The average verbal SAT score for the entire class of entering freshmen is 530. However, if you select a sample of 20 freshmen and compute their average verbal SAT score you probably will not get exactly 530. What statistical concept explains the natural difference that exists between a sample mean and the corresponding population mean?

The average verbal SAT score for the entire class of entering freshmen is 530. However, if you select a sample of 20 freshmen and compute their average verbal SAT score you probably will not get exactly 530. What statistical concept explains the natural difference that exists between a sample mean and the corresponding population mean?

• A. Standard error
• B. Sampling error
• C. Bias
• D. Variability

Answer: (B)

The key idea is sampling error: the difference between a sample statistic and the corresponding population parameter that arises simply because you’re looking at a subset rather than the whole group. When you take a sample of 20 freshmen, the average you compute is just one possible outcome from the sampling distribution of the mean. That distribution has variability, so this particular sample mean is likely to differ from the true class average of 530. In other words, the observed gap between the sample mean and 530 is the sampling error you get by chance from drawing a subset. To connect the related terms: the standard error measures how much sample means would vary across many such samples, giving a sense of the typical size of sampling error; bias would imply a systematic tilt that pushes results in one direction, which isn’t implied here; variability describes dispersion in the scores themselves, not the difference between a sample mean and the population mean.

The key idea is sampling error: the difference between a sample statistic and the corresponding population parameter that arises simply because you’re looking at a subset rather than the whole group. When you take a sample of 20 freshmen, the average you compute is just one possible outcome from the sampling distribution of the mean. That distribution has variability, so this particular sample mean is likely to differ from the true class average of 530. In other words, the observed gap between the sample mean and 530 is the sampling error you get by chance from drawing a subset.

To connect the related terms: the standard error measures how much sample means would vary across many such samples, giving a sense of the typical size of sampling error; bias would imply a systematic tilt that pushes results in one direction, which isn’t implied here; variability describes dispersion in the scores themselves, not the difference between a sample mean and the population mean.