Which statistic describes the variability we expect in the arithmetic means of multiple samples from the same population?

• A. Standard Error
• B. Confidence Limits (Intervals)
• C. Range
• D. Variance

Answer: (A)

The variability of arithmetic means across repeated samples from the same population is described by the standard error. This statistic is the standard deviation of the sampling distribution of the mean, showing how far a typical sample mean is expected to be from the true population mean. It decreases as sample size increases, making the sample mean a more precise estimator. This is different from the standard deviation or variance, which describe spread among individual data points within a single sample, not the variation of means across samples. The range looks at extremes within one sample, not the dispersion of means across many samples, and confidence limits describe a range for the population mean based on the observed mean and its standard error, rather than directly quantifying how much sample means vary.