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The variance of n numbers a_1, a_2, ... , a_n, which the arithmetic mean is am, equals σ^2 = (a_1 - am)^2 + (a_2 - am)^2 + ... + (a_n - am)^2. σ - its name is sigma. The standard deviation σ is a square root from the variance σ = √(σ)^2. Example. Grades: 2, 5, 1, 3. The arithmetic mean: am = (2 + 5 + 1 + 3) / 4 ≈ 2.8 The variance σ^2 = ( (2 - 2.8)^2 + (5 - 2.8)^2 + (1 - 2.8)^2 + (3-2.8)^2 ) / 4 = 1.5 The variance and the standard deviation is a measure of how spread out numbers (i.e. ages, grades, heights) are around the arithmetic mean. The small variance indicates that more numbers are close to the arithmetic mean e.g. 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, am = 3, σ ≈ 1.1. The high variance indicates that numbers are very spread out. More numbers are close to edges of sequence e.g. 1, 1, 1, 2, 3, 3, 4, 5, 5, 5. am = 3, σ ≈ 1.6