I'll give you an example: Find the first and third quartiles using this set of data - 3, 5, 7, 8, 9, 11, 15, 16, 20, 21.
Step 1: Put the numbers in order. 3, 5, 7, 8, 9, 11, 15, 16, 20, 21. Step 2: Make a mark in the center of the data: 3, 5, 7, 8, 9, | 11, 15, 16, 20, 21. Step 3: Place parentheses around the numbers above and below the mark you made in Step 2–it makes Q1 and Q3 easier to spot. (3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Step 4: Find Q1 and Q3 Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data. (3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Q1 = 7 and Q3 = 16.
The first quartile, denoted by Q1 , is the median of the lower half of the data set. This means that about 25% of the numbers in the data set lie below Q1 and about 75% lie above Q1 .The third quartile, denoted by Q3 , is the median of the upper half of the data set. This means that about 75% of the numbers in the data set lie below Q3 and about 25% lie above Q3
