How this calculator works
Ordering determines the centre independently of the original entry positions. An odd-sized list has one central observation. An even-sized list has two, and their arithmetic average is the conventional numeric median. Ties are retained as separate observations. The median keeps the original measurement unit and can lie between observations when the list has even length.
Formula
For ordered x: median = x((n + 1)/2) when n is odd; median = (x(n/2) + x(n/2 + 1))/2 when n is even.
Worked example
The values 8, 2, 4, 6 sort to 2, 4, 6, 8. The middle pair is 4 and 6, so the median is 5.
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Frequently asked questions
Does the median have to appear in the list?
No. The average of an even-sized central pair may be a new value.
Should I remove duplicate values?
No. Duplicates represent repeated observations and affect the centre.
What happens with one observation?
That observation is the median and both displayed central values. An empty list has no median.