We assumed that each individual measurement \( x_{ij} \) is represented by stochastic variables which independent and identically distributed (iid). This defined the sample mean of of experiment \( i \) with \( n \) samples as

$$ \overline{x}_i=\frac{1}{n}\sum_{j} x_{ij}. $$

and the sample variance

$$ \sigma^2_i=\frac{1}{n}\sum_{j} \left(x_{ij}-\overline{x}_i\right)^2. $$