mean (mu) of the natural logarithm of the income is 10, and the standard deviation (sigma) is 0.5.
LOGNORM.INV Formula
To find the income level corresponding to the 90th percentile, you would use the LOGNORM.INV function as follows:
EXCEL
=LOGNORM.INV(0.90, 10, 0.5)
In this formula:
0.90is the probability for which you want to find the corresponding income level.10is the mean (mu) of the natural logarithm of the income.0.5is the standard deviation (sigma) of the natural logarithm of the income.
Result of the Formula
When you apply the LOGNORM.INV formula, it will return the income level that corresponds to the 90th percentile. For example, if the result is approximately 22000, it means that 90% of the population earns less than $22,000.
Income Distribution Table with Results:
| Percentile | Probability | Income Level |
|---|---|---|
| 10% | 0.10 | 12,000 |
| 50% | 0.50 | 20,000 |
| 90% | 0.90 | 22,000 |
Why Use LOGNORM.INV?
LOGNORM.INV is beneficial because it allows analysts and researchers to work with lognormally distributed data effectively. It provides a straightforward way to determine thresholds or cutoffs based on probabilities, which is essential for making informed decisions in various fields. Additionally, it helps in understanding the distribution of data, especially when dealing with skewed datasets.
Key Takeaways:
- LOGNORM.INV: A statistical function that calculates the inverse of the lognormal distribution.
- Use Cases: Ideal for analyzing income distributions, environmental data, and any scenario where lognormal distribution is applicable.
- Understanding Data: Helps in determining income levels or other thresholds based on specified probabilities, enhancing data analysis capabilities.
LOGNORM.INV is an essential function for anyone working with statistical data in Google Sheets, providing a powerful tool for analyzing and interpreting lognormally distributed datasets.
Happy spreadsheeting!