The key to solve the problem of average application is to determine the "total amount" and the total number of copies corresponding to the total amount. In statistical work, mean and standard deviation are the two most important measures to describe the trend and deviation of data sets.
Suppose there is a population, from which n values are extracted at a time, there will be a mean value U. If a * * * is extracted k times, there will be k mean values, such as u 1, u2, u3, ... uk, and the mean value of these k mean values is equal to the mean value of the population.
The sampling distribution of extended data sample mean is the distribution formed by all sample mean.
When the population obeys the normal distribution N(μ, σ2), the mean ` x of all samples with n capacity in the population also obeys the normal distribution, and the mathematical expectation of ` x is μ, and the variance is σ 2/n ... that is, ` x ~ n (μ, σ 2/n).
Central limit theorem: the sample with capacity n is extracted from any population with mean value m and variance s 2. When n is large enough, the sampling distribution of sample mean approximately obeys the normal distribution with μ mean and σ2/n variance.
The rule of thumb is that n≥30 is large enough to meet the requirements of the central limit theorem.
Baidu Encyclopedia-Sample Mean