A parameter describes an entire population; a statistic describes a sample taken from that population.

Core idea in one line

  • Parameter = number about everyone you care about (the full population).
  • Statistic = number about some of them (a sample), usually used to estimate the parameter.

Simple definitions

  • Parameter
    • A fixed (but usually unknown) numerical value.
    • Describes a population : all individuals or items of interest.
    • Examples:
      • The true average height of all adults in a country (population mean).
      • The true percentage of all voters who support a candidate (population proportion).
  • Statistic
    • A calculated number that can change from sample to sample.
    • Describes a sample : a subset of the population that you actually measure.
    • Examples:
      • The average height of 500 adults you measured from that country (sample mean).
      • The percentage of 1 000 surveyed voters who support the candidate (sample proportion).

Key differences at a glance

Population vs. sample

  • Parameter: tied to population (everyone in the group).
  • Statistic: tied to sample (only those you actually observed).

Known vs. unknown

  • Parameter: usually unknown in practice, because measuring everyone is hard.
  • Statistic: known , because you compute it from your sample data.

Fixed vs. variable

  • Parameter: one fixed value for a given population (doesn’t change unless the population itself changes).
  • Statistic: changes from one sample to another; it varies due to sampling.

Typical notation

  • Parameters: often Greek letters, e.g.
    • μ\mu μ = population mean, σ\sigma σ = population standard deviation, ppp = population proportion.
  • Statistics: often Roman letters, e.g.
    • xˉ\bar{x}xˉ = sample mean, sss = sample standard deviation, p^\hat{p}p^​ = sample proportion.

Quick analogy

Imagine you care about the average age of all students in a school :

  • That true average (if you could somehow ask every student) is the parameter.
  • You instead randomly pick 50 students and compute their average age; that number is a statistic that you use to estimate the true school-wide average.

One-sentence wrap-up

A parameter is the (usually unknown) true number that describes a whole population, while a statistic is the computed number from a sample that we use to estimate that parameter.

Information gathered from public forums or data available on the internet and portrayed here.