diff --git a/xarray/core/nputils.py b/xarray/core/nputils.py
index a9971e7125a..769af03fe6a 100644
--- a/xarray/core/nputils.py
+++ b/xarray/core/nputils.py
@@ -209,6 +209,7 @@ def f(values, axis=None, **kwargs):
 
         if (
             _USE_BOTTLENECK
+            and isinstance(values, np.ndarray)
             and bn_func is not None
             and not isinstance(axis, tuple)
             and values.dtype.kind in "uifc"
diff --git a/xarray/core/variable.py b/xarray/core/variable.py
index 4c095f3a062..c10ea7b4996 100644
--- a/xarray/core/variable.py
+++ b/xarray/core/variable.py
@@ -1697,18 +1697,24 @@ def rank(self, dim, pct=False):
         """
         import bottleneck as bn
 
-        if isinstance(self.data, dask_array_type):
+        data = self.data
+
+        if isinstance(data, dask_array_type):
             raise TypeError(
                 "rank does not work for arrays stored as dask "
                 "arrays. Load the data via .compute() or .load() "
                 "prior to calling this method."
             )
+        elif not isinstance(data, np.ndarray):
+            raise TypeError(
+                "rank is not implemented for {} objects.".format(type(data))
+            )
 
         axis = self.get_axis_num(dim)
         func = bn.nanrankdata if self.dtype.kind == "f" else bn.rankdata
-        ranked = func(self.data, axis=axis)
+        ranked = func(data, axis=axis)
         if pct:
-            count = np.sum(~np.isnan(self.data), axis=axis, keepdims=True)
+            count = np.sum(~np.isnan(data), axis=axis, keepdims=True)
             ranked /= count
         return Variable(self.dims, ranked)
 
diff --git a/xarray/tests/test_sparse.py b/xarray/tests/test_sparse.py
index 74805b225fa..3c1b49f9e43 100644
--- a/xarray/tests/test_sparse.py
+++ b/xarray/tests/test_sparse.py
@@ -173,11 +173,13 @@ def test_variable_property(prop):
             False,
             marks=xfail(reason="'COO' object has no attribute 'item'"),
         ),
-        param(do("max"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
         param(
-            do("median"), False, marks=xfail(reason="Coercion to dense via bottleneck")
+            do("median"),
+            False,
+            marks=xfail(reason="Missing implementation for np.nanmedian"),
         ),
-        param(do("min"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
+        param(do("max"), False),
+        param(do("min"), False),
         param(
             do("no_conflicts", other=make_xrvar({"x": 10, "y": 5})),
             True,
@@ -201,7 +203,7 @@ def test_variable_property(prop):
         param(
             do("rank", dim="x"),
             False,
-            marks=xfail(reason="Coercion to dense via bottleneck"),
+            marks=xfail(reason="Only implemented for NumPy arrays (via bottleneck)"),
         ),
         param(
             do("reduce", func=np.sum, dim="x"),
@@ -216,13 +218,17 @@ def test_variable_property(prop):
         param(
             do("shift", x=2), True, marks=xfail(reason="mixed sparse-dense operation")
         ),
-        param(do("std"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
+        param(
+            do("std"), False, marks=xfail(reason="Missing implementation for np.nanstd")
+        ),
         param(
             do("sum"),
             False,
             marks=xfail(reason="Missing implementation for np.result_type"),
         ),
-        param(do("var"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
+        param(
+            do("var"), False, marks=xfail(reason="Missing implementation for np.nanvar")
+        ),
         param(do("to_dict"), False, marks=xfail(reason="Coercion to dense")),
         param(
             do("where", cond=make_xrvar({"x": 10, "y": 5}) > 0.5),
@@ -478,16 +484,14 @@ def test_dataarray_property(prop):
             False,
             marks=xfail(reason="'COO' object has no attribute 'item'"),
         ),
-        param(do("max"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
+        param(do("max"), False),
+        param(do("min"), False),
         param(
-            do("median"), False, marks=xfail(reason="Coercion to dense via bottleneck")
-        ),
-        param(do("min"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
-        param(
-            do("notnull"),
+            do("median"),
             False,
-            marks=xfail(reason="'COO' object has no attribute 'notnull'"),
+            marks=xfail(reason="Missing implementation for np.nanmedian"),
         ),
+        param(do("notnull"), True),
         param(
             do("pipe", np.sum, axis=1),
             True,
@@ -506,7 +510,7 @@ def test_dataarray_property(prop):
         param(
             do("rank", "x"),
             False,
-            marks=xfail(reason="Coercion to dense via bottleneck"),
+            marks=xfail(reason="Only implemented for NumPy arrays (via bottleneck)"),
         ),
         param(
             do("reduce", np.sum, dim="x"),
@@ -534,13 +538,17 @@ def test_dataarray_property(prop):
             True,
             marks=xfail(reason="Indexing COO with more than one iterable index"),
         ),  # noqa
-        param(do("std"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
+        param(
+            do("std"), False, marks=xfail(reason="Missing implementation for np.nanstd")
+        ),
         param(
             do("sum"),
             False,
             marks=xfail(reason="Missing implementation for np.result_type"),
         ),
-        param(do("var"), False, marks=xfail(reason="Coercion to dense via bottleneck")),
+        param(
+            do("var"), False, marks=xfail(reason="Missing implementation for np.nanvar")
+        ),
         param(
             do("where", make_xrarray({"x": 10, "y": 5}) > 0.5),
             False,