I went to archive.org and searched for intro books in statistics (there are a lot!). All of them gave preference to the average of the two middle values. One of them also pointed out there were valid alternatives.
"Since there are 10 values [in the sorted list], the median is the average of the fifth and sixth values. However, it could be also be 4.1, or 4.9, or any other value between 4 or 5, since each of these values divides the 10 values into two equal groups." - https://archive.org/details/introductiontost0000chao/page/54...
"If there were an even number of observations (say, six instead of five), the calculation would be more complex. We would need to find the middle pair of numbers (the third and fourth observations), and then find the value that’s halfway between them, by adding the values together and dividing by two." - https://archive.org/details/introductiontost0000haan/page/n6...
I went to archive.org and searched for intro books in statistics (there are a lot!). All of them gave preference to the average of the two middle values. One of them also pointed out there were valid alternatives.
"Since there are 10 values [in the sorted list], the median is the average of the fifth and sixth values. However, it could be also be 4.1, or 4.9, or any other value between 4 or 5, since each of these values divides the 10 values into two equal groups." - https://archive.org/details/introductiontost0000chao/page/54...
"For a sample of size n, the sample median is the ... Average of the two order statistics in the middle if n is even." - https://archive.org/details/introductiontost0000salv/page/64...
"We find no middle value; therefore, the median is the mean of the two middle values" - https://archive.org/details/US_Navy_Training_Course_-_Introd...
"The sample median for this collection is given by the middle observation if n is odd. If n is even, the sample median is the average of the two middle observations." - https://archive.org/details/introductiontost0000milt_g9m2/pa...
"sample median = ... the average of the middle two values if n is even" - https://archive.org/details/introductiontost0000peck_o4j9/pa...
"If there were an even number of observations (say, six instead of five), the calculation would be more complex. We would need to find the middle pair of numbers (the third and fourth observations), and then find the value that’s halfway between them, by adding the values together and dividing by two." - https://archive.org/details/introductiontost0000haan/page/n6...
"If there is an even number of values, the median is equal to the mean of the two middle values of the ordered set." - https://archive.org/details/introductiontoec0000merr/page/18...