Question

Explain what it means when we say the value of a sample statistic varies from sample to sample.

Short answer

The value of a sample statistic varying from sample to sample means that if different samples are taken from the same population and the same statistic is computed for each, it is likely to get different results each time. This variability is inherent due to sampling and forms the basis of statistical inference.

Step-by-step solution

Definition of Sample Statistic

A sample statistic is a numerical value that describes a characteristic of a sample. Samples are subsets of a population, and a sample statistic gives information about some aspect of this sample. Examples include mean, median, mode and standard deviation.

Variability of Sample Statistic

When we say that the value of a sample statistic varies from sample to sample, it means that if we were to take multiple samples from the same population, and compute the same statistic for each, we would likely get different results each time. This is primarily due to the fact that each sample, unless it is a census including all members of the population, only contains a subset of the data from the population.

Implication of the Variability

The variability of a sample statistic from sample to sample is important because it introduces uncertainty. This concept forms the basis of statistical inference. The goal of statistical inference is to make conclusions about an entire population based on findings from a smaller sample. Understanding the variability in the sample statistics helps counter this uncertainty.