Here, Xi represents a random variable, that is, every observed value in the sample, and I is only its serial number, from 1 to n, so each Xi is a specific observed value, for example, X 1 represents the first observed value in the sample. Of course, Xi is also a random variable, because the value you get from each sampling may be different.

The expectation E(Xi) of the sample usually refers to the expectation of the random variable Xi, not the expectation of the sample. The expectation of random variables can usually be understood as the weighted average of possible values of random variables, and the weight is the probability of each value.

The literal meaning of σ Xi is to find the sum of all Xi, that is, the sum of all observed values, which is usually called sample sum.

Summing does not mean averaging each sample and then summing the average of each sample. If σ Xi represents the sum of all observations, then σ Xi/n is what you call the sample mean, that is, the average of all observations.