Quartiles are values that divide ordered data into four equal parts: Q1 (25th percentile) marks the boundary below which 25% of data falls, Q2 (the median, 50th percentile) splits the data in half, and Q3 (75th percentile) marks the boundary below which 75% falls.
If you line up 100 people by height and divide into 4 equal groups, quartiles mark the dividing points. Q1 is where the shortest 25% ends, Q2 is the middle, Q3 is where the tallest 25% begins.
Showing a random 20 of 50 problems.
Example 1
medium
Ordered ages: 14,15,16,17,18,19,20. Find Q3.
Example 2
easy
For ordered 1,2,3,4,5,6,7, find Q1.
Example 3
medium
For 4,8,15,16,23,42, find Q1 and Q3.Read Q₁ and Q₃ off the box plot.
Example 4
medium
Ordered ages: 14,15,16,17,18,19,20. Find Q1.
Example 5
medium
For ordered 6,9,11,14,17,20, find Q3.
Example 6
hard
If a data set has 20 values, between which two ordered positions is Q1 found (inclusive method)?
Example 7
easy
For ordered 1,2,3,4,5,6,7, find Q3.
Example 8
easy
Find the median (Q2) of 2,4,6,8,10.
Example 9
medium
Test scores: 55,62,68,75,80,88,92,95. Find Q1,Q2,Q3.Find Q₁, Q₂, Q₃ from the test-score distribution.
Example 10
easy
For ordered 2,4,6,8, find Q2.
Example 11
medium
For ordered 6,9,11,14,17,20, find Q2.
Example 12
easy
What percentile does Q3 represent?
Example 13
easy
Order 12,5,9,3,7 from least to greatest.
Example 14
easy
For ordered 3,5,7,9,11, find Q1.
Example 15
hard
For {3,7,8,12,14,21,22,27,30,35}, find Q1,Q2,Q3.Find all three quartiles for this 10-value data set.
Example 16
medium
For 5,7,8,9,10,12,13,14,15, find Q1.Find Q₁ — shown as ? on the box.
Example 17
hard
Annual rainfalls (in inches) over 9 years: 20,22,25,28,30,32,35,40,50. Find all three quartiles.Find Q₁, Q₂, Q₃ for the rainfall data.
Example 18
easy
Order 9,3,7,1 before finding quartiles. Give the ordered list.
Example 19
medium
For 1,2,3,4,5,6,7,8, find all three quartiles.Find all three quartiles Q₁, Q₂, Q₃ — each shown as ? on the box.
Example 20
medium
If Q1=10 and Q3=22, where do the middle 50% of values lie?The shaded box shows where the middle 50% of values lie.