Ruutkeskmise

Ruutkeskmise, also known as the root mean square (RMS) or quadratic mean, is a statistical measure. It is a type of average, specifically used to quantify the magnitude of a varying quantity. It is calculated by taking the square root of the mean of the squares of a set of values.

The formula for ruutkeskmise for a set of numbers x1, x2, ..., xn is given by:

RMS = sqrt((x1^2 + x2^2 + ... + xn^2) / n)

Ruutkeskmise is particularly useful when dealing with oscillating or fluctuating quantities where the average value might be zero, such as in alternating current (AC) circuits or signal processing. It provides a measure of the effective value of these fluctuating quantities. For example, the RMS voltage of an AC supply represents the equivalent DC voltage that would produce the same amount of power dissipation in a resistive load.

Compared to the arithmetic mean, ruutkeskmise gives greater weight to larger values due to the squaring operation. This makes it sensitive to extreme values in a dataset. It is a non-negative value, reflecting the magnitude rather than direction or sign.