The median of 7, 5, 8, x, 12, 17 is 10, then what is the value of x?

To find the value of x, we need to apply the definition of the median for a dataset with an even number of observations.

Step-by-Step Calculation
Arrange the known numbers in ascending order:
The numbers are 7, 5, 8, x, 12, 17.
The known values in ascending order are: 5, 7, 8, 12, 17.

Understand the median position:
Since there are 6 numbers in total (an even number), the median is the average of the 3rd and 4th terms when the list is sorted.
Median = (3rd term + 4th term) / 2 = 10.

Set up the equation:
The sum of the 3rd and 4th terms must be 20 (since 20 / 2 = 10).
Looking at our sorted known values (5, 7, 8, 12, 17), we need to insert x such that the average of the middle two terms is 10.
If we choose x = 12, the sorted list becomes: 5, 7, 8, 12, 12, 17.
The 3rd term is 8 and the 4th term is 12.
Average = (8 + 12) / 2 = 20 / 2 = 10.