Variation in Data and Samples

Variation is present in any set of data. For example, 16-ounce cans of beverage may contain more or less than 16 ounces of liquid. In one study, eight 16-ounce cans were measured and produced the following amounts (in ounces): 15.8; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5. Measurements may vary because different people make the measurements or because the exact amount of 16 ounces was not put into the cans. Manufacturers regularly run tests to determine if the amount falls within the desired range.

Two or more samples from the same population, taken randomly and having close to the same characteristics of the population, will likely be different from each other. Suppose Doreen and Jung both decide to study the average amount of time students at their college sleep each night. Each takes a sample of 500 students. Doreen uses systematic sampling and Jung uses cluster sampling. Their samples will be different. Even if they used the same sampling method, in all likelihood their samples would be different. Neither would be wrong, however.

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) might 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.

The size of a sample (often called the number of observations) is important. Samples of only a few hundred observations, or even smaller, are sufficient for many purposes. In polling, samples that are from 1,200 to 1,500 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.

Be aware that many large samples are biased. For example, call-in surveys are invariably biased, because people choose to respond or not.

Sample size and bias

Consider the radio station example: A local radio station has a fan base of 20,000 listeners. The station wants to know if its audience would prefer more music or more talk shows. Asking all 20,000 listeners is an almost impossible task. The station uses convenience sampling and surveys the first 200 people they meet at one of the station's music concert events. 24 people said they'd prefer more talk shows, and 176 people said they'd prefer more music. Do you think that this sample is representative of the entire 20,000 listener population?

Now apply the idea of variation to a new scenario.