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Mean

Status: Stable

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

Description

Mean[data] gives the mean estimate of the elements in data.

Examples

All examples below are verified against the current Mathilda build.

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

In[2]:= Mean[{{a, u}, {b, v}, {c, w}}]
Out[2]= {1/3 (a + b + c), 1/3 (u + v + w)}

Implementation notes

Algorithm. builtin_mean first probes its argument with MatrixQ; if true it computes column-wise means via apply_columnwise (which is Map[Mean, Transpose[matrix]]). Otherwise it requires a List (ListQ). For a vector of length n it dispatches on element kinds: if any element is EXPR_REAL, it sums to a double and returns expr_new_real(sum/n); if all elements are exact integers/rationals it accumulates the sum in int64_t numerator/denominator pairs (reducing by gcd each step) and returns make_rational(sum_n, sum_d * n). Anything symbolic falls back to (1/n) * (Plus @@ data) built as Times/Apply nodes and re-evaluated.

Limits. The exact-rational accumulator uses fixed int64_t arithmetic, so it can overflow for large/many rationals (no GMP promotion in this path). Empty list returns NULL.

  • Protected.
  • Supports numerical and symbolic data.
  • For vectors, computes $(1/n) \sum x_i$.
  • For matrices, computes means of elements in each column.

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

In[1]:= Mean[{a, b, c}]
Out[1]= 1/3 (a + b + c)

In[1]:= Mean[{1/2, 1/3, 1/6}]
Out[1]= 1/3

In[1]:= Mean[Table[k^2, {k, 1, 10}]]
Out[1]= 77/2

Notes

Mean[data] is the arithmetic mean — the sum of the elements divided by their count. It works symbolically as well as numerically: Mean[{a, b, c}] returns the exact closed form (a + b + c)/3. Numeric data stays in exact rational arithmetic, so Mean[{1, 2, 3, 4}] is 5/2 (not 2.5) and the mean of the first ten squares is 77/2, with no round-off. Combined with generators like Table and Range, Mean gives exact averages of structured data sets.