gen-define-the-standard-error-and-give-one-short-worked-example-07e0

Define the standard error and give one short worked example.

# Standard Error ## Definition The **standard error (SE)** is the standard deviation of a sampling distribution of a statistic. It measures how much a sample statistic (like a sample mean) typically varies from the true population parameter. The most common form is the **standard error of the mean (SEM)**: $$SE = \frac{s}{\sqrt{n}}$$ where: - *s* = sample standard deviation - *n* = sample size ## Worked Example **Problem:** A researcher measures the heights of 25 randomly selected adults and finds a sample standard deviation of 10 cm. What is the standard error of the mean? **Solution:** - *s* = 10 cm - *n* = 25 $$SE = \frac{10}{\sqrt{25}} = \frac{10}{5} = 2 \text{ cm}$$ **Interpretation:** If we repeatedly took samples of 25 adults, the sample means would typically vary by about 2 cm from the true population mean.