Determine the standard variation of the data below. (1, 2, 3, 4, 5)

Solution:

Given raw data, X : 1 2 3 4 5 = ΣX = 15

X²: 1 4 9 16 25 = ΣX² = 55

We have standard deviation = S.D

= sqrt{ΣX²/n - (ΣX /n)²}

= sqrt{55/5 - (15/5)²}

= sqrt(11 - 9) = sqrt(2)

Example: Determine the standard deviation of the data 6, 7, 8, 9 10

Given raw data x: 6 7 8 9 10 = ΣX =40

X²: 36 49 64 81 100

= ΣX²

= 330

We have standard deviation =S.D = sqrt{ΣX²/n - (ΣX /n)²} = sqrt{ 330/5 - (40/5)²}

= sqrt(66 - 64) = sqrt(2)

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Determine the standard variation of the data below. (1, 2, 3, 4, 5)

Summary:

Standard variation of the data (1, 2, 3, 4, 5) is sqrt (2)