diff --git a/narwhals/_dask/expr.py b/narwhals/_dask/expr.py
index 9b4b5f6a0b..8bd3588c4c 100644
--- a/narwhals/_dask/expr.py
+++ b/narwhals/_dask/expr.py
@@ -443,26 +443,20 @@ def max(self) -> Self:
         )
 
     def std(self, ddof: int) -> Self:
-        expr = self._from_call(
+        return self._from_call(
             lambda _input, ddof: _input.std(ddof=ddof),
             "std",
             ddof=ddof,
             returns_scalar=True,
         )
-        if ddof != 1:
-            expr._depth += 1
-        return expr
 
     def var(self, ddof: int) -> Self:
-        expr = self._from_call(
+        return self._from_call(
             lambda _input, ddof: _input.var(ddof=ddof),
             "var",
             ddof=ddof,
             returns_scalar=True,
         )
-        if ddof != 1:
-            expr._depth += 1
-        return expr
 
     def skew(self: Self) -> Self:
         return self._from_call(
diff --git a/narwhals/_dask/group_by.py b/narwhals/_dask/group_by.py
index af269abd78..7bda88ee5d 100644
--- a/narwhals/_dask/group_by.py
+++ b/narwhals/_dask/group_by.py
@@ -36,14 +36,38 @@ def agg(s0: pd.core.groupby.generic.SeriesGroupBy) -> int:
     )
 
 
+def var(
+    ddof: int = 1,
+) -> Callable[
+    [pd.core.groupby.generic.SeriesGroupBy], pd.core.groupby.generic.SeriesGroupBy
+]:
+    from functools import partial
+
+    import dask_expr as dx
+
+    return partial(dx._groupby.GroupBy.var, ddof=ddof)
+
+
+def std(
+    ddof: int = 1,
+) -> Callable[
+    [pd.core.groupby.generic.SeriesGroupBy], pd.core.groupby.generic.SeriesGroupBy
+]:
+    from functools import partial
+
+    import dask_expr as dx
+
+    return partial(dx._groupby.GroupBy.std, ddof=ddof)
+
+
 POLARS_TO_DASK_AGGREGATIONS = {
     "sum": "sum",
     "mean": "mean",
     "median": "median",
     "max": "max",
     "min": "min",
-    "std": "std",
-    "var": "var",
+    "std": std,
+    "var": var,
     "len": "size",
     "n_unique": n_unique,
     "count": "count",
@@ -137,8 +161,12 @@ def agg_dask(
                 function_name = POLARS_TO_DASK_AGGREGATIONS.get(
                     expr._function_name, expr._function_name
                 )
-                for output_name in expr._output_names:
-                    simple_aggregations[output_name] = (keys[0], function_name)
+                simple_aggregations.update(
+                    {
+                        output_name: (keys[0], function_name)
+                        for output_name in expr._output_names
+                    }
+                )
                 continue
 
             # e.g. agg(nw.mean('a')) # noqa: ERA001
@@ -149,13 +177,26 @@ def agg_dask(
                 raise AssertionError(msg)
 
             function_name = remove_prefix(expr._function_name, "col->")
-            function_name = POLARS_TO_DASK_AGGREGATIONS.get(function_name, function_name)
+            kwargs = (
+                {"ddof": expr._kwargs.get("ddof", 1)}
+                if function_name in {"std", "var"}
+                else {}
+            )
 
+            agg_function = POLARS_TO_DASK_AGGREGATIONS.get(function_name, function_name)
             # deal with n_unique case in a "lazy" mode to not depend on dask globally
-            function_name = function_name() if callable(function_name) else function_name
-
-            for root_name, output_name in zip(expr._root_names, expr._output_names):
-                simple_aggregations[output_name] = (root_name, function_name)
+            agg_function = (
+                agg_function(**kwargs) if callable(agg_function) else agg_function
+            )
+
+            simple_aggregations.update(
+                {
+                    output_name: (root_name, agg_function)
+                    for root_name, output_name in zip(
+                        expr._root_names, expr._output_names
+                    )
+                }
+            )
         result_simple = grouped.agg(**simple_aggregations)
         return from_dataframe(result_simple.reset_index())
 
diff --git a/tests/group_by_test.py b/tests/group_by_test.py
index 3c57ce0276..22c3b6f195 100644
--- a/tests/group_by_test.py
+++ b/tests/group_by_test.py
@@ -137,12 +137,7 @@ def test_group_by_depth_1_std_var(
     constructor: Constructor,
     attr: str,
     ddof: int,
-    request: pytest.FixtureRequest,
 ) -> None:
-    if "dask" in str(constructor):
-        # Complex aggregation for dask
-        request.applymarker(pytest.mark.xfail)
-
     data = {"a": [1, 1, 1, 2, 2, 2], "b": [4, 5, 6, 0, 5, 5]}
     _pow = 0.5 if attr == "std" else 1
     expected = {