diff --git a/lib/matplotlib/artist.py b/lib/matplotlib/artist.py
@@ -1251,19 +1251,33 @@ def format_cursor_data(self, data):
             method yourself.
 
         The default implementation converts ints and floats and arrays of ints
-        and floats into a comma-separated string enclosed in square brackets.
+        and floats into a comma-separated string enclosed in square brackets,
+        unless the artist has an associated colorbar, in which case scalar
+        values are formatted using the colorbar's formatter.
 
         See Also
         --------
         get_cursor_data
         """
-        try:
-            data[0]
-        except (TypeError, IndexError):
-            data = [data]
-        data_str = ', '.join('{:0.3g}'.format(item) for item in data
-                             if isinstance(item, Number))
-        return "[" + data_str + "]"
+        if np.ndim(data) == 0 and getattr(self, "colorbar", None):
+            # This block logically belongs to ScalarMappable, but can't be
+            # implemented in it because most ScalarMappable subclasses inherit
+            # from Artist first and from ScalarMappable second, so
+            # Artist.format_cursor_data would always have precedence over
+            # ScalarMappable.format_cursor_data.
+            return (
+                "["
+                + cbook.strip_math(
+                    self.colorbar.formatter.format_data_short(data)).strip()
+                + "]")
+        else:
+            try:
+                data[0]
+            except (TypeError, IndexError):
+                data = [data]
+            data_str = ', '.join('{:0.3g}'.format(item) for item in data
+                                 if isinstance(item, Number))
+            return "[" + data_str + "]"
 
     @property
     def mouseover(self):

diff --git a/lib/matplotlib/collections.py b/lib/matplotlib/collections.py
@@ -1930,7 +1930,7 @@ def draw(self, renderer):
 
 
 class QuadMesh(Collection):
-    """
+    r"""
     Class for the efficient drawing of a quadrilateral mesh.
 
     A quadrilateral mesh is a grid of M by N adjacent qudrilaterals that are
@@ -1957,6 +1957,10 @@ class QuadMesh(Collection):
 
     Notes
     -----
+    Unlike other `.Collection`\s, the default *pickradius* of `.QuadMesh` is 0,
+    i.e. `~.Artist.contains` checks whether the test point is within any of the
+    mesh quadrilaterals.
+
     There exists a deprecated API version ``QuadMesh(M, N, coords)``, where
     the dimensions are given explicitly and ``coords`` is a (M*N, 2)
     array-like. This has been deprecated in Matplotlib 3.5. The following
@@ -1984,8 +1988,8 @@ class QuadMesh(Collection):
     For example, the first entry in *coordinates* is the coordinates of the
     vertex at mesh coordinates (0, 0), then the one at (0, 1), then at (0, 2)
     .. (0, meshWidth), (1, 0), (1, 1), and so on.
-
     """
+
     def __init__(self, *args, **kwargs):
         # signature deprecation since="3.5": Change to new signature after the
         # deprecation has expired. Also remove setting __init__.__signature__,
@@ -2017,6 +2021,7 @@ def __init__(self, *args, **kwargs):
                         "coordinates must be 2D; all parameters except "
                         "coordinates will be keyword-only.")
             coords = np.asarray(coords, np.float64).reshape((h + 1, w + 1, 2))
+        kwargs.setdefault("pickradius", 0)
         # end of signature deprecation code
 
         super().__init__(**kwargs)
@@ -2031,7 +2036,7 @@ def __init__(self, *args, **kwargs):
     # Only needed during signature deprecation
     __init__.__signature__ = inspect.signature(
         lambda self, coordinates, *,
-               antialiased=True, shading='flat', **kwargs: None)
+               antialiased=True, shading='flat', pickradius=0, **kwargs: None)
 
     def get_paths(self):
         if self._paths is None:
@@ -2162,3 +2167,11 @@ def draw(self, renderer):
         gc.restore()
         renderer.close_group(self.__class__.__name__)
         self.stale = False
+
+    def get_cursor_data(self, event):
+        contained, info = self.contains(event)
+        if len(info["ind"]) == 1:
+            ind, = info["ind"]
+            return self.get_array()[ind]
+        else:
+            return None
diff --git a/lib/matplotlib/image.py b/lib/matplotlib/image.py
@@ -995,16 +995,6 @@ def get_cursor_data(self, event):
         else:
             return arr[i, j]
 
-    def format_cursor_data(self, data):
-        if np.ndim(data) == 0 and self.colorbar:
-            return (
-                "["
-                + cbook.strip_math(
-                    self.colorbar.formatter.format_data_short(data)).strip()
-                + "]")
-        else:
-            return super().format_cursor_data(data)
-
 
 class NonUniformImage(AxesImage):
     mouseover = False  # This class still needs its own get_cursor_data impl.

diff --git a/lib/matplotlib/tests/test_collections.py b/lib/matplotlib/tests/test_collections.py
@@ -7,6 +7,7 @@
 
 import matplotlib as mpl
 import matplotlib.pyplot as plt
+from matplotlib.backend_bases import MouseEvent
 import matplotlib.collections as mcollections
 import matplotlib.colors as mcolors
 import matplotlib.transforms as mtransforms
@@ -972,3 +973,16 @@ def test_array_wrong_dimensions():
     pc = plt.pcolormesh(z)
     pc.set_array(z)  # 2D is OK for Quadmesh
     pc.update_scalarmappable()
+
+
+def test_quadmesh_cursor_data():
+    fig, ax = plt.subplots()
+    *_, qm = ax.hist2d(
+        np.arange(11)**2, 100 + np.arange(11)**2)  # width-10 bins
+    x, y = ax.transData.transform([1, 101])
+    event = MouseEvent('motion_notify_event', fig.canvas, x, y)
+    assert qm.get_cursor_data(event) == 4  # (0**2, 1**2, 2**2, 3**2)
+    for out_xydata in []:
+        x, y = ax.transData.transform([-1, 101])
+        event = MouseEvent('motion_notify_event', fig.canvas, x, y)
+        assert qm.get_cursor_data(event) is None