I am learning Descriptive Statistics from UC BERKELEY online edx course. Median even according to wikipedia is defined as (n/2)th term if number of terms are odd and avg of (n/2)th+((n+1)/2)th if terms are even of the ordered list.But according to the lecture,it is defined as-
"The pth percentile of a list of numbers is the smallest number that is at least as large as p% of the list."
Using this definition yields significantly different answers than the one stated above
For example-
0, 2, 4, 7, 7,12 median = 5.5(according to traditional way)
0, 2, 4, 7, 7,12 median = 4(using the above defintion)
The traditional way for an odd number of terms is the $\frac {n+1}2$th term. It agrees that the median is $4$, as with $5$ terms we want the $3$rd. The two $7$s count as separate terms. The traditional way you cite does not account for other percentile values.