Descriptive Measures for Populations|Parameter|Statistic|standardized variable|z-score

3.4 Descriptive Measures for Populations; Use of Samples

For a particular variable on a particular population：

1.There is only one population mean—namely, the mean of all possible observations of the variable for the entire population.

2.There are many sample means—one for each possible sample of the population

population variance：

Parameter and Statistic：

Thus, for example, μ and σ are parameters, whereas x¯ and s are statistics.

Standardized Variables：

A standardized variable（eg，x的标准型是z） always has mean 0 and standard deviation 1，即：

标准化之后可以依据统一标准进行比较，z-score 便是z值：即更清楚标准差如何分割数据

将数字转化为标准型的好处：Percentiles usually give a more exact method of measuring relative standing than do z-scores. However, if only the mean and standard deviation of a variable are known, z-scores provide a feasible alternative to percentiles for measuring relative standing