Keskikeskiarvo

Keskikeskiarvo is a statistical measure of central tendency known in English as the midmean or central mean. It is computed by ordering the data, removing a fixed proportion of the smallest and largest observations, and then taking the arithmetic mean of the remaining values. The trimming level is specified as a fraction of the sample size; for example, trimming 25 percent on each end leaves the central 50 percent of the data. When no trimming is applied, keskikeskiarvo equals the ordinary arithmetic mean.

Calculation can be illustrated with a simple example. Consider the data set 1, 2, 3, 4, 5, 6, 7, 100. If the lowest and highest 25 percent are removed (two observations from each end for a sample of eight), the remaining values are 3, 4, 5, and 6, whose mean is 4.5. This demonstrates how outliers such as 100 have less influence than they would on the regular mean.

Keskikeskiarvo is a form of trimmed mean and is thus more robust to outliers than the ordinary mean, though it is not as robust as the median. The choice of trimming level affects bias and efficiency; common practice uses moderate trimming (for example, 10–25 percent) depending on the data and context.

Applications of keskikeskiarvo include situations where data contain outliers or extreme values that would distort the ordinary mean, such as sensor readings, environmental measurements, or some income datasets. It is a component of robust statistics and is related to concepts such as the trimmed mean and the midmean.

See also: trimmed mean, median, robust statistics, midmean.