William W. answered • 06/04/21
Top Prealgebra Tutor
The median is the middle number. For example, take the set of numbers 3, 2, 8, 4, 1, 5, 4. To find the middle number, put them in order from smallest to largest:
1, 2, 3, 4, 4, 5, 8 and you can see that the 4th number (a "4") has 3 numbers to the left of it (1, 2, 3) and 3 numbers to the right of it (4, 5, 8) so 4 is the median.
Example 2: For the set of numbers 12, 19, 5, 11, 10, 15, 7, 20. Put them in order and you have:
5, 7, 10, 11, 12, 15, 19, 20
Now, notice that there really isn't a middle number since there are an even number of numbers. The TWO middle numbers are 11 and 12 since there are 3 numbers to the left of 11 (5, 7, 10) and 3 numbers to the right of 12 (15, 19, 20). So the median is halfway between 11 and 12 or 11.5.
The quartiles Q1 and Q3 are the middle numbers of the first and last halves. So Q1 is 7 because it is the middle number of the 1st half (5, 7, 10) and Q3 is 19 because it is the middle number of the last half (15, 19, 20)
