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Median

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Median[data]
    gives the median estimate of the elements in data.
Median[dist]
    gives the median of the distribution dist.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= Median[<|"a" -> 1, "b" -> 3, "c" -> 5|>]
Out[1]= 3

In[2]:= Variance[<|"a" -> 2, "b" -> 4, "c" -> 6|>]
Out[2]= 4

In[3]:= StandardDeviation[<|"a" -> 2, "b" -> 4, "c" -> 6|>]
Out[3]= 2

Implementation notes

Algorithm. builtin_median requires a List. If the first element is itself a List it treats the input as a matrix/tensor and reduces column-wise through apply_columnwise (Map[Median, Transpose[...]]). For a 1-D vector it first verifies every element is a real numeric via the helper is_real_numeric (which checks NumericQ and FreeQ[#, I]); non-real data prints Median::rectn and leaves the call unevaluated. It then evaluates Sort[data]: for odd n it returns the middle element (sorted[n/2]); for even n it returns (sorted[n/2-1] + sorted[n/2]) / 2, built as Plus then Divide and re-evaluated so the result stays exact (rational) when the inputs are exact. ATTR_PROTECTED.

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= Median[{5, 1, 3, 2, 4}]
Out[1]= 3

In[1]:= Median[{1, 2, 3, 4}]
Out[1]= 5/2

In[1]:= Median[Table[k^2, {k, 1, 10}]]
Out[1]= 61/2

Notes

Median[data] returns the middle value of the sorted data. For an odd number of elements it is the single central element (the first example sorts to {1, 2, 3, 4, 5}, giving 3); for an even number it is the exact average of the two central elements, so Median[{1, 2, 3, 4}] is 5/2. The result is kept in exact arithmetic — the median of the first ten squares is 61/2, the average of the 5th and 6th sorted values 25 and 36. Median expects numeric data; an even-length list of unresolved symbols cannot be averaged and is left unevaluated with a Median::rectn message.