Question

Explain why the standard error of a sampling distribution will always be smaller than the standard deviation of a population. For you answer do not discuss the formula (since formulas are just the shorthand notation for concepts), explain this phenomenon conceptually.

Answer 1

The standard deviation (SD) measures the amount of variability, or dispersion, for a subject set of data from the mean.

The standard error of the mean (SEM) measures how far the sample mean of the data is likely to be from the true population mean.

The SEM is always smaller than the SD.

Standard error functions as a way to validate the accuracy of a sample or the accuracy of multiple samples by analyzing deviation within the means.

The SEM describes how precise the mean of the sample is versus the true mean of the population. As the size of the sample data grows larger, the SEM decreases versus the SD.

As the sample size increases, the true mean of the population is known with greater specificity.

So standard error of a sampling distribution will always be smaller than the standard deviation of a population.

In contrast, increasing the sample size also provides a more specific measure of the SD.

However, the SD may be more or less depending on the dispersion of the additional data added to the sample.

The standard error is considered part of descriptive statistics.

It represents the standard deviation of the mean within a dataset.

This serves as a measure of variation for random variables, providing a measurement for the spread.

The smaller the spread, the more accurate the dataset.