Why do most of the sample means differ somewhat from the population mean? What is this difference called?
Are you talking about the standard error of the mean?
http://www.google.com/search?client=safari&rls=en&q=standard+error+of+the+mean&ie=UTF-8&oe=UTF-8
This is one of the questions that is asked in the back of the fifth edition of elementary statistics book. I am not sure of the answer, the number of the problem is an even number. Meaning that I cannot see the the answer in the back of the book:( So I was wondering if anyone could help me understand it as well.
Most of the sample means differ somewhat from the population mean due to a statistical phenomenon known as sampling error.
Sampling error refers to the variation or discrepancy between the sample statistic (such as the mean of a sample) and the corresponding population parameter (such as the population mean). It occurs because we cannot collect data from an entire population, but instead, we use samples to make inferences about the population as a whole.
Sampling error arises from the fact that each sample will have its own unique composition or characteristics, which may differ from the overall population. The extent of the sampling error depends on factors such as the sample size and the variability within the population. Smaller sample sizes typically have larger sampling errors, while larger sample sizes tend to minimize the sampling error.
To calculate the sampling error for a sample mean, you would typically subtract the sample mean from the population mean. The difference would represent the extent of the sampling error.
It's important to note that while sampling error causes variability between sample means and the population mean, it does not necessarily imply that the sample means are incorrect or unreliable. Through statistical analysis, we can estimate the magnitude of sampling error and draw valid conclusions about the population based on the sample data.