diff --git a/Project.toml b/Project.toml
index 0a64b638..3e5a53bb 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,12 +6,22 @@ version = "0.9.0-dev"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
+[weakdeps]
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[extensions]
+FixedPointNumbersStatisticsExt = "Statistics"
+
 [compat]
+# Update this version specifier when Statistics.jl v1.11.2 is released.
+# https://github.com/JuliaStats/Statistics.jl/issues/165
+Statistics = "< 1.11.2"
 julia = "1"
 
 [extras]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Documenter", "Test"]
+test = ["Documenter", "Statistics", "Test"]
diff --git a/ext/FixedPointNumbersStatisticsExt.jl b/ext/FixedPointNumbersStatisticsExt.jl
new file mode 100644
index 00000000..5cf777fa
--- /dev/null
+++ b/ext/FixedPointNumbersStatisticsExt.jl
@@ -0,0 +1,13 @@
+module FixedPointNumbersStatisticsExt
+
+using FixedPointNumbers
+import FixedPointNumbers: Treduce
+using Statistics
+
+import Statistics
+if isdefined(Statistics, :_mean_promote)
+    # https://github.com/JuliaMath/FixedPointNumbers.jl/pull/183
+    Statistics._mean_promote(x::Real, y::FixedPoint) = Treduce(y)
+end
+
+end
diff --git a/src/FixedPointNumbers.jl b/src/FixedPointNumbers.jl
index 927d84a5..bcfc56e7 100644
--- a/src/FixedPointNumbers.jl
+++ b/src/FixedPointNumbers.jl
@@ -9,7 +9,6 @@ import Base: ==, <, <=, -, +, *, /, ~, isapprox,
              signed, unsigned, copysign, flipsign, signbit,
              length
 
-import Statistics   # for _mean_promote
 import Random: Random, AbstractRNG, SamplerType, rand!
 
 import Base.Checked: checked_neg, checked_abs, checked_add, checked_sub, checked_mul,
@@ -557,10 +556,6 @@ Base.mul_prod(x::FixedPoint, y::FixedPoint) = Treduce(x) * Treduce(y)
 Base.reduce_empty(::typeof(Base.mul_prod), ::Type{F}) where {F<:FixedPoint} = one(Treduce)
 Base.reduce_first(::typeof(Base.mul_prod), x::FixedPoint)  = Treduce(x)
 
-if isdefined(Statistics, :_mean_promote)
-    Statistics._mean_promote(x::Real, y::FixedPoint) = Treduce(y)
-end
-
 """
     sd, ad = scaledual(s::Number, a)
 
@@ -624,6 +619,10 @@ function rand!(r::AbstractRNG, A::Array{X}, ::SamplerType{X}) where {T, X <: Fix
     A
 end
 
+if !isdefined(Base, :get_extension)
+    include("../ext/FixedPointNumbersStatisticsExt.jl")
+end
+
 if VERSION >= v"1.1" # work around https://github.com/JuliaLang/julia/issues/34121
     include("precompile.jl")
     _precompile_()