diff --git a/src/function/statistics/variance.js b/src/function/statistics/variance.js
index 814a17442..13720f293 100644
--- a/src/function/statistics/variance.js
+++ b/src/function/statistics/variance.js
@@ -97,7 +97,7 @@ export const createVariance = /* #__PURE__ */ factory(name, dependencies, ({ typ
    * @private
    */
   function _var (array, normalization) {
-    let sum = 0
+    let sum
     let num = 0
 
     if (array.length === 0) {
@@ -107,7 +107,7 @@ export const createVariance = /* #__PURE__ */ factory(name, dependencies, ({ typ
     // calculate the mean and number of elements
     deepForEach(array, function (value) {
       try {
-        sum = add(sum, value)
+        sum = sum === undefined ? value : add(sum, value)
         num++
       } catch (err) {
         throw improveErrorMessage(err, 'variance', value)
@@ -118,10 +118,10 @@ export const createVariance = /* #__PURE__ */ factory(name, dependencies, ({ typ
     const mean = divide(sum, num)
 
     // calculate the variance
-    sum = 0
+    sum = undefined
     deepForEach(array, function (value) {
       const diff = subtract(value, mean)
-      sum = add(sum, multiply(diff, diff))
+      sum = sum === undefined ? multiply(diff, diff) : add(sum, multiply(diff, diff))
     })
 
     if (isNaN(sum)) {
diff --git a/test/unit-tests/expression/transform/std.transform.test.js b/test/unit-tests/expression/transform/std.transform.test.js
index d2e905fc8..656e6474d 100644
--- a/test/unit-tests/expression/transform/std.transform.test.js
+++ b/test/unit-tests/expression/transform/std.transform.test.js
@@ -1,4 +1,5 @@
 import assert from 'assert'
+import approx from '../../../../tools/approx'
 import math from '../../../../src/bundleAny'
 
 const Unit = math.Unit
@@ -34,7 +35,6 @@ describe('std', function () {
 
   it('should throw an error if called with invalid type of arguments', function () {
     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, 4, 6], [1, 3, 5]], 'biased', 0) }, /Cannot convert "biased" to a number/)
@@ -49,4 +49,25 @@ describe('std', function () {
     const expression = math.parse('std(1,2,3)')
     assert.strictEqual(expression.toTex(), '\\mathrm{std}\\left(1,2,3\\right)')
   })
+
+  it('should compute the standard deviation value of quantities with units', function () {
+    const a = new Unit(2, 'cm')
+    const b = new Unit(5, 'cm')
+    const c = new Unit(8, 'cm')
+    const res = math.unit(3, 'cm')
+    approx.equal(std([a, b, c]).toNumber('cm'), res.toNumber('cm'))
+  })
+
+  it('should compute the standard deviation value of quantities with compatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'cm')
+    const c = math.unit(math.sqrt(1250), 'cm')
+    approx.equal(std([a, b]).toNumber('cm'), c.toNumber('cm'))
+  })
+
+  it('should not compute the standard deviation value of quantities with incompatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'kg')
+    assert.throws(function () { std([a, b]) }, /Units do not match/)
+  })
 })
diff --git a/test/unit-tests/expression/transform/variance.transform.test.js b/test/unit-tests/expression/transform/variance.transform.test.js
index 73d41ee62..8a99c2b34 100644
--- a/test/unit-tests/expression/transform/variance.transform.test.js
+++ b/test/unit-tests/expression/transform/variance.transform.test.js
@@ -1,7 +1,7 @@
 import assert from 'assert'
+import approx from '../../../../tools/approx'
 import math from '../../../../src/bundleAny'
 
-const Unit = math.Unit
 const variance = math.expression.transform.variance
 
 describe('variance', function () {
@@ -34,7 +34,6 @@ describe('variance', function () {
 
   it('should throw an error if called with invalid type of arguments', function () {
     assert.throws(function () { variance(new Date(), 2) }, /Cannot calculate variance, unexpected type of argument/)
-    assert.throws(function () { variance(new Unit(5, 'cm'), new Unit(10, 'cm')) }, /Cannot calculate variance, unexpected type of argument/)
     assert.throws(function () { variance(2, 3, null) }, /Cannot calculate variance, unexpected type of argument/)
     assert.throws(function () { variance([2, 3, null]) }, /Cannot calculate variance, unexpected type of argument/)
     assert.throws(function () { variance([[2, 4, 6], [1, 3, 5]], 'biased', 0) }, /Cannot convert "biased" to a number/)
@@ -49,4 +48,24 @@ describe('variance', function () {
     const expression = math.parse('variance(1,2,3)')
     assert.strictEqual(expression.toTex(), '\\mathrm{Var}\\left(1,2,3\\right)')
   })
+
+  it('should compute the variance of quantities with units', function () {
+    const a = math.unit(10, 'cm')
+    const b = math.unit(20, 'cm')
+    const c = math.unit(50, 'cm^2')
+    approx.equal(variance([a, b]).toNumber('cm^2'), c.toNumber('cm^2'))
+  })
+
+  it('should compute the variance of quantities with compatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'cm')
+    const c = math.unit(1250, 'cm^2')
+    approx.equal(variance([a, b]).toNumber('cm^2'), c.toNumber('cm^2'))
+  })
+
+  it('should not compute the variance of quantities with incompatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'kg')
+    assert.throws(function () { variance([a, b]) }, /Units do not match/)
+  })
 })
diff --git a/test/unit-tests/function/statistics/std.test.js b/test/unit-tests/function/statistics/std.test.js
index 06d75e33b..2ab8ba085 100644
--- a/test/unit-tests/function/statistics/std.test.js
+++ b/test/unit-tests/function/statistics/std.test.js
@@ -106,7 +106,6 @@ describe('std', function () {
 
   it('should throw an error if called with invalid type of arguments', function () {
     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, 4, 6], [1, 3, 5]], 'biased', 0) }, /Cannot convert "biased" to a number/)
@@ -121,4 +120,25 @@ describe('std', function () {
     const expression = math.parse('std(1,2,3)')
     assert.strictEqual(expression.toTex(), '\\mathrm{std}\\left(1,2,3\\right)')
   })
+
+  it('should compute the standard deviation value of quantities with units', function () {
+    const a = new Unit(2, 'cm')
+    const b = new Unit(5, 'cm')
+    const c = new Unit(8, 'cm')
+    const res = math.unit(3, 'cm')
+    approx.equal(std([a, b, c]).toNumber('cm'), res.toNumber('cm'))
+  })
+
+  it('should compute the standard deviation value of quantities with compatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'cm')
+    const c = math.unit(math.sqrt(1250), 'cm')
+    approx.equal(std([a, b]).toNumber('cm'), c.toNumber('cm'))
+  })
+
+  it('should not compute the standard deviation value of quantities with incompatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'kg')
+    assert.throws(function () { std([a, b]) }, /Units do not match/)
+  })
 })
diff --git a/test/unit-tests/function/statistics/variance.test.js b/test/unit-tests/function/statistics/variance.test.js
index 166304d4d..d5d8be319 100644
--- a/test/unit-tests/function/statistics/variance.test.js
+++ b/test/unit-tests/function/statistics/variance.test.js
@@ -1,9 +1,9 @@
 import assert from 'assert'
+import approx from '../../../../tools/approx'
 import math from '../../../../src/bundleAny'
 const BigNumber = math.BigNumber
 const Complex = math.Complex
 const DenseMatrix = math.DenseMatrix
-const Unit = math.Unit
 const variance = math.variance
 
 describe('variance', function () {
@@ -109,7 +109,6 @@ describe('variance', function () {
 
   it('should throw an error if called with invalid type of arguments', function () {
     assert.throws(function () { variance(new Date(), 2) }, /Cannot calculate variance, unexpected type of argument/)
-    assert.throws(function () { variance(new Unit(5, 'cm'), new Unit(10, 'cm')) }, /Cannot calculate variance, unexpected type of argument/)
     assert.throws(function () { variance(2, 3, null) }, /Cannot calculate variance, unexpected type of argument/)
     assert.throws(function () { variance([2, 3, null]) }, /Cannot calculate variance, unexpected type of argument/)
     assert.throws(function () { variance([[2, 4, 6], [1, 3, 5]], 'biased', 0) }, /Cannot convert "biased" to a number/)
@@ -128,4 +127,24 @@ describe('variance', function () {
     const expression = math.parse('variance(1,2,3)')
     assert.strictEqual(expression.toTex(), '\\mathrm{Var}\\left(1,2,3\\right)')
   })
+
+  it('should compute the variance of quantities with units', function () {
+    const a = math.unit(10, 'cm')
+    const b = math.unit(20, 'cm')
+    const c = math.unit(50, 'cm^2')
+    approx.equal(variance([a, b]).toNumber('cm^2'), c.toNumber('cm^2'))
+  })
+
+  it('should compute the variance of quantities with compatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'cm')
+    const c = math.unit(1250, 'cm^2')
+    approx.equal(variance([a, b]).toNumber('cm^2'), c.toNumber('cm^2'))
+  })
+
+  it('should not compute the variance of quantities with incompatible units', function () {
+    const a = math.unit(1, 'm')
+    const b = math.unit(50, 'kg')
+    assert.throws(function () { variance([a, b]) }, /Units do not match/)
+  })
 })