The first quartile, denoted Q1, is the median of the lower half of a sorted data set. It marks the 25th percentile, meaning 25% of the observations fall below Q1 while 75% lie above.
Q1 is the middle value of the lower half of an ordered list of numbers.
1. Sort the data in ascending order.
2. Find the median of the entire set to split it into two halves.
3. Take the lower half (all values below the median) and compute its median. That median is Q1.
Given the data set:
{1, 2, 15, 8, 5, 9, 12, 42, 25, 16, 20, 23, 32, 28, 36}
Sorted:
{1, 2, 5, 8, 9, 12, 15, 16, 20, 23, 25, 28, 32, 36, 42}
With 15 numbers, the overall median is the 8th value, 16. The lower half contains {1, 2, 5, 8, 9, 12, 15}. Its median is the 4th value, 8. Thus, Q1 = 8.
If the data count were even, the median would be the average of the two middle numbers.
Q3 (the third quartile) is the median of the upper half of the data. In the example, the upper half is {20, 23, 25, 28, 32, 36, 42}, yielding Q3 = 28.
The interquartile range (IQR) is the difference between Q3 and Q1: IQR = 28 – 8 = 20. IQR captures the spread of the middle 50% of observations and is less affected by outliers than the full range.
In a box‑and‑whisker plot, the box spans from Q1 to Q3, the line inside the box marks the median, and the whiskers extend to the smallest and largest non‑outlier values.
Use an online quartile calculator to automatically compute Q1, median, Q3, and IQR for any data set. Enter your numbers, and the tool will provide all key quartile statistics.
