Statistics and Probability / Why Random Samples?

Understanding

Students contrast the distribution of “judgment” sample means with a distribution of sample means selected by random sampling.

What to look for

It is worthwhile to discuss how biases might impact a judgment sample. For example, it is much easier to overlook the small segments (length 1 for example) than it is to overlook the larger segments.

Sample Assessment

Which of the following is a true statement about a random sample of students from your class? A random sample is:

a. choosing whoever comes to mind as you think about students in the class

b. choosing two boys and two girls, one of each who gets good grades and one of each who gets lower grades

c. a sample where every student in the class has the same chance to be selected

d. a sample selected by the teacher based on student grades

Answer: C

The Big Idea

Random sampling is a better method of collecting data than using an “expert” opinion.

What are the students doing?

Students discuss three estimation methods—educated guess, judgment sample, or random sample—and whether one is more likely to give a sample that is most representative of the population.

What is the teacher doing?

Be sure that students recognize that, in statistics, a method produces a representative sample if, over the long run (i.e., many, many samples), on average, the estimate is correct.