**Sample Means**. The

**sample mean**from a group of observations is an estimate of the population

**mean**. Given a

**sample**of size n, consider n independent random variables X

_{1}, X

_{2}, , X

_{n}, each corresponding to one randomly selected observation. The

**sample mean**is defined to be .

Besides, is the population mean always the same as the sample mean?

The

**mean**of the distribution of**sample means**is called the Expected Value of M and is**always equal**to the**population mean**μ. 3. The shape of the distribution of**sample means**tends to be normal. You should realize that**sample means**are variable.Is sample mean larger than population mean?

The

**mean**of a**population**is denoted by μ; not x. When**sampling**with replacement,**sample**size can be**greater than population**size. And the**population mean**is a parameter; the**sample mean**is a statistic.What is the mean of the population?

The

**population mean**is an average of a group characteristic. The group could be a person, item, or thing, like “all the people living in the United States” or “all dog owners in Georgia”. A characteristic is just an item of interest. For example: In a school of 1,013 students, the average GPA is 3.1.