Standard Deviation Formula For Single Data

Standard Deviation formula for Single Data

Perhaps the most widely used deviation size is the standard deviation, because it has mathematical properties that are very important and useful for theoretical discussion and subsequent statistical analysis.

Standard Deviation formula for Single Data

S = √((1/n) ∑(x_i - X̄)²)

Information :

S = Standard deviation

x_i = ith-data (x₁. x₂, x₃, ... , x_n)

X̄ = Mean of data

n = Amount frequency of data

Example :

Please determine the standard deviation of 4, 6, 7, 8, 10, 10, 11 !

Answer :

n = 7

X̄ = (4 +6 + 7 + 8 + 10 + 10 + 11)/7

X̄ = 56/7

X̄ = 8

∑(x_i - X̄)² = (x₁ - X̄)²  + (x₂ - X̄)² + (x₃ - X̄)² + (x₄ - X̄)² + (x₅ - X̄)² + (x₆ - X̄)² + (x₇ - X̄)²

∑(x_i - X̄)² = (4 - 8)²  + (6 - 8)² + (7 - 8)² + (8 - 8)² + (10 - 8)² + (10 - 8)² + (11 - 8)²

∑(x_i - X̄)² = (-4)²  + (-2)² + (-1)² + (0)² + (2)² + (2)² + (3)²

∑(x_i - X̄)² = 16  + 4 + 1 + 0 + 4 + 4 + 9

∑(x_i - X̄)² = 38

S = √((1/n) ∑(x_i - X̄)²)

S = √((1/7) 38)

S = √(38/7)

S = √(38/7)

S = √5.43

S = 2.33

So the standard deviation of 4, 6, 7, 8, 10, 10, 11 is 2.33

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Reference :

• Book math group sales and accounting essay To'ali class 12

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