CHAPTER 16
INTRODUCTION TO SAMPLING ERROR OF MEANS
The message of Chapter 14 seemed to be that unsatisfactory sampling plans can
result in samples that are unrepresentative of the larger population. Recall that it was
stated that the major purpose of using a sample was to provide a practical means of
estimating one or more parameters of the population to which you want to generalize your
results. For example, perhaps it is the mean (F) height of 4th grade youngsters that you
want to estimate and to do that, you measure the heights of a sample of 4th graders in your
state. The statistic X bar (sample mean) will be used as your best estimate of the
corresponding population parameter. But, it is highly unlikely that the mean in any one
particular sample will be identical to the true population mean. Thus, regardless of the
sampling method used, good or bad, there is likely to be some error in the sample statistic
in representing the parameter. Error due to sampling is a fact of life and one can never
eliminate that problem unless you have access to the total population on which to do your
analysis. But, that is an improbable situation. For example, the United States census
attempts to contact everybody (emphasis on body) to make counts of various things such
as the amount of homelessness, number of senior citizens, and the like. However, even
when the government tries to obtain parameter information, they are unable to do it. So,
even they are faced with error due to imperfect data collection. The concept of sampling
error will be explored in more detail in this section using the sample mean as the statistic.
The sample mean is a relatively easy way to introduce the concept of sampling error since
the error of sample means follows rather straightforward rules.
Sampling from Populations
The first thing you have to understand is that one could draw or take many different
samples from a given population. Assuming that you are using a good sampling plan such
as random sampling, different samples will include differen