feat: add variance algorithm

Author: sarthakgupta1907-cell

Maths/Variance.js

@@ -0,0 +1,23 @@
+/**
+ * @function variance
+ * @description Calculates the variance of an array of numbers.
+ *   Variance measures how far each number in the set is from the mean.
+ *   This calculates population variance.
+ * @param {number[]} arr - An array of numbers
+ * @returns {number} - The variance
+ * @see https://en.wikipedia.org/wiki/Variance
+ * @example variance([2, 4, 4, 4, 5, 5, 7, 9]) => 4
+ * @example variance([1, 2, 3]) => 0.667
+ */
+const variance = (arr) => {
+  if (!Array.isArray(arr) || arr.length === 0) {
+    throw new TypeError('Input must be a non-empty array')
+  }
+  if (!arr.every((n) => typeof n === 'number' && !isNaN(n))) {
+    throw new TypeError('All elements must be numbers')
+  }
+  const mean = arr.reduce((sum, n) => sum + n, 0) / arr.length
+  return arr.reduce((sum, n) => sum + Math.pow(n - mean, 2), 0) / arr.length
+}
+
+export { variance }

Maths/test/Variance.test.js

@@ -0,0 +1,45 @@
+import { variance } from '../Variance.js'
+
+describe('variance', () => {
+  test('variance([2,4,4,4,5,5,7,9]) returns 4', () => {
+    expect(variance([2, 4, 4, 4, 5, 5, 7, 9])).toBeCloseTo(4)
+  })
+
+  test('variance([1,2,3]) returns ~0.667', () => {
+    expect(variance([1, 2, 3])).toBeCloseTo(0.667, 2)
+  })
+
+  test('variance of identical elements returns 0', () => {
+    expect(variance([5, 5, 5, 5])).toBe(0)
+  })
+
+  test('variance single element returns 0', () => {
+    expect(variance([42])).toBe(0)
+  })
+
+  test('variance works with negative numbers', () => {
+    expect(variance([-2, -1, 0, 1, 2])).toBeCloseTo(2)
+  })
+
+  test('variance([1,2,3,4,5]) returns 2', () => {
+    expect(variance([1, 2, 3, 4, 5])).toBeCloseTo(2)
+  })
+
+  test('variance does not mutate original array', () => {
+    const arr = [1, 2, 3]
+    variance(arr)
+    expect(arr).toEqual([1, 2, 3])
+  })
+
+  test('throws TypeError for empty array', () => {
+    expect(() => variance([])).toThrow(TypeError)
+  })
+
+  test('throws TypeError for non-array input', () => {
+    expect(() => variance('123')).toThrow(TypeError)
+  })
+
+  test('throws TypeError for array with non-numbers', () => {
+    expect(() => variance([1, 'two', 3])).toThrow(TypeError)
+  })
+})