Keskiluvun

Keskiluvun is the Finnish term for the arithmetic mean, the central value used to summarize a data set. It is a fundamental measure of central tendency in statistics and is widely used in Finnish-language textbooks, reports, and data analyses to provide a single representative value for a collection of numbers.

Etymology and usage. The word derives from kesk- meaning center and luku meaning number, reflecting its role as a central value. In everyday Finnish, keskiarvo is a common term for the mean, but keskiluvun appears in formal statistical language and in compound expressions such as keskiluvun laskeminen (calculation of the mean). The genitive form keskiluvun is used in phrases describing the mean’s properties or computations, for example otoksen keskiluvun laskeminen.

Computation and notation. For a data set x1, x2, ..., xn, the Keskiluvun value is the sum of all observations divided by the number of observations: (x1 + x2 + ... + xn) / n. In statistical practice, the sample mean is often denoted x̄ (x-bar) and the population mean is denoted μ. The mean can also be adapted for grouped or weighted data, yielding a weighted mean.

Properties and considerations. The mean is sensitive to extreme values and may not accurately represent skewed distributions. It minimizes the sum of squared deviations from the data points and is central to many statistical methods, including variance and hypothesis testing. In symmetric distributions, the mean coincides with other measures of central tendency like the median, but this is not guaranteed for all data sets.

See also. Related concepts include keskiarvo (the general term for mean), aritmeettinen keskiarvo (arithmetic mean), weighted mean, and measures of central tendency such as median and mode.