Quartile: Definition, Finding, and Using

What are Quartiles?

Quartiles are three values that split your dataset into quarters. They are a type of quantile that splits the data into four equal-sized groups and tells you where a score stands relative to other scores.

These values are the following:

• Q1 First quartile: 25% of the data are below this value (aka lower quartile).
• Q2 Second quartile / Median: This value splits the data in half.
• Q3 Third quartile: 25% of the data are above this value (aka upper quartile).

Quartiles also correspond to percentiles. Q1 is the 25^th percentile, Q2 is the 50^th, and Q3 is the 75^th.

How to Find Quartiles

The simple method for finding quartiles is to list the values in your dataset in numeric order. Then find the three values that split your data into quarters, as shown below.

Note that quartiles are the values that make the “cuts” in a dataset.

Depending on the size of your dataset, you might not be able to divide it into even quarters using the data values. When that occurs, you can average two adjacent values or interpolate between them to find the quartile. Learn about these methods in my post about Percentiles.

Using Them

Quartiles are surprisingly useful in a variety of contexts. They can help you understand your dataset’s central tendency and variability and even help you find outliers. Using a boxplot to graph them can help you understand the distribution of your data. For more details, click the links below!

The median is Q2, and it splits the dataset in half. It is a handy measure of central tendency for skewed distributions.

The interquartile range (IQR) is a measure of variability. It is the range between the first and third quartiles.

IQR = Q3 – Q1

Larger IQRs indicate a broader spread of values. Half of the observations fall within the interquartile range regardless of the distribution’s shape.

Unlike the more familiar mean and standard deviation, the median and interquartile range are robust measures. Outliers do not strongly affect either statistic because they don’t hinge on every value. Additionally, the interquartile range is excellent for skewed distributions like the median.

Quartiles can also help you find outliers. After finding Q1 and Q3, calculate the following outlier fences:

• Lower fence: Q1 – (1.5 * IQR)
• Upper fence: Q3 + (1.5 * IQR)

Values below the lower fence and above the upper fence are potential outliers that you should investigate. To see an example, read my post about identifying outliers.

Finally, boxplots graph the quartiles and IQR along with the minimum and maximum values. They help you understand the distribution of your data because you can see where your data fall. Frequently, these plots use outlier fences to identify outliers on the graph. Learn more about the Box Plot Explained with Examples!