SamplingDistributionQuith - Sampling Distribution(excerpted...

Sampling Distribution(excerpted from Learning to Live With Statistics: From Concepts to
Practice)
What is a sampling distribution? A sampling distribution is the hypothetical distribution of a
statistic taken from a large number of random samples (of a given size) drawn from a particular
population. An example illustrates what this means. Imagine a university student body of 30,000
people.
Say we take a random sample of 100 students, we ask each one and the times he or she
attended any kind of organized religious service last month. We get the average for the sample;
let's call it
x
1
. We replace those students into the population and repeat the whole procedure.
We get the mean number of services intended for our second random sample of 100 students
and label it
x
2.
We continue doing this ad infinitum, each time or place the last sample, taking
another hundred students at random, and recording the mean. We have a very large number of
sample averages:
x
1
x
2
,
x
3
,
x
4
,
x
5
; imagine now that we construct a graph or frequency
polygon for all our sample means. In fact, we are treating example meet as a single observation.