diff --git a/Orange/widgets/visualize/owboxplot.py b/Orange/widgets/visualize/owboxplot.py
index e65be8b73dd..0a28058c25c 100644
--- a/Orange/widgets/visualize/owboxplot.py
+++ b/Orange/widgets/visualize/owboxplot.py
@@ -44,6 +44,38 @@ def compute_scale(min_, max_):
     return first_val, step
 
 
+def _quantiles(a, freq, q, interpolation="midpoint"):
+    """
+    Somewhat like np.quantiles, but with explicit sample frequencies.
+
+    * Only 'higher', 'lower' and 'midpoint' interpolation.
+    * `a` MUST be sorted.
+    """
+    a = np.asarray(a)
+    freq = np.asarray(freq)
+    assert a.size > 0 and a.size == freq.size
+    cumdist = np.cumsum(freq)
+    cumdist /= cumdist[-1]
+
+    if interpolation == "midpoint":  # R quantile(..., type=2)
+        left = np.searchsorted(cumdist, q, side="left")
+        right = np.searchsorted(cumdist, q, side="right")
+        # no mid point for the right most position
+        np.clip(right, 0, a.size - 1, out=right)
+        # right and left will be different only on the `q` boundaries
+        # (excluding the right most sample)
+        return (a[left] + a[right]) / 2
+    elif interpolation == "higher":  # R quantile(... type=1)
+        right = np.searchsorted(cumdist, q, side="right")
+        np.clip(right, 0, a.size - 1, out=right)
+        return a[right]
+    elif interpolation == "lower":
+        left = np.searchsorted(cumdist, q, side="left")
+        return a[left]
+    else:  # pragma: no cover
+        raise ValueError("invalid interpolation: '{}'".format(interpolation))
+
+
 class BoxData:
     def __init__(self, dist, attr, group_val_index=None, group_var=None):
         self.dist = dist
@@ -55,24 +87,12 @@ def __init__(self, dist, attr, group_val_index=None, group_var=None):
         self.mean = float(np.sum(dist[0] * dist[1]) / n)
         self.var = float(np.sum(dist[1] * (dist[0] - self.mean) ** 2) / n)
         self.dev = math.sqrt(self.var)
-        s = 0
-        thresholds = [n / 4, n / 2, n / 4 * 3]
-        thresh_i = 0
-        q = []
-        for i, e in enumerate(dist[1]):
-            s += e
-            if s >= thresholds[thresh_i]:
-                if s == thresholds[thresh_i] and i + 1 < dist.shape[1]:
-                    q.append(float((dist[0, i] + dist[0, i + 1]) / 2))
-                else:
-                    q.append(float(dist[0, i]))
-                thresh_i += 1
-                if thresh_i == 3:
-                    self.q25, self.median, self.q75 = q
-                    break
-        else:
-            self.q25 = self.q75 = None
-            self.median = q[1] if len(q) == 2 else None
+        a, freq = np.asarray(dist)
+        q25, median, q75 = _quantiles(a, freq, [0.25, 0.5, 0.75])
+        self.median = median
+        # The code below omits the q25 or q75 in the plot when they are None
+        self.q25 = None if q25 == median else q25
+        self.q75 = None if q75 == median else q75
         self.conditions = [FilterContinuous(attr, FilterContinuous.Between,
                                             self.q25, self.q75)]
         if group_val_index is not None:
diff --git a/Orange/widgets/visualize/tests/test_owboxplot.py b/Orange/widgets/visualize/tests/test_owboxplot.py
index 51a2617b90a..1466a38965b 100644
--- a/Orange/widgets/visualize/tests/test_owboxplot.py
+++ b/Orange/widgets/visualize/tests/test_owboxplot.py
@@ -1,12 +1,15 @@
 # Test methods with long descriptive names can omit docstrings
 # pylint: disable=missing-docstring
+import unittest
 
 import numpy as np
 from AnyQt.QtCore import QItemSelectionModel
 from AnyQt.QtTest import QTest
 
 from Orange.data import Table, ContinuousVariable, StringVariable, Domain
-from Orange.widgets.visualize.owboxplot import OWBoxPlot, FilterGraphicsRectItem
+from Orange.widgets.visualize.owboxplot import (
+    OWBoxPlot, FilterGraphicsRectItem, _quantiles
+)
 from Orange.widgets.tests.base import WidgetTest, WidgetOutputsTestMixin
 
 
@@ -208,3 +211,40 @@ def __select_value(self, list, value):
             if m.data(idx) == value:
                 list.selectionModel().setCurrentIndex(
                     idx, QItemSelectionModel.ClearAndSelect)
+
+
+class TestUtils(unittest.TestCase):
+    def test(self):
+        np.testing.assert_array_equal(
+            _quantiles(range(1, 8 + 1), [1.] * 8, [0.0, 0.25, 0.5, 0.75, 1.0]),
+            [1., 2.5, 4.5, 6.5, 8.]
+        )
+        np.testing.assert_array_equal(
+            _quantiles(range(1, 8 + 1), [1.] * 8, [0.0, 0.25, 0.5, 0.75, 1.0]),
+            [1., 2.5, 4.5, 6.5, 8.]
+        )
+        np.testing.assert_array_equal(
+            _quantiles(range(1, 4 + 1), [1., 2., 1., 2],
+                       [0.0, 0.25, 0.5, 0.75, 1.0]),
+            [1.0, 2.0, 2.5, 4.0, 4.0]
+        )
+        np.testing.assert_array_equal(
+            _quantiles(range(1, 4 + 1), [2., 1., 1., 2.],
+                       [0.0, 0.25, 0.5, 0.75, 1.0]),
+            [1.0, 1.0, 2.5, 4.0, 4.0]
+        )
+        np.testing.assert_array_equal(
+            _quantiles(range(1, 4 + 1), [1., 1., 1., 1.],
+                       [0.0, 0.25, 0.5, 0.75, 1.0]),
+            [1.0, 1.5, 2.5, 3.5, 4.0]
+        )
+        np.testing.assert_array_equal(
+            _quantiles(range(1, 4 + 1), [1., 1., 1., 1.],
+                       [0.0, 0.25, 0.5, 0.75, 1.0], interpolation="higher"),
+            [1, 2, 3, 4, 4]
+        )
+        np.testing.assert_array_equal(
+            _quantiles(range(1, 4 + 1), [1., 1., 1., 1.],
+                       [0.0, 0.25, 0.5, 0.75, 1.0], interpolation="lower"),
+            [1, 1, 2, 3, 4]
+        )