diff --git a/src/groupeddataframe/splitapplycombine.jl b/src/groupeddataframe/splitapplycombine.jl
index 72aaa348b6..858a859bd3 100644
--- a/src/groupeddataframe/splitapplycombine.jl
+++ b/src/groupeddataframe/splitapplycombine.jl
@@ -477,8 +477,9 @@ struct Reduce{O, C, A} <: AbstractAggregate
     op::O
     condf::C
     adjust::A
+    checkempty::Bool
 end
-Reduce(f, condf=nothing) = Reduce(f, condf, nothing)
+Reduce(f, condf=nothing, adjust=nothing) = Reduce(f, condf, adjust, false)
 
 check_aggregate(f::Any) = f
 check_aggregate(::typeof(sum)) = Reduce(Base.add_sum)
@@ -488,9 +489,9 @@ check_aggregate(::typeof(minimum)) = Reduce(min)
 check_aggregate(::typeof(mean)) = Reduce(Base.add_sum, nothing, /)
 check_aggregate(::typeof(sum∘skipmissing)) = Reduce(Base.add_sum, !ismissing)
 check_aggregate(::typeof(prod∘skipmissing)) = Reduce(Base.mul_prod, !ismissing)
-check_aggregate(::typeof(maximum∘skipmissing)) = Reduce(max, !ismissing)
-check_aggregate(::typeof(minimum∘skipmissing)) = Reduce(min, !ismissing)
 check_aggregate(::typeof(mean∘skipmissing)) = Reduce(Base.add_sum, !ismissing, /)
+check_aggregate(::typeof(maximum∘skipmissing)) = Reduce(max, !ismissing, nothing, true)
+check_aggregate(::typeof(minimum∘skipmissing)) = Reduce(min, !ismissing, nothing, true)
 
 # Other aggregate functions which are not strictly reductions
 struct Aggregate{F, C} <: AbstractAggregate
@@ -609,10 +610,10 @@ function copyto_widen!(res::AbstractVector{T}, x::AbstractVector) where T
     return res
 end
 
-function groupreduce!(res, f, op, condf, adjust,
+function groupreduce!(res, f, op, condf, adjust, checkempty::Bool,
                       incol::AbstractVector{T}, gd::GroupedDataFrame) where T
     n = length(gd)
-    if adjust !== nothing
+    if adjust !== nothing || checkempty
         counts = zeros(Int, n)
     end
     groups = gd.groups
@@ -621,15 +622,20 @@ function groupreduce!(res, f, op, condf, adjust,
         x = incol[i]
         if gix > 0 && (condf === nothing || condf(x))
             res[gix] = op(res[gix], f(x, gix))
-            adjust !== nothing && (counts[gix] += 1)
+            if adjust !== nothing || checkempty
+                counts[gix] += 1
+            end
         end
     end
     outcol = adjust === nothing ? res : map(adjust, res, counts)
+    if checkempty && any(iszero, counts)
+        throw(ArgumentError("some groups contain only missing values"))
+    end
     # Undo pool sharing done by groupreduce_init
-    if outcol isa CategoricalVector
+    if outcol isa CategoricalVector && outcol.pool === incol.pool
         U = Union{CategoricalArrays.leveltype(outcol),
                   eltype(outcol) >: Missing ? Missing : Union{}}
-        outcol = CategoricalArray{U, 1}(outcol.refs, incol.pool)
+        outcol = CategoricalArray{U, 1}(outcol.refs, copy(outcol.pool))
     end
     if isconcretetype(eltype(outcol))
         return outcol
@@ -639,20 +645,21 @@ function groupreduce!(res, f, op, condf, adjust,
 end
 
 # Function barrier works around type instability of _groupreduce_init due to applicable
-groupreduce(f, op, condf, adjust, incol::AbstractVector, gd::GroupedDataFrame) =
+groupreduce(f, op, condf, adjust, checkempty::Bool,
+            incol::AbstractVector, gd::GroupedDataFrame) =
     groupreduce!(groupreduce_init(op, condf, incol, gd),
-                 f, op, condf, adjust, incol, gd)
+                 f, op, condf, adjust, checkempty, incol, gd)
 # Avoids the overhead due to Missing when computing reduction
-groupreduce(f, op, condf::typeof(!ismissing), adjust,
+groupreduce(f, op, condf::typeof(!ismissing), adjust, checkempty::Bool,
             incol::AbstractVector, gd::GroupedDataFrame) =
     groupreduce!(disallowmissing(groupreduce_init(op, condf, incol, gd)),
-                 f, op, condf, adjust, incol, gd)
+                 f, op, condf, adjust, checkempty, incol, gd)
 
 (r::Reduce)(incol::AbstractVector, gd::GroupedDataFrame) =
-    groupreduce((x, i) -> x, r.op, r.condf, r.adjust, incol, gd)
+    groupreduce((x, i) -> x, r.op, r.condf, r.adjust, r.checkempty, incol, gd)
 
 function (agg::Aggregate{typeof(var)})(incol::AbstractVector, gd::GroupedDataFrame)
-    means = groupreduce((x, i) -> x, Base.add_sum, agg.condf, /, incol, gd)
+    means = groupreduce((x, i) -> x, Base.add_sum, agg.condf, /, false, incol, gd)
     # !ismissing check is purely an optimization to avoid a copy later
     if eltype(means) >: Missing && agg.condf !== !ismissing
         T = Union{Missing, real(eltype(means))}
@@ -660,8 +667,9 @@ function (agg::Aggregate{typeof(var)})(incol::AbstractVector, gd::GroupedDataFra
         T = real(eltype(means))
     end
     res = zeros(T, length(gd))
-    groupreduce!(res, (x, i) -> @inbounds(abs2(x - means[i])), +,
-                 agg.condf, (x, l) -> x / (l-1), incol, gd)
+    groupreduce!(res, (x, i) -> @inbounds(abs2(x - means[i])), +, agg.condf,
+                 (x, l) -> l <= 1 ? oftype(x / (l-1), NaN) : x / (l-1),
+                 false, incol, gd)
 end
 
 function (agg::Aggregate{typeof(std)})(incol::AbstractVector, gd::GroupedDataFrame)
diff --git a/test/grouping.jl b/test/grouping.jl
index 4e7a597883..d28f4550a6 100644
--- a/test/grouping.jl
+++ b/test/grouping.jl
@@ -841,6 +841,19 @@ Base.isless(::TestType, ::TestType) = false
         expected = combine(gd, y = :x3 => x -> f(collect(skipmissing(x))))
         @test res ≅ expected
         @test typeof(res.y) == typeof(expected.y)
+
+        # Test reduction over group with only missing values
+        gd = groupby_checked(df, :a, skipmissing=skip, sort=sort)
+        indices && @test gd.idx !== nothing # Trigger computation of indices
+        gd[1][:, :x3] .= missing
+        if f in (maximum, minimum, first, last)
+            @test_throws ArgumentError combine(gd, y = :x3 => f∘skipmissing)
+        else
+            res = combine(gd, y = :x3 => f∘skipmissing)
+            expected = combine(gd, y = :x3 => x -> f(collect(skipmissing(x))))
+            @test res ≅ expected
+            @test typeof(res.y) == typeof(expected.y)
+        end
     end
     # Test complex numbers
     for f in (sum, prod, mean, var, std, first, last, length)