diff --git a/Project.toml b/Project.toml
index 12c96773..56ff8442 100644
--- a/Project.toml
+++ b/Project.toml
@@ -6,8 +6,9 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [extras]
+Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Random", "Test"]
+test = ["Dates", "Random", "Test"]
diff --git a/src/Statistics.jl b/src/Statistics.jl
index b3bf26b3..16e87fbb 100644
--- a/src/Statistics.jl
+++ b/src/Statistics.jl
@@ -957,7 +957,7 @@ function _quantilesort!(v::AbstractArray, sorted::Bool, minp::Real, maxp::Real)
         sort!(v, 1, lv, Base.Sort.PartialQuickSort(lo:hi), Base.Sort.Forward)
     end
     ismissing(v[end]) && throw(ArgumentError("quantiles are undefined in presence of missing values"))
-    isnan(v[end]) && throw(ArgumentError("quantiles are undefined in presence of NaNs"))
+    applicable(isnan, v[end]) && isnan(v[end]) && throw(ArgumentError("quantiles are undefined in presence of NaNs"))
     return v
 end
 
@@ -985,7 +985,7 @@ end
         b = v[j + 1]
     end
     
-    if isfinite(a) && isfinite(b)
+    if applicable(isfinite, a) && isfinite(a) && isfinite(b)
         return a + γ*(b-a)
     else
         return (1-γ)*a + γ*b
diff --git a/test/runtests.jl b/test/runtests.jl
index 3434bb76..660ee6c2 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -2,6 +2,7 @@
 
 using Statistics, Test, Random, LinearAlgebra, SparseArrays
 using Test: guardseed
+using Dates
 
 Random.seed!(123)
 
@@ -559,6 +560,8 @@ end
     @test quantile(skipmissing([1, missing, 2]), 0.5) === 1.5
     @test quantile([1], 0.5) === 1.0
 
+    @test quantile(Millisecond.(1:10), 0.5) == Millisecond(5)
+
     # make sure that type inference works correctly in normal cases
     for T in [Int, BigInt, Float64, Float16, BigFloat, Rational{Int}, Rational{BigInt}]
         for S in [Float64, Float16, BigFloat, Rational{Int}, Rational{BigInt}]