[tex]The \ standard \ deviation =
\sqrt{ \frac{1}{n} \sum ( x_{i} - \mu )^2 }
\\ where: \\
n \ is\ the \ number \ of \ elements \\
x_{i} \ element \ number \ i \\
\mu \ is \ the \ mean \ of \ the \ elements
[/tex]
The elements are :
2,3,5,8,2.03,2.20,2.6,4.5
n = 8
μ = ( 2 + 3 + 5 + 8 + 2.03 + 2.20 + 2.6 + 4.5
)/8 = 3.66625
sum = ( 2 - 3.66625)² + ( 3 - 3.66625)² + ( 5 - 3.66625)² + ( 8 - 3.66625)² +
( 2.03 - 3.66625)² + ( 2.20 - 3.66625)² + ( 2.6 - 3.66625)² + ( 4.5 - 3.66625)²
= 30.44
∴ The standard deviation = √ (30.44 / 8)
≈ 1.95 ( to the nearest hundredth )
