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# Sampling and Data: Variation in Samples

Summary: This module is a DRAFT.

Note: You are viewing an old version of this document. The latest version is available here.

## Note:

This module is a DRAFT.

It was mentioned previously that two or more samples from the same population and having the same characteristics as the population may be different from each other. Suppose Doreen and Jung both decide to study the average amount of time students sleep each night and use all students at their college as the population. Doreen uses systematic sampling and Jung uses cluster sampling. Doreen's sample will be different from Jung's sample even though both samples have the characteristics of the population. Even if Doreen and Jung used the same sampling method, in all likelihood their samples would be different. Neither would be wrong, however.

Think about what contributes to making Doreen's and Jung's samples different.

If Doreen and Jung took larger samples (i.e. the number of data values is increased), their sample results (the average amount of time a student sleeps) would be closer to the actual population average. But still, their samples would be, in all likelihood, different from each other. This variability in samples cannot be stressed enough.

### Size of a Sample

The size of a sample (often called the number of observations) is important. The examples you have seen in this book so far have been small. Small samples can "work" but the person taking the sample must be very careful. Samples that are from 1200 to 1500 observations are considered large enough and good enough if the survey is random and is well done. You will learn why when you study confidence intervals.

### Optional Collaborative Classroom Exercise

#### Exercise 1

Divide into groups of two, three, or four. Your instructor will give each group one 6-sided die. Try this experiment twice. Roll one fair die (6-sided) 20 times. Record the number of ones, twos, threes, fours, fives, and sixes you get below ("frequency" is the number of times a particular face of the die occurs):

Table 1: First Experiment (20 rolls)
Face on DieFrequency
1
2
3
4
5
6
Table 2: Second Experiment (20 rolls)
Face on DieFrequency
1
2
3
4
5
6

Did the two experiments have the same results? Probably not. If you did the experiment a third time, do you expect the results to be identical to the first or second experiment? (Answer yes or no.) Why or why not?

Which experiment had the correct results? They both did. The job of the statistician is to see through the variability and draw appropriate conclusions.

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