Standard Deviation formula for Single Data ~ Matematika Akuntansi -->

Friday, February 23, 2018

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) ∑(xi - X̄)2)

Information :
S = Standard deviation
xi = ith-data (x1. x2, x3, ... , xn)

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

∑(xi - X̄)2 = (x1 - X̄)2  + (x2 - X̄)2 + (x3 - X̄)2 + (x4 - X̄)2 + (x5 - X̄)2 + (x6 - X̄)2 + (x7 - X̄)2
∑(xi - X̄)2 = (4 - 8)2  + (6 - 8)2 + (7 - 8)2 + (8 - 8)2 + (10 - 8)2 + (10 - 8)2 + (11 - 8)2
∑(xi - X̄)2 = (-4)2  + (-2)2 + (-1)2 + (0)2 + (2)2 + (2)2 + (3)2
∑(xi - X̄)2 = 16  + 4 + 1 + 0 + 4 + 4 + 9
∑(xi - X̄)2 = 38
S = √((1/n) ∑(xi - 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 :
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