Key formulas
From the Sampling & CLT formula sheet
- Standard Error of xbar:
SE_xbar = sigma / sqrt(n)— Standard deviation of the sampling distribution of the sample mean.
Module 4 · Sampling & CLT · Topic 1
Population vs Sample
Population. A population is the entire group of individuals or items that you want to study. Population values are called parameters and are typically denoted by Greek letters (μ, σ, p).
Sample. A sample is a subset of the population actually observed. Sample values are called statistics and are denoted by Latin letters (x̄, s, p̂).
Why Sample?. Studying an entire population is usually too expensive, time-consuming, or impossible. A well-chosen sample lets us make reliable inferences about the population at a fraction of the cost.
Worked example
Example
Population: all 10,000 students at a university. Sample: 200 randomly selected students. If the sample mean GPA is 3.2, we use that to estimate the population mean GPA.
Related glossary terms
- Parameter: A number that describes an entire population. Example: The true mean height of all students at a university.
- Statistic: A number computed from a sample. Example: The mean height of 80 sampled students.
- Standard Error: The standard deviation of a statistic across repeated samples. Example: The standard error of xbar is sigma divided by sqrt(n).
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