The standard deviation is calculated using the following formula (36):

$\sigma =\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^N{\left(x_i-\mu \right)}^2}}$

where, $x_i$ is the mean; the average of the numbers, µ is the actual numbers to be calculated the standard deviation of, and

$\frac{1}{N}{\displaystyle \sum _{i=1}^N{\left(x_i-\mu \right)}^2}$

is the variance.

The standard deviation for standard enthalpy of formation for 1-fluroethanol is calculated to be ± 0.1. The calculation of standard deviation for this molecule is as follows:

N = 2, µ₁ = −101.60, µ₂ = −101.86

Step 1, X_i = (−101.60 − 101.86)/2 = −101.73

Step 2, (X_i − µ₁) = (−101.73 + 101.60)² = 0.0169

(X_i − µ₂) = (−101.73 + 101.86)² = 0.0169

Step 3, 1/2 (0.0169 + 0.0169) = 0.0169

Step 4, square root of 0.0169 = 0.13 = ±0.1