ianmcook commented on a change in pull request #10887:
URL: https://github.com/apache/arrow/pull/10887#discussion_r690709164



##########
File path: docs/source/cpp/compute.rst
##########
@@ -234,6 +238,90 @@ Notes:
 
 * \(6) Output is Float64 or input type, depending on QuantileOptions.
 
+* \(7) tdigest/t-digest computes approximate quantiles, and so only needs a
+  fixed amount of memory. See the `reference implementation
+  <https://github.com/tdunning/t-digest>`_ for details.
+
+Grouped Aggregations ("group by")
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Grouped aggregations are not directly invokable, but are used as part of a
+group by operation. Like scalar aggregations, grouped aggregations reduce
+multiple input values to a single output value. Instead of aggregating all
+values of the input, however, grouped aggregations partition of the input
+values on some set of "key" columns, then aggregate each group individually,
+and emit one output per input group.
+
+As an example, for the following table:
+
++-----------------+--------------+
+| Column "x"      | Column "key" |
++=================+==============+
+| 2               | "a"          |
++-----------------+--------------+
+| 5               | "a"          |
++-----------------+--------------+
+| null            | "b"          |
++-----------------+--------------+
+| null            | "b"          |
++-----------------+--------------+
+| null            | null         |
++-----------------+--------------+
+| 5               | null         |
++-----------------+--------------+
+
+We compute a sum of column "x", grouped on the key column "key". This gives us
+three groups:
+
++-----------------+--------------+
+| Column "sum(x)" | Column "key" |
++=================+==============+
+| 7               | "a"          |
++-----------------+--------------+
+| null            | "b"          |
++-----------------+--------------+
+| 5               | null         |
++-----------------+--------------+
+
+The supported aggregation functions are as follows.

Review comment:
       Could you add a sentence here explaining the meaning of the `hash_` 
prefix in these function names?




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