diff --git a/quantile_estimator/__init__.py b/quantile_estimator/__init__.py
index c4beb84..3c41560 100644
--- a/quantile_estimator/__init__.py
+++ b/quantile_estimator/__init__.py
@@ -48,10 +48,10 @@ def __init__(self, *invariants):
             self._invariants = _DEFAULT_INVARIANTS
         else:
             self._invariants = [_Quantile(q, e) for (q, e) in invariants]
+
         self._buffer = []
         self._head = None
         self._observations = 0
-        self._items = 0
 
     def observe(self, value):
         """Samples an observation's value.
@@ -90,7 +90,7 @@ def query(self, rank):
             return current._value
 
         mid_rank = math.floor(rank * self._observations)
-        max_rank = mid_rank + math.floor(self._invariant(mid_rank, self._observations) / 2)
+        max_rank = mid_rank + math.ceil(self._invariant(mid_rank, self._observations) / 2)
 
         rank = 0.0
         while current._successor:
@@ -115,7 +115,8 @@ def _replace_batch(self):
             return
 
         if not self._head:
-            self._head, self._buffer = self._record(self._buffer[0], 1, 0, None), self._buffer[1:]
+            self._head = self._record(self._buffer[0], 1, 0, None)
+            self._buffer = self._buffer[1:]
 
         rank = 0.0
         current = self._head
@@ -136,7 +137,6 @@ def _replace_batch(self):
     def _record(self, value, rank, delta, successor):
         """Catalogs a sample."""
         self._observations += 1
-        self._items += 1
 
         return _Sample(value, rank, delta, successor)
 
@@ -187,10 +187,10 @@ def __init__(self, quantile, inaccuracy):
 
     """Computes the delta for the observation."""
     def _delta(self, rank, n):
-        if rank <= math.floor((self._quantile * n)):
+        if rank <= math.floor(self._quantile * n):
             return self._coefficient_i * (n - rank)
-
-        return self._coefficient_ii * rank
+        else:
+            return self._coefficient_ii * rank
 
 
 _DEFAULT_INVARIANTS = [_Quantile(0.50, 0.01), _Quantile(0.99, 0.001)]
diff --git a/tests/test_estimator.py b/tests/test_estimator.py
index 71dd8c5..a6e36d7 100644
--- a/tests/test_estimator.py
+++ b/tests/test_estimator.py
@@ -1,3 +1,4 @@
+import math
 import random
 
 import pytest
@@ -7,19 +8,26 @@
 
 @pytest.mark.parametrize("num_observations", [1, 10, 100, 1000, 10000, 100000])
 def test_random_observations(num_observations):
-    estimator = Estimator()
-    for _ in range(num_observations):
-        estimator.observe(random.randint(1, 1000) / 100)
+    invariants = (0.5, 0.01), (0.9, 0.01), (0.99, 0.01)
+    estimator = Estimator(*invariants)
 
-    assert 0 <= estimator.query(0.5) <= estimator.query(0.9) <= estimator.query(0.99) <= 10
+    values = [random.uniform(0, 100) for _ in range(num_observations)]
+    for value in values:
+        estimator.observe(value)
+
+    values.sort()
+    for quantile, inaccuracy in invariants:
+        min_rank = math.floor(quantile * num_observations - inaccuracy * num_observations)
+        max_rank = min(math.ceil(quantile * num_observations + inaccuracy * num_observations), num_observations - 1)
+        assert 0 <= values[min_rank] <= estimator.query(quantile) <= values[max_rank] <= 100
 
 
 def test_border_invariants():
     estimator = Estimator((0.0, 0.0), (1.0, 0.0))
 
-    values = [random.randint(1, 1000) for _ in range(1000)]
-    for x in values:
-        estimator.observe(x)
+    values = [random.uniform(0, 100) for _ in range(500)]
+    for value in values:
+        estimator.observe(value)
 
-    assert estimator.query(0) == min(values)
-    assert estimator.query(1) == max(values)
+    assert estimator.query(0.0) == min(values)
+    assert estimator.query(1.0) == max(values)