diff --git a/Orange/widgets/data/owpreprocess.py b/Orange/widgets/data/owpreprocess.py
index b80143d2072..981918e784b 100644
--- a/Orange/widgets/data/owpreprocess.py
+++ b/Orange/widgets/data/owpreprocess.py
@@ -1,27 +1,22 @@
 import sys
-import bisect
-import contextlib
-import warnings
 from collections import OrderedDict
 import pkg_resources
 
 import numpy
 
 from AnyQt.QtWidgets import (
-    QWidget, QButtonGroup, QGroupBox, QRadioButton, QSlider, QFocusFrame,
-    QDoubleSpinBox, QComboBox, QSpinBox, QListView, QDockWidget, QLabel,
-    QScrollArea, QVBoxLayout, QHBoxLayout, QFormLayout, QSpacerItem,
-    QSizePolicy, QStyle, QStylePainter, QAction, QLabel,
-    QApplication, QCheckBox
+    QWidget, QButtonGroup, QGroupBox, QRadioButton, QSlider,
+    QDoubleSpinBox, QComboBox, QSpinBox, QListView, QLabel,
+    QScrollArea, QVBoxLayout, QHBoxLayout, QFormLayout,
+    QSizePolicy, QApplication, QCheckBox
 )
 
 from AnyQt.QtGui import (
-    QCursor, QIcon, QPainter, QPixmap, QStandardItemModel, QStandardItem,
-    QDrag, QKeySequence
+    QIcon, QStandardItemModel, QStandardItem
 )
 
 from AnyQt.QtCore import (
-    Qt, QObject, QEvent, QSize, QModelIndex, QMimeData, QTimer
+    Qt, QEvent, QSize, QMimeData, QTimer
 )
 
 from AnyQt.QtCore import pyqtSignal as Signal, pyqtSlot as Slot
@@ -34,7 +29,6 @@
 from Orange.widgets import widget, gui, settings
 from Orange.widgets.utils.overlay import OverlayWidget
 from Orange.widgets.utils.sql import check_sql_input
-from Orange.util import Reprable
 
 from Orange.widgets.data.utils.preprocess import (
     BaseEditor, blocked, StandardItemModel, DescriptionRole,
@@ -271,9 +265,9 @@ class ImputeEditor(BaseEditor):
 
     Imputers = {
         NoImputation: (None, {}),
-#         Constant: (None, {"value": 0})
+        #         Constant: (None, {"value": 0})
         Average: (preprocess.impute.Average(), {}),
-#         Model: (preprocess.impute.Model, {}),
+        #         Model: (preprocess.impute.Model, {}),
         Random: (preprocess.impute.Random(), {}),
         DropRows: (None, {})
     }
@@ -1175,7 +1169,7 @@ def apply(self):
             self.error()
             try:
                 data = preprocessor(self.data)
-            except ValueError as e:
+            except (ValueError, ZeroDivisionError) as e:
                 self.error(str(e))
                 return
         else:
@@ -1258,4 +1252,3 @@ def test_main(argv=sys.argv):
 
 if __name__ == "__main__":
     sys.exit(test_main())
-
diff --git a/Orange/widgets/data/tests/test_owpreprocess.py b/Orange/widgets/data/tests/test_owpreprocess.py
index 8a49125167e..a96acbbaaca 100644
--- a/Orange/widgets/data/tests/test_owpreprocess.py
+++ b/Orange/widgets/data/tests/test_owpreprocess.py
@@ -9,7 +9,7 @@
 from Orange.preprocess import discretize, impute, fss, score
 from Orange.widgets.data import owpreprocess
 from Orange.widgets.data.owpreprocess import OWPreprocess
-from Orange.widgets.tests.base import WidgetTest
+from Orange.widgets.tests.base import WidgetTest, datasets
 
 
 class TestOWPreprocess(WidgetTest):
@@ -44,6 +44,20 @@ def test_normalize(self):
         np.testing.assert_allclose(output.X.mean(0), 0, atol=1e-7)
         np.testing.assert_allclose(output.X.std(0), 1, atol=1e-7)
 
+    def test_data_column_nans(self):
+        """
+        ZeroDivisonError - Weights sum to zero, can't be normalized
+        In case when all rows in a column are NaN then it throws that error.
+        GH-2064
+        """
+        table = datasets.data_one_column_nans()
+        saved = {"preprocessors": [("orange.preprocess.scale",
+                                    {"center": Scale.CenteringType.Mean,
+                                     "scale": Scale.ScalingType.Std})]}
+        model = self.widget.load(saved)
+        self.widget.set_model(model)
+        self.send_signal("Data", table)
+
 
 # Test for editors
 class TestDiscretizeEditor(WidgetTest):
diff --git a/Orange/widgets/tests/base.py b/Orange/widgets/tests/base.py
index 420f419a6f7..998a0d55bd7 100644
--- a/Orange/widgets/tests/base.py
+++ b/Orange/widgets/tests/base.py
@@ -13,7 +13,7 @@
 from Orange.classification.base_classification import (
     LearnerClassification, ModelClassification
 )
-from Orange.data import Table
+from Orange.data import Table, Domain, DiscreteVariable, ContinuousVariable
 from Orange.modelling import Fitter
 from Orange.preprocess import RemoveNaNColumns, Randomize
 from Orange.preprocess.preprocess import PreprocessorList
@@ -685,3 +685,26 @@ def missing_data_3(cls):
         data : Orange.data.Table
         """
         return Table(cls.path("missing_data_3.tab"))
+
+    @classmethod
+    def data_one_column_nans(cls):
+        """
+        Data set with two continuous features and one discrete. One continuous
+        columns has missing values (NaN).
+
+        Returns
+        -------
+        data : Orange.data.Table
+        """
+        table = Table(
+            Domain(
+                [ContinuousVariable("a"),
+                 ContinuousVariable("b"),
+                 DiscreteVariable("c", values=["y", "n"])]
+            ),
+            list(zip(
+                [42.48, 16.84, 15.23, 23.8],
+                ["", "", "", ""],
+                "ynyn"
+            )))
+        return table