diff --git a/Project.toml b/Project.toml
index 4badf8e..b4d1889 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,15 +3,18 @@ uuid = "8197267c-284f-5f27-9208-e0e47529a953"
 version = "0.7.8"
 
 [deps]
-Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [weakdeps]
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [extensions]
+IntervalSetsRandomExt = "Random"
 IntervalSetsStatisticsExt = "Statistics"
+IntervalSetsStatsBaseExt = "StatsBase"
 
 [compat]
 Aqua = "0.7"
@@ -20,11 +23,13 @@ julia = "1.6"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [targets]
-test = ["Aqua", "Test", "Random", "OffsetArrays", "Statistics", "Unitful"]
+test = ["Aqua", "Dates", "Test", "Random", "OffsetArrays", "StatsBase", "Statistics", "Unitful"]
diff --git a/ext/IntervalSetsRandomExt.jl b/ext/IntervalSetsRandomExt.jl
new file mode 100644
index 0000000..16c3d2f
--- /dev/null
+++ b/ext/IntervalSetsRandomExt.jl
@@ -0,0 +1,17 @@
+module IntervalSetsRandomExt
+
+using IntervalSets
+using IntervalSets: TypedEndpointsInterval
+using Random
+
+# random sampling from interval
+Random.gentype(::Type{Interval{L,R,T}}) where {L,R,T} = float(T)
+function Random.rand(rng::AbstractRNG, i::Random.SamplerTrivial{<:TypedEndpointsInterval{:closed, :closed, T}}) where T<:Real
+    _i = i[]
+    isempty(_i) && throw(ArgumentError("The interval should be non-empty."))
+    a,b = endpoints(_i)
+    t = rand(rng, float(T)) # technically this samples from [0, 1), but we still allow it with TypedEndpointsInterval{:closed, :closed} for convenience
+    return clamp(t*a+(1-t)*b, _i)
+end
+
+end
diff --git a/ext/IntervalSetsStatsBaseExt.jl b/ext/IntervalSetsStatsBaseExt.jl
new file mode 100644
index 0000000..dda2400
--- /dev/null
+++ b/ext/IntervalSetsStatsBaseExt.jl
@@ -0,0 +1,8 @@
+module IntervalSetsStatsBaseExt
+
+using IntervalSets
+using StatsBase
+
+StatsBase.geomean(d::AbstractInterval) = sqrt(leftendpoint(d) * rightendpoint(d))
+
+end
diff --git a/src/IntervalSets.jl b/src/IntervalSets.jl
index 05ef38c..2e59285 100644
--- a/src/IntervalSets.jl
+++ b/src/IntervalSets.jl
@@ -4,10 +4,6 @@ using Base: @pure
 import Base: eltype, convert, show, in, length, isempty, isequal, isapprox, issubset, ==, hash,
              union, intersect, minimum, maximum, extrema, range, clamp, mod, float, ⊇, ⊊, ⊋
 
-using Random
-
-using Dates
-
 export AbstractInterval, Interval, OpenInterval, ClosedInterval,
             ⊇, .., ±, ordered, width, leftendpoint, rightendpoint, endpoints,
             isopenset, isclosedset, isleftclosed, isrightclosed,
@@ -283,6 +279,9 @@ include("findall.jl")
 
 if !isdefined(Base, :get_extension)
     include("../ext/IntervalSetsStatisticsExt.jl")
+    include("../ext/IntervalSetsRandomExt.jl")
+    # We don't support the extension with StatsBase.jl before Julia v1.9.
+    # include("../ext/IntervalSetsStatsBaseExt.jl")
 end
 
 end # module
diff --git a/src/interval.jl b/src/interval.jl
index 569d417..0496068 100644
--- a/src/interval.jl
+++ b/src/interval.jl
@@ -158,16 +158,6 @@ function _union(A::TypedEndpointsInterval{L1,R1}, B::TypedEndpointsInterval{L2,R
     Interval{L,R}(left, right)
 end
 
-# random sampling from interval
-Random.gentype(::Type{Interval{L,R,T}}) where {L,R,T} = float(T)
-function Random.rand(rng::AbstractRNG, i::Random.SamplerTrivial{<:TypedEndpointsInterval{:closed, :closed, T}}) where T<:Real
-    _i = i[]
-    isempty(_i) && throw(ArgumentError("The interval should be non-empty."))
-    a,b = endpoints(_i)
-    t = rand(rng, float(T)) # technically this samples from [0, 1), but we still allow it with TypedEndpointsInterval{:closed, :closed} for convenience
-    return clamp(t*a+(1-t)*b, _i)
-end
-
 ClosedInterval{T}(i::AbstractUnitRange{I}) where {T,I<:Integer} = ClosedInterval{T}(minimum(i), maximum(i))
 ClosedInterval(i::AbstractUnitRange{I}) where {I<:Integer} = ClosedInterval{I}(minimum(i), maximum(i))
 
diff --git a/test/runtests.jl b/test/runtests.jl
index f2db5c5..2f62f9a 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,7 @@
 using IntervalSets
 using Test
 using Dates
+using StatsBase: geomean
 using Statistics
 import Statistics: mean
 using Random
@@ -136,6 +137,7 @@ struct IncompleteInterval <: AbstractInterval{Int} end
         @test width(ClosedInterval(4.0,8.0)) ≡ 4.0
 
         @test mean(0..1) == 0.5
+        VERSION ≥ v"1.9" && @test geomean(1..100) == 10
 
         @test promote(1..2, 1.0..2.0) === (1.0..2.0, 1.0..2.0)
     end