STAT 1053 Lecture Notes - Lecture 12: Central Limit Theorem, Standard Deviation, Statistic
Document Summary
Vital fact about a sample statistic it is a random quantity that can vary from sample to sample. Thus one can think of its probability distribution, called its sampling distribution. As a random variable, one can define, for a sample statistic, its expected value and its variance and standard deviation. The expected value is the mean/average with respect to repeated sampling, and the standard deviation measures its variability from one sample to another. For the sample mean for a sample of size n from a population with mean. Example: suppose that a population of gpa scores has population mean. The sample mean gpa varies from sample to sample, but we can think of its average value and its variability. X = / ( n) = 0. 4/ (100) = 0. 4/10 = 0. 04, much smaller than , the variability among individual gpa values in the population.
