diff --git a/HISTORY.md b/HISTORY.md
index 2a04f04cb..776ea941a 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -25,6 +25,10 @@ Breaking changes:
 - `null` is no longer implicitly casted to a number `0`, so input like
   `math.add(2, null)` is no longer supported. See #830, #353.
 
+Non breaking changes:
+
+- Improved error messages for statistical functions.
+
 
 ## 2018-01-17, version 3.20.1
 
diff --git a/lib/function/statistics/mad.js b/lib/function/statistics/mad.js
index a2e9bb29e..bf5426cf5 100644
--- a/lib/function/statistics/mad.js
+++ b/lib/function/statistics/mad.js
@@ -7,6 +7,7 @@ function factory (type, config, load, typed) {
   var map      = load(require('../matrix/map'));
   var median   = load(require('../statistics/median'));
   var subtract = load(require('../arithmetic/subtract'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
 
   /**
    * Compute the median absolute deviation of a matrix or a list with values.
@@ -50,13 +51,23 @@ function factory (type, config, load, typed) {
     array = flatten(array.valueOf());
 
     if (array.length === 0) {
-      throw new Error('Cannot calculate median absolute deviation of an empty array');
+      throw new Error('Cannot calculate median absolute deviation (mad) of an empty array');
     }
 
-    var med = median(array);
-    return median(map(array, function (value) {
-      return abs(subtract(value, med));
-    }));
+    try {
+      var med = median(array);
+      return median(map(array, function (value) {
+        return abs(subtract(value, med));
+      }));
+    }
+    catch (err) {
+      if (err instanceof TypeError && err.message.indexOf('median') !== -1) {
+        throw new TypeError(err.message.replace('median', 'mad'));
+      }
+      else {
+        throw improveErrorMessage(err, 'mad');
+      }
+    }
   }
 }
 
diff --git a/lib/function/statistics/max.js b/lib/function/statistics/max.js
index 57a51a8f7..420345d73 100644
--- a/lib/function/statistics/max.js
+++ b/lib/function/statistics/max.js
@@ -6,6 +6,7 @@ var containsCollections = require('../../utils/collection/containsCollections');
 
 function factory (type, config, load, typed) {
   var larger = load(require('../relational/larger'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
 
   /**
    * Compute the maximum value of a matrix or a  list with values.
@@ -68,8 +69,13 @@ function factory (type, config, load, typed) {
    * @returns {*} Returns x when x is largest, or y when y is largest
    * @private
    */
-  function _largest(x, y){
-    return larger(x, y) ? x : y;
+  function _largest(x, y) {
+    try {
+      return larger(x, y) ? x : y;
+    }
+    catch (err) {
+      throw improveErrorMessage(err, 'max', y);
+    }
   }
 
   /**
@@ -82,8 +88,13 @@ function factory (type, config, load, typed) {
     var max = undefined;
 
     deepForEach(array, function (value) {
-      if (max === undefined || larger(value, max)) {
-        max = value;
+      try {
+        if (max === undefined || larger(value, max)) {
+          max = value;
+        }
+      }
+      catch (err) {
+        throw improveErrorMessage(err, 'max', value);
       }
     });
 
@@ -93,6 +104,7 @@ function factory (type, config, load, typed) {
 
     return max;
   }
+
 }
 
 exports.name = 'max';
diff --git a/lib/function/statistics/mean.js b/lib/function/statistics/mean.js
index 7bf8e30f0..e36258ef3 100644
--- a/lib/function/statistics/mean.js
+++ b/lib/function/statistics/mean.js
@@ -8,6 +8,7 @@ var containsCollections = require('../../utils/collection/containsCollections');
 function factory (type, config, load, typed) {
   var add = load(require('../arithmetic/add'));
   var divide = load(require('../arithmetic/divide'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
 
   /**
    * Compute the mean value of matrix or a list with values.
@@ -41,7 +42,7 @@ function factory (type, config, load, typed) {
     'Array | Matrix': _mean,
 
       // mean([a, b, c, d, ...], dim)
-    'Array | Matrix, number | BigNumber': _nmean,
+    'Array | Matrix, number | BigNumber': _nmeanDim,
 
     // mean(a, b, c, d, ...)
     '...': function (args) {
@@ -65,10 +66,15 @@ function factory (type, config, load, typed) {
    * @return {number} mean
    * @private
    */
-  function _nmean(array, dim){
-    var sum = reduce(array, dim, add);
-    var s = Array.isArray(array) ? size(array) : array.size();
-    return divide(sum, s[dim]);
+  function _nmeanDim(array, dim) {
+    try {
+      var sum = reduce(array, dim, add);
+      var s = Array.isArray(array) ? size(array) : array.size();
+      return divide(sum, s[dim]);
+    }
+    catch (err) {
+      throw improveErrorMessage(err, 'mean');
+    }
   }
 
   /**
@@ -82,8 +88,13 @@ function factory (type, config, load, typed) {
     var num = 0;
 
     deepForEach(array, function (value) {
-      sum = add(sum, value);
-      num++;
+      try {
+        sum = add(sum, value);
+        num++;
+      }
+      catch (err) {
+        throw improveErrorMessage(err, 'mean', value);
+      }
     });
 
     if (num === 0) {
diff --git a/lib/function/statistics/median.js b/lib/function/statistics/median.js
index 29732630b..66c8b49a4 100644
--- a/lib/function/statistics/median.js
+++ b/lib/function/statistics/median.js
@@ -8,6 +8,7 @@ function factory (type, config, load, typed) {
   var divide = load(require('../arithmetic/divideScalar'));
   var compare = load(require('../relational/compare'));
   var partitionSelect = load(require('../matrix/partitionSelect'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
 
   /**
    * Compute the median of a matrix or a list with values. The values are
@@ -64,33 +65,38 @@ function factory (type, config, load, typed) {
    * @private
    */
   function _median(array) {
-    array = flatten(array.valueOf());
+    try {
+      array = flatten(array.valueOf());
 
-    var num = array.length;
-    if (num == 0) {
-      throw new Error('Cannot calculate median of an empty array');
-    }
-
-    if (num % 2 == 0) {
-      // even: return the average of the two middle values
-      var mid = num / 2 - 1;
-      var right = partitionSelect(array, mid + 1);
-
-      // array now partitioned at mid + 1, take max of left part
-      var left = array[mid];
-      for (var i = 0; i < mid; ++i) {
-        if (compare(array[i], left) > 0) {
-          left = array[i];
-        }
+      var num = array.length;
+      if (num == 0) {
+        throw new Error('Cannot calculate median of an empty array');
       }
 
-      return middle2(left, right);
-    }
-    else {
-      // odd: return the middle value
-      var m = partitionSelect(array, (num - 1) / 2);
+      if (num % 2 == 0) {
+        // even: return the average of the two middle values
+        var mid = num / 2 - 1;
+        var right = partitionSelect(array, mid + 1);
 
-      return middle(m);
+        // array now partitioned at mid + 1, take max of left part
+        var left = array[mid];
+        for (var i = 0; i < mid; ++i) {
+          if (compare(array[i], left) > 0) {
+            left = array[i];
+          }
+        }
+
+        return middle2(left, right);
+      }
+      else {
+        // odd: return the middle value
+        var m = partitionSelect(array, (num - 1) / 2);
+
+        return middle(m);
+      }
+    }
+    catch (err) {
+      throw improveErrorMessage(err, 'median');
     }
   }
 
diff --git a/lib/function/statistics/min.js b/lib/function/statistics/min.js
index 4671a17c0..d1fabb395 100644
--- a/lib/function/statistics/min.js
+++ b/lib/function/statistics/min.js
@@ -6,6 +6,7 @@ var containsCollections = require('../../utils/collection/containsCollections');
 
 function factory (type, config, load, typed) {
   var smaller = load(require('../relational/smaller'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
   
   /**
    * Compute the maximum value of a matrix or a  list of values.
@@ -69,7 +70,12 @@ function factory (type, config, load, typed) {
    * @private
    */
   function _smallest(x, y) {
-    return smaller(x, y) ? x : y;
+    try {
+      return smaller(x, y) ? x : y;
+    }
+    catch (err) {
+      throw improveErrorMessage(err, 'min', y);
+    }
   }
 
   /**
@@ -82,8 +88,13 @@ function factory (type, config, load, typed) {
     var min = undefined;
 
     deepForEach(array, function (value) {
-      if (min === undefined || smaller(value, min)) {
-        min = value;
+      try {
+        if (min === undefined || smaller(value, min)) {
+          min = value;
+        }
+      }
+      catch (err) {
+        throw improveErrorMessage(err, 'min', value);
       }
     });
 
diff --git a/lib/function/statistics/prod.js b/lib/function/statistics/prod.js
index 9f59dca7f..5b5d80ad2 100644
--- a/lib/function/statistics/prod.js
+++ b/lib/function/statistics/prod.js
@@ -4,6 +4,7 @@ var deepForEach = require('../../utils/collection/deepForEach');
 
 function factory (type, config, load, typed) {
   var multiply = load(require('../arithmetic/multiplyScalar'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
 
   /**
    * Compute the product of a matrix or a list with values.
@@ -61,7 +62,12 @@ function factory (type, config, load, typed) {
     var prod = undefined;
 
     deepForEach(array, function (value) {
-      prod = (prod === undefined) ? value : multiply(prod, value);
+      try {
+        prod = (prod === undefined) ? value : multiply(prod, value);
+      }
+      catch (err) {
+        throw improveErrorMessage(err, 'prod', value);
+      }
     });
 
     if (prod === undefined) {
diff --git a/lib/function/statistics/std.js b/lib/function/statistics/std.js
index 5f0b879ba..f74e5ede6 100644
--- a/lib/function/statistics/std.js
+++ b/lib/function/statistics/std.js
@@ -66,7 +66,17 @@ function factory (type, config, load, typed) {
       throw new SyntaxError('Function std requires one or more parameters (0 provided)');
     }
 
-    return sqrt(variance.apply(null, arguments));
+    try {
+      return sqrt(variance.apply(null, arguments));
+    }
+    catch (err) {
+      if (err instanceof TypeError && err.message.indexOf(' var') !== -1) {
+        throw new TypeError(err.message.replace(' var', ' std'));
+      }
+      else {
+        throw err;
+      }
+    }
   }
 }
 
diff --git a/lib/function/statistics/sum.js b/lib/function/statistics/sum.js
index c03fd47f6..c62a98d26 100644
--- a/lib/function/statistics/sum.js
+++ b/lib/function/statistics/sum.js
@@ -4,6 +4,7 @@ var deepForEach = require('../../utils/collection/deepForEach');
 
 function factory (type, config, load, typed) {
   var add = load(require('../arithmetic/addScalar'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
 
   /**
    * Compute the sum of a matrix or a list with values.
@@ -60,7 +61,12 @@ function factory (type, config, load, typed) {
     var sum = undefined;
 
     deepForEach(array, function (value) {
-      sum = (sum === undefined) ? value : add(sum, value);
+      try {
+        sum = (sum === undefined) ? value : add(sum, value);
+      }
+      catch (err) {
+        throw improveErrorMessage(err, 'sum', value);
+      }
     });
 
     if (sum === undefined) {
diff --git a/lib/function/statistics/utils/improveErrorMessage.js b/lib/function/statistics/utils/improveErrorMessage.js
new file mode 100644
index 000000000..68b961ba0
--- /dev/null
+++ b/lib/function/statistics/utils/improveErrorMessage.js
@@ -0,0 +1,40 @@
+
+
+function factory (type, config, load, typed) {
+  var getType = load(require('../../utils/typeof'));
+
+  /**
+   * Improve error messages for statistics functions. Errors are typically
+   * thrown in an internally used function like larger, causing the error
+   * not to mention the function (like max) which is actually used by the user.
+   *
+   * @param {Error} err
+   * @param {String} fnName
+   * @param {*} [value]
+   * @return {Error}
+   */
+  return function improveErrorMessage(err, fnName, value) {
+    // TODO: add information with the index (also needs transform in expression parser)
+    var details;
+
+    if (String(err).indexOf('Unexpected type') !== -1) {
+      details = arguments.length > 2
+          ? ' (type: ' + getType(value) + ', value: ' + JSON.stringify(value) + ')'
+          : ' (type: ' + err.data.actual + ')';
+
+      return new TypeError('Cannot calculate ' + fnName + ', unexpected type of argument' + details);
+    }
+
+    if (String(err).indexOf('complex numbers') !== -1) {
+      details = arguments.length > 2
+          ? ' (type: ' + getType(value) + ', value: ' + JSON.stringify(value) + ')'
+          : '';
+
+      return new TypeError('Cannot calculate ' + fnName + ', no ordering relation is defined for complex numbers' + details);
+    }
+
+    return err;
+  }
+}
+
+exports.factory = factory;
diff --git a/lib/function/statistics/var.js b/lib/function/statistics/var.js
index fb94a50db..6c58ba40d 100644
--- a/lib/function/statistics/var.js
+++ b/lib/function/statistics/var.js
@@ -9,6 +9,7 @@ function factory (type, config, load, typed) {
   var subtract = load(require('../arithmetic/subtract'));
   var multiply = load(require('../arithmetic/multiplyScalar'));
   var divide = load(require('../arithmetic/divideScalar'));
+  var improveErrorMessage = load(require('./utils/improveErrorMessage'));
 
   /**
    * Compute the variance of a matrix or a  list with values.
@@ -92,8 +93,13 @@ function factory (type, config, load, typed) {
 
     // calculate the mean and number of elements
     deepForEach(array, function (value) {
-      sum = add(sum, value);
-      num++;
+      try {
+        sum = add(sum, value);
+        num++;
+      }
+      catch (err) {
+        throw improveErrorMessage(err, 'var', value);
+      }
     });
     if (num === 0) throw new Error('Cannot calculate var of an empty array');
 
diff --git a/test/function/statistics/mad.test.js b/test/function/statistics/mad.test.js
index 2f37599ea..8a719a05f 100644
--- a/test/function/statistics/mad.test.js
+++ b/test/function/statistics/mad.test.js
@@ -3,6 +3,7 @@ var approx = require('../../../tools/approx');
 var math = require('../../../index');
 var BigNumber = math.type.BigNumber;
 var DenseMatrix = math.type.DenseMatrix;
+var Complex = math.type.Complex;
 var mad = math.mad;
 
 describe('mad', function() {
@@ -52,6 +53,15 @@ describe('mad', function() {
     assert.throws(function() {mad([])});
   });
 
+  it('should throw an error if called with invalid type of arguments', function() {
+    assert.throws(function () {mad(2, new Complex(2,5))}, /TypeError: Cannot calculate mad, no ordering relation is defined for complex numbers/);
+    assert.throws(function () {mad(new Complex(2,3), new Complex(2,1))}, /TypeError: Cannot calculate mad, no ordering relation is defined for complex numbers/);
+
+    assert.throws(function() {mad([2,new Date(), 4])}, /TypeError: Cannot calculate mad, unexpected type of argument/);
+    assert.throws(function() {mad([2,null, 4])}, /TypeError: Cannot calculate mad, unexpected type of argument/);
+    assert.throws(function() {mad([[2, 5], [4, null], [1, 7]], 0)}, /TypeError: Cannot calculate mad, unexpected type of argument/);
+  });
+
   it('should LaTeX mad', function () {
     var expression = math.parse('mad(1,2,3)');
     assert.equal(expression.toTex(), '\\mathrm{mad}\\left(1,2,3\\right)');
diff --git a/test/function/statistics/max.test.js b/test/function/statistics/max.test.js
index b134f0dfb..e125f177b 100644
--- a/test/function/statistics/max.test.js
+++ b/test/function/statistics/max.test.js
@@ -68,16 +68,6 @@ describe('max', function() {
         [[2, 4, 6], [7, 9, 11]]);
   });
 
-  it('should throw an error when called with complex numbers', function() {
-    assert.throws(function () {max(new Complex(2,3), new Complex(2,1))}, TypeError);
-    assert.throws(function () {max(new Complex(2,3), new Complex(2,5))}, TypeError);
-
-    assert.throws(function () {max(new Complex(3,4), 4)}, TypeError);
-    assert.throws(function () {max(new Complex(3,4), 5)}, TypeError);
-    assert.throws(function () {max(5, new Complex(3,4))}, TypeError);
-    assert.throws(function () {max(new Complex(3,4), 6)}, TypeError);
-  });
-
   it('should throw an error when called multiple arrays or matrices', function() {
     assert.throws(function () {max([1,2], [3,4])}, /Scalar values expected/);
     assert.throws(function () {max(math.matrix([1,2]), math.matrix([3,4]))}, /Scalar values expected/);
@@ -93,6 +83,16 @@ describe('max', function() {
     assert.throws(function() {max([], 2, 3)});
   });
 
+  it('should throw an error if called with invalid type of arguments', function() {
+    assert.throws(function () {max(2, new Complex(2,5))}, /TypeError: Cannot calculate max, no ordering relation is defined for complex numbers/);
+    assert.throws(function () {max(new Complex(2,3), new Complex(2,1))}, /TypeError: Cannot calculate max, no ordering relation is defined for complex numbers/);
+
+    assert.throws(function() {max([[2,undefined, 4]])}, /TypeError: Cannot calculate max, unexpected type of argument/);
+    assert.throws(function() {max([[2,new Date(), 4]])}, /TypeError: Cannot calculate max, unexpected type of argument/);
+    assert.throws(function() {max([2,null, 4])}, /TypeError: Cannot calculate max, unexpected type of argument/);
+    assert.throws(function() {max([[2, 5], [4, null], [1, 7]], 0)}, /TypeError: Cannot calculate max, unexpected type of argument/);
+  });
+
   it('should return undefined if called with an empty array', function() {
     assert.throws(function() {max([])});
   });
diff --git a/test/function/statistics/mean.test.js b/test/function/statistics/mean.test.js
index 879fedff9..77c630869 100644
--- a/test/function/statistics/mean.test.js
+++ b/test/function/statistics/mean.test.js
@@ -92,6 +92,13 @@ describe('mean', function() {
     assert.throws(function() {mean([])});
   });
 
+  it('should throw an error if called with invalid type of arguments', function() {
+    assert.throws(function() {mean([[2,undefined, 4]])}, /TypeError: Cannot calculate mean, unexpected type of argument/);
+    assert.throws(function() {mean([[2,new Date(), 4]])}, /TypeError: Cannot calculate mean, unexpected type of argument/);
+    assert.throws(function() {mean([2,null, 4])}, /TypeError: Cannot calculate mean, unexpected type of argument/);
+    assert.throws(function() {mean([[2, 5], [4, null], [1, 7]], 0)}, /TypeError: Cannot calculate mean, unexpected type of argument/);
+  });
+
   it('should LaTeX mean', function () {
     var expression = math.parse('mean(1,2,3,4)');
     assert.equal(expression.toTex(), '\\mathrm{mean}\\left(1,2,3,4\\right)');
diff --git a/test/function/statistics/median.test.js b/test/function/statistics/median.test.js
index cac362d82..0d095827d 100644
--- a/test/function/statistics/median.test.js
+++ b/test/function/statistics/median.test.js
@@ -82,9 +82,13 @@ describe('median', function() {
     assert.throws(function() {median([], 2)}, /not yet supported/);
   });
 
-  it('should throw an error if called with unsupported type of arguments', function() {
-    assert.throws(function () {median(new Date(), 2, 3)}, /TypeError: Unexpected type of argument/);
-    assert.throws(function () {median(new Complex(2,3), new Complex(-1,2))}, /TypeError: No ordering relation is defined for complex numbers/);
+  it('should throw an error if called with invalid type of arguments', function() {
+    assert.throws(function () {median(2, new Complex(2,5))}, /TypeError: Cannot calculate median, no ordering relation is defined for complex numbers/);
+    assert.throws(function () {median(new Complex(2,3), new Complex(2,1))}, /TypeError: Cannot calculate median, no ordering relation is defined for complex numbers/);
+
+    assert.throws(function() {median([[2,undefined, 4]])}, /TypeError: Cannot calculate median, unexpected type of argument/);
+    assert.throws(function() {median([[2,new Date(), 4]])}, /TypeError: Cannot calculate median, unexpected type of argument/);
+    assert.throws(function() {median([2,null, 4])}, /TypeError: Cannot calculate median, unexpected type of argument/);
   });
 
   it('should throw an error if called with an empty array', function() {
diff --git a/test/function/statistics/min.test.js b/test/function/statistics/min.test.js
index 1992a50eb..d058ac478 100644
--- a/test/function/statistics/min.test.js
+++ b/test/function/statistics/min.test.js
@@ -77,16 +77,6 @@ describe('min', function() {
       [[1, 2], [3,4], [5,6]]);
   });
 
-  it('should throw an error when called with complex numbers', function() {
-    assert.throws(function () {min(new Complex(2,3), new Complex(2,1))}, TypeError);
-    assert.throws(function () {min(new Complex(2,3), new Complex(2,5))}, TypeError);
-
-    assert.throws(function () {min(new Complex(3,4), 4)}, TypeError);
-    assert.throws(function () {min(new Complex(3,4), 5)}, TypeError);
-    assert.throws(function () {min(5, new Complex(3,4))}, TypeError);
-    assert.throws(function () {min(new Complex(3,4), 6)}, TypeError);
-  });
-
   it('should throw an error when called multiple arrays or matrices', function() {
     assert.throws(function () {min([1,2], [3,4])}, /Scalar values expected/);
     assert.throws(function () {min(math.matrix([1,2]), math.matrix([3,4]))}, /Scalar values expected/);
@@ -106,6 +96,16 @@ describe('min', function() {
     assert.throws(function() {min([])});
   });
 
+  it('should throw an error if called with invalid type of arguments', function() {
+    assert.throws(function () {min(2, new Complex(2,5))}, /TypeError: Cannot calculate min, no ordering relation is defined for complex numbers/);
+    assert.throws(function () {min(new Complex(2,3), new Complex(2,1))}, /TypeError: Cannot calculate min, no ordering relation is defined for complex numbers/);
+
+    assert.throws(function() {min([[2,undefined, 4]])}, /TypeError: Cannot calculate min, unexpected type of argument/);
+    assert.throws(function() {min([[2,new Date(), 4]])}, /TypeError: Cannot calculate min, unexpected type of argument/);
+    assert.throws(function() {min([2,null, 4])}, /TypeError: Cannot calculate min, unexpected type of argument/);
+    assert.throws(function() {min([[2, 5], [4, null], [1, 7]], 0)}, /TypeError: Cannot calculate min, unexpected type of argument/);
+  });
+
   it('should LaTeX min', function () {
     var expression = math.parse('min(1,2,3)');
     assert.equal(expression.toTex(), '\\min\\left(1,2,3\\right)');
diff --git a/test/function/statistics/prod.test.js b/test/function/statistics/prod.test.js
index 839014612..b9b7df7e6 100644
--- a/test/function/statistics/prod.test.js
+++ b/test/function/statistics/prod.test.js
@@ -63,6 +63,12 @@ describe('prod', function() {
     assert.throws(function() {prod([])});
   });
 
+  it('should throw an error if called with invalid type of arguments', function() {
+    assert.throws(function() {prod([[2,undefined, 4]])}, /TypeError: Cannot calculate prod, unexpected type of argument/);
+    assert.throws(function() {prod([[2,new Date(), 4]])}, /TypeError: Cannot calculate prod, unexpected type of argument/);
+    assert.throws(function() {prod([2,null, 4])}, /TypeError: Cannot calculate prod, unexpected type of argument/);
+  });
+
   it('should LaTeX prod', function () {
     var expression = math.parse('prod(1,2,3)');
     assert.equal(expression.toTex(), '\\mathrm{prod}\\left(1,2,3\\right)');
diff --git a/test/function/statistics/quantileSeq.test.js b/test/function/statistics/quantileSeq.test.js
index 146f3a85c..88274ce3b 100644
--- a/test/function/statistics/quantileSeq.test.js
+++ b/test/function/statistics/quantileSeq.test.js
@@ -156,7 +156,12 @@ describe('quantileSeq', function() {
     assert.throws(function () {quantileSeq('A', 'C', 'B')}, math.error.UnsupportedTypeError);
     assert.throws(function () {quantileSeq(true, false, true)}, math.error.UnsupportedTypeError);
     assert.throws(function () {quantileSeq(0, 'B')}, math.error.UnsupportedTypeError);
-    assert.throws(function () {quantileSeq(math.complex(2,3), math.complex(-1,2))}, TypeError);
+
+    assert.throws(function () {quantileSeq(math.complex(2,3), math.complex(-1,2))}, /TypeError: Unexpected type of argument in function quantileSeq/);
+    assert.throws(function () {quantileSeq(2, null)}, /TypeError: Unexpected type of argument in function quantileSeq/);
+
+    // TODO: improve error messages of quantileSeq
+    assert.throws(function () {quantileSeq([2, null], 2)}, /TypeError: Unexpected type of argument in function compare/);
   });
 
   it('should throw error for bad probabilities and splits', function() {
diff --git a/test/function/statistics/std.test.js b/test/function/statistics/std.test.js
index 35fa2ba91..d82876753 100644
--- a/test/function/statistics/std.test.js
+++ b/test/function/statistics/std.test.js
@@ -71,8 +71,10 @@ describe('std', function() {
   });
 
   it('should throw an error if called with invalid type of arguments', function() {
-    assert.throws(function() {std(new Date(), 2)}, TypeError);
-    assert.throws(function() {std(new Unit('5cm'), new Unit('10cm'))}, TypeError);
+    assert.throws(function() {std(new Date(), 2)}, /Cannot calculate std, unexpected type of argument/);
+    assert.throws(function() {std(new Unit(5, 'cm'), new Unit(10, 'cm'))}, /Cannot calculate std, unexpected type of argument/);
+    assert.throws(function() {std(2, 3, null)}, /Cannot calculate std, unexpected type of argument/);
+    assert.throws(function() {std([2, 3, null])}, /Cannot calculate std, unexpected type of argument/);
     assert.throws(function() {std([2,3,4], 5)}, /Unknown normalization "5"/);
   });
 
diff --git a/test/function/statistics/sum.test.js b/test/function/statistics/sum.test.js
index 00af8e728..450350e29 100644
--- a/test/function/statistics/sum.test.js
+++ b/test/function/statistics/sum.test.js
@@ -84,6 +84,12 @@ describe('sum', function() {
     assert.equal(math.equal(fracMath.sum([]), new fracMath.type.Fraction(0)), true);
   });
 
+  it('should throw an error if called with invalid type of arguments', function() {
+    assert.throws(function() {sum(new Date(), 2)}, /Cannot calculate sum, unexpected type of argument/);
+    assert.throws(function() {sum(2, 3, null)}, /Cannot calculate sum, unexpected type of argument/);
+    assert.throws(function() {sum([2, 3, null])}, /Cannot calculate sum, unexpected type of argument/);
+  });
+
   it('should LaTeX sum', function () {
     var expression = math.parse('sum(1,2,3)');
     assert.equal(expression.toTex(), '\\mathrm{sum}\\left(1,2,3\\right)');
diff --git a/test/function/statistics/var.test.js b/test/function/statistics/var.test.js
index df5f83a02..9ae2ffacc 100644
--- a/test/function/statistics/var.test.js
+++ b/test/function/statistics/var.test.js
@@ -69,8 +69,10 @@ describe('variance', function() {
   });
 
   it('should throw an error if called with invalid type of arguments', function() {
-    assert.throws(function() {variance(new Date(), 2)}, /TypeError/);
-    assert.throws(function() {variance(new Unit('5cm'), new Unit('10cm'))}, /TypeError/);
+    assert.throws(function() {variance(new Date(), 2)}, /Cannot calculate var, unexpected type of argument/);
+    assert.throws(function() {variance(new Unit(5, 'cm'), new Unit(10, 'cm'))}, /Cannot calculate var, unexpected type of argument/);
+    assert.throws(function() {variance(2, 3, null)}, /Cannot calculate var, unexpected type of argument/);
+    assert.throws(function() {variance([2, 3, null])}, /Cannot calculate var, unexpected type of argument/);
     assert.throws(function() {variance([2,3,4], 5)}, /Unknown normalization "5"/);
   });