diff --git a/ext/ReactantStatisticsExt.jl b/ext/ReactantStatisticsExt.jl
index 40db81a8ed..1c9e3f9f33 100644
--- a/ext/ReactantStatisticsExt.jl
+++ b/ext/ReactantStatisticsExt.jl
@@ -4,18 +4,22 @@ using Reactant: AnyTracedRArray
 using Reactant.TracedUtils: materialize_traced_array
 using Statistics: Statistics
 
-function Statistics.mean(A::AnyTracedRArray{T,N}; dims=:) where {T,N}
-    A = materialize_traced_array(A)
+function Statistics._mean(f::F, A::AnyTracedRArray{T,N}, dims) where {F,T,N}
     denom = dims isa Colon ? length(A) : prod(Base.Fix1(size, A), dims)
-    return mapreduce(identity, +, A; dims) / denom
+    return mapreduce(f, +, A; dims) / denom
 end
 
-function Statistics.var(
-    A::AnyTracedRArray{T,N}; dims=:, mean=nothing, corrected=true
+function Statistics._var(
+    A::AnyTracedRArray{T,N}, corrected::Bool, mean, ::Colon
 ) where {T,N}
-    A = materialize_traced_array(A)
+    mean === nothing && (mean = Statistics.mean(A))
+    denom = length(A) - corrected
+    return mapreduce(abs2, +, A .- mean; dims=:) / denom
+end
+
+function Statistics._var(A::AnyTracedRArray{T,N}, corrected::Bool, mean, dims) where {T,N}
     mean === nothing && (mean = Statistics.mean(A; dims))
-    denom = (dims isa Colon ? length(A) : prod(Base.Fix1(size, A), dims)) - corrected
+    denom = prod(Base.Fix1(size, A), dims) - corrected
     return mapreduce(abs2, +, A .- mean; dims) / denom
 end
 
diff --git a/test/basic.jl b/test/basic.jl
index 1783a44c36..d05d3d968a 100644
--- a/test/basic.jl
+++ b/test/basic.jl
@@ -176,16 +176,22 @@ end
     mean_fn2(x) = mean(x; dims=1)
     mean_fn3(x) = mean(x; dims=(1, 2))
     mean_fn4(x) = mean(x; dims=(1, 3))
+    mean_f1abs2(x) = mean(abs2, x)
+    mean_f2abs2(x) = mean(abs2, x; dims=1)
 
     mean_fn1_compiled = @compile mean_fn1(x_ca)
     mean_fn2_compiled = @compile mean_fn2(x_ca)
     mean_fn3_compiled = @compile mean_fn3(x_ca)
     mean_fn4_compiled = @compile mean_fn4(x_ca)
+    mean_f1abs2_compiled = @compile mean_f1abs2(x_ca)
+    mean_f2abs2_compiled = @compile mean_f2abs2(x_ca)
 
     @test mean_fn1(x) ≈ mean_fn1_compiled(x_ca)
     @test mean_fn2(x) ≈ mean_fn2_compiled(x_ca)
     @test mean_fn3(x) ≈ mean_fn3_compiled(x_ca)
     @test mean_fn4(x) ≈ mean_fn4_compiled(x_ca)
+    @test mean_f1abs2(x) ≈ mean_f1abs2_compiled(x_ca)
+    @test mean_f2abs2(x) ≈ mean_f2abs2_compiled(x_ca)
 
     # XXX: @jit doesn't work with `;`
     # @test @jit(var(x_ca)) ≈ var(x)