In classical statistics, a parameter is a fixed but unknown quantity that represents a characteristic of a population through some kind of summary measure. For example, if the measurement of interest is the weight of all newborn lambs born in the year 2021, and the weight follows a normal distribution, one parameter that might be of interest is the average weight of all the lambs (denoted by ?).
As it is likely not practical to be able to record the weight of every single lamb born across the world in the entire year, the essence of statistics is to take a sample that is representative of the entire population but does not require physically measuring every single sheep. If an appropriate sample of 1000 lambs is taken, the population weight could be estimated by computing the sample mean among those sheep (usually denoted by
). An estimate of a population parameter computed from a sample is referred to as a statistic.
