diff --git a/src/Statistics.jl b/src/Statistics.jl
index aad352b..da23c21 100644
--- a/src/Statistics.jl
+++ b/src/Statistics.jl
@@ -1017,7 +1017,7 @@ function _quantilesort!(v::AbstractVector, sorted::Bool, minp::Real, maxp::Real)
         sort!(v, 1, lv, Base.Sort.PartialQuickSort(lo:hi), Base.Sort.Forward)
     end
     if (sorted && (ismissing(v[end]) || (v[end] isa Number && isnan(v[end])))) ||
-        any(x -> ismissing(x) || (x isa Number && isnan(x)), v)
+        any(x -> ismissing(x) || (applicable(isnan, v[end]) && isnan(x)), v)
         throw(ArgumentError("quantiles are undefined in presence of NaNs or missing values"))
     end
     return v
@@ -1049,7 +1049,7 @@ end
 
     # When a ≉ b, b-a may overflow
     # When a ≈ b, (1-γ)*a + γ*b may not be increasing with γ due to rounding
-    if isfinite(a) && isfinite(b) &&
+    if applicable(isfinite, a) && isfinite(a) && isfinite(b) &&
         (!(a isa Number) || !(b isa Number) || a ≈ b)
         return a + γ*(b-a)
     else
diff --git a/test/runtests.jl b/test/runtests.jl
index 2d732d0..698fb78 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -2,6 +2,7 @@
 
 using Statistics, Test, Random, LinearAlgebra, SparseArrays, Dates
 using Test: guardseed
+using Dates
 
 Random.seed!(123)
 
@@ -695,6 +696,8 @@ 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}]