Traditional Culture Encyclopedia - Traditional virtues - What is the formula of sample mean?
What is the formula of sample mean?
U ~ N(0, 1),
Therefore, D(U)= 1.
This X~N(μ, σ 2) indicates that the population X obeys the normal distribution with the population mean μ and population standard deviation σ. Because the sample mean is asked, it is (x1+...+xn)/n.
Because it is a simple random sample, the samples are independent of each other, so there are:
E (x1+x2+...+xn) = e (x1)+e (x2)+...+e (xn) = μ+μ+...+μ = nμ.
d(x 1+X2+……+Xn)= 1
d(x 1)+d(x2)+……+d(xn)=nσ^2
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.
It is an indicator reflecting the trend of data concentration. 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.
Reference source; Baidu Encyclopedia-Sample Mean
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