How do you calculate Q1, Q2, Q3, and Q4?

How to Calculate Quartiles in Statistics

Understanding quartiles is key to interpreting data distributions, especially when analyzing test scores, income levels, or any set of numerical values. Quartiles divide a dataset into four equal parts, giving you insight into how values are spread out. The first quartile (Q1), second quartile (Q2), third quartile (Q3), and fourth quartile (Q4) each represent a 25% segment of the data.

Calculating these quartiles starts with ordering your data from smallest to largest. Q1, or the 25th percentile, can be found using the formula: (n + 1) × 1/4, where n is the number of data points. This gives you the position of the value below which 25% of the data falls. Similarly, Q2—also known as the median—uses (n + 1) × 2/4, effectively splitting the data in half. Half the values are below the median, and half are above.

Then comes Q3, calculated with (n + 1) × 3/4, marking the 75th percentile. This tells you where the top 25% of values begins. While Q4 technically represents the maximum value, it’s rarely referred to in practice since the focus is usually on spread and central tendency.

For example, if you have 11 ordered data points, Q1 falls at position 3 (since (11+1)/4 = 3), Q2 at position 6, and Q3 at position 9. If the position isn’t a whole number, interpolation between nearby values is used.

These measures are part of the five-number summary—minimum, Q1, median, Q3, and maximum—and are essential for building box plots and spotting outliers. With a clear understanding of quartiles, you gain a stronger sense of your data’s story.