population mean

In statistics, the population mean represents a characteristic of an entire group. Because it's often impractical to collect data from every member of a population, a sample (a subset of the population) is used to estimate the population mean. This process is called statistical inference.1

A sample mean, denoted as x̄, serves as a point estimate for the population mean, μ. However, using a sample introduces sampling error, the difference between the sample mean and the true population mean. To account for this, statisticians use confidence intervals, which provide a range of values likely to contain the population mean, along with a degree of confidence. For large samples, a 95% confidence interval is commonly calculated as x̄ ± 1.96σ/√n, where σ is the population standard deviation and n is the sample size. Larger sample sizes lead to narrower intervals and a more precise estimate.1