# Excel Quartile Functions Compared: Inclusive vs Exclusive

Written by Kasper Langmann

The quartile function in Excel is a powerful tool that allows users to calculate the statistical quartile of a set of values. It’s an essential function for anyone working with large data sets, as it provides a way to understand the distribution of values within the data. However, Excel offers two different methods for calculating quartiles: the inclusive method and the exclusive method. Understanding the differences between these two methods is crucial for accurate data analysis.

## The Basics of Quartiles

Before diving into the specifics of Excel’s quartile functions, it’s important to understand the basics of quartiles. In statistics, a quartile is a type of quantile that divides a data set into four equal parts. The first quartile (Q1) is the value below which 25% of the data falls, the second quartile (Q2) is the median of the data, and the third quartile (Q3) is the value below which 75% of the data falls. The range between Q1 and Q3 is known as the interquartile range, and it’s often used to measure statistical dispersion, or how spread out the values in a data set are.

Quartiles are a fundamental concept in descriptive statistics, and they’re used in a wide range of applications, from business and economics to social sciences and engineering. They provide a simple way to summarize a large data set and to compare different data sets. In Excel, you can calculate quartiles using the QUARTILE function, which takes two arguments: the array of data you want to analyze, and the quartile number you want to calculate (0 for the minimum value, 1 for Q1, 2 for Q2, 3 for Q3, and 4 for the maximum value).

## Excel’s Inclusive Quartile Function

The inclusive quartile function in Excel, denoted as QUARTILE.INC, uses the inclusive method to calculate quartiles. This method includes all data points in the calculation, meaning that the minimum and maximum values are considered the 0th and 4th quartiles, respectively. The inclusive method is the default method used by Excel, and it’s the one most people are familiar with.

The inclusive method calculates the quartiles as follows: Q1 is the median of the lower half of the data (including the median if the data set has an odd number of values), Q2 is the median of the data, and Q3 is the median of the upper half of the data (again, including the median if the data set has an odd number of values). This method is straightforward and intuitive, but it can sometimes give misleading results if the data set has outliers or is not symmetrically distributed.

## Excel’s Exclusive Quartile Function

The exclusive quartile function in Excel, denoted as QUARTILE.EXC, uses the exclusive method to calculate quartiles. This method excludes the minimum and maximum values from the calculation, meaning that the 0th and 4th quartiles are not defined. The exclusive method is less commonly used than the inclusive method, but it can provide a more accurate picture of the data distribution in certain situations.

The exclusive method calculates the quartiles as follows: Q1 is the value below which 25% of the data falls, Q2 is the median of the data, and Q3 is the value below which 75% of the data falls. However, these values are calculated using a formula that interpolates between the closest data points, rather than simply taking the median of the upper and lower halves of the data. This method is more complex than the inclusive method, but it can give more accurate results if the data set has outliers or is not symmetrically distributed.

## Comparing the Two Methods

So, which method should you use? The answer depends on your specific needs and the nature of your data. If your data set is symmetrically distributed and doesn’t have any outliers, the inclusive method will give you accurate results. However, if your data set is skewed or has outliers, the exclusive method may provide a better representation of the data distribution.

It’s also worth noting that the choice between the inclusive and exclusive methods can have a significant impact on your results. For example, if you’re using quartiles to calculate the interquartile range (a common measure of statistical dispersion), the exclusive method will give you a smaller range than the inclusive method, because it excludes the minimum and maximum values. This could lead to different conclusions about the variability of your data.

## Conclusion

In conclusion, both the inclusive and exclusive quartile functions in Excel have their strengths and weaknesses. The inclusive method is simpler and more intuitive, but it can give misleading results if the data set is not symmetrically distributed or has outliers. The exclusive method is more complex, but it can provide a more accurate picture of the data distribution in certain situations.

Ultimately, the choice between the two methods should be guided by a thorough understanding of your data and the specific requirements of your analysis. By understanding the differences between these two methods, you can make more informed decisions and perform more accurate data analysis in Excel.