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

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