Median is that.
This type of "average" is called the median.
That is the Median of the numbers.
It is the median
Median is the middle number, when the whole set of numbers is arranged from least to greatest. If there are two middle numbers, the median is the average of both of the middle numbers (when the set of numbers is arranged from least to greatest)
When numbers are put in order either least to greatest or greatest to least, the one in the middle is the median. In an even set of numbers the average of the middle two numbers is the median. 30.5 is the median of these 3 numbers.
Arrange the numbers from smallest to greatest. The mean of the middle two numbers is the median.
If there is an odd number of elements in the set, then it is the median. If there is an even number, then there is no middle number.
After ordering the numbers from least to greatest, average the two middle numbers.
Not strictly: the smallest and largest quarter of them can be in any order (within those subsets), the middle half can be in any order. But it makes it much easier if they are all ordered.