How to Find a Quartile for an Eight Number Set

Quartiles divide a set of numbers into four equal parts.

You can find the quartiles of an 8-number set of values to determine how the values are distributed throughout the set. The three quartiles divide a set of values into four equal parts and make it easier to analyze the data by showing key points. For example, 25 percent of the values fall below the first quartile and 25 percent fall above the third quartile. The second quartile, or the median, splits the set of values in half. For example, students who score above the third quartile on a test rank in the top 25 percent of students who took the test.

Instructions

1. Write an 8-number set of values in order from smallest to largest. For this example, use the set 5, 9, 2, 1, 4, 7, 12 and 17. This yields 1, 2, 4, 5, 7, 9, 12 and 17 in order.

2. Determine the value that's in the middle of the set that separates the set into exactly two halves with four values to the left and four to the right. This number is between the fourth and fifth values, 5 and 7, respectively, because the set has an even number of values.

3. Calculate the average of 5 and 7 -- (5 + 7)/2 equals 6. This is the second quartile, or median, of the set of numbers.

4. Determine the value that separates the lower half of values below the median -- 1, 2, 4 and 5 -- into two halves. This value is between 2 and 4 because there is an even number of values in the lower half.

5. Calculate the average of 2 and 4 -- (2 + 4)/2 equals 3. This is the first quartile of the set of values.

6. Determine the value that separates the upper half of values above the median -- 7, 9, 12 and 17 -- into two halves. This value is between 9 and 12 because there is an even number of values in the upper half.

7. Calculate the average of 9 and 12 -- (9 + 12)/2 equals 10.5. This is the third quartile of the set of values.

Tips & Warnings

• If a set of values has an odd number of values, the median will be the exact value in the middle of the set.

References

• Montana State University: Statistical Terms and Examples
• Minnesota State University, Moorhead; First Quartile and Third Quartile; Kris Montis, et al.; 2010

Resources

• Cliffs Notes: Box Plot (Box and Whiskers)