The sample mean is a statistic and a random variable, and the sample mean has the corresponding observation value only after the sample observation value is obtained. In the absence of sample observation, we can only regard it as a random variable, and then it has numerical characteristics such as mathematical expectation and variance.

Mathematical expectation is an important numerical feature, which reflects the average value of random variables and is the sum of the probabilities of each possible result multiplied by its result in the experiment. The word "expectation" here comes from gambling, which probably refers to how much money you expect to win when you bet.

Extended data:

Mean is an important concept in statistics. In statistics, arithmetic mean is often used to represent the overall level of statistical objects, and it is a statistic that describes the position in the data set. It can be used not only to reflect the general situation and average level of a group of data, but also to compare the data of different groups and see the differences between groups. It is intuitive and concise to represent a set of data by average, so it is often used in daily life, such as average speed, average height, average yield, average score and so on.

Baidu Encyclopedia-Sample Mean