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Often both A-weighted and 468-weighted figures are quoted for noise, especially in microphone specifications. While not intended for this application, the 468 curve has also been used (offset to place the 0 dB point at 2 kHz rather than 1 kHz) as "M weighting" in standards such as ISO 21727 [ 5 ] intended to gauge loudness or annoyance of ...
Unweighted, or "elementary", price indices only compare prices of a single type of good between two periods. They do not make any use of quantities or expenditure weights. They are called "elementary" because they are often used at the lower levels of aggregation for more comprehensive price indices. [2]
A weighting curve is a graph of a set of factors, that are used to 'weight' measured values of a variable according to their importance in relation to some outcome. An important example is frequency weighting in sound level measurement where a specific set of weighting curves known as A-, B-, C-, and D-weighting as defined in IEC 61672 [1] are used.
A graph of the A-, B-, C- and D-weightings across the frequency range 10 Hz – 20 kHz Video illustrating A-weighting by analyzing a sine sweep (contains audio). A-weighting is a form of frequency weighting and the most commonly used of a family of curves defined in the International standard IEC 61672:2003 and various national standards relating to the measurement of sound pressure level. [1]
In the measurement of loudness, for example, an A-weighting filter is commonly used to emphasize frequencies around 3–6 kHz where the human ear is most sensitive, while attenuating very high and very low frequencies to which the ear is insensitive. The aim is to ensure that measured loudness corresponds well with subjectively perceived loudness.
When treating the weights as constants, and having a sample of n observations from uncorrelated random variables, all with the same variance and expectation (as is the case for i.i.d random variables), then the variance of the weighted mean can be estimated as the multiplication of the unweighted variance by Kish's design effect (see proof):
B-weighted sound pressure level is written either as dB B or L B, and C-weighted sound pressure level is written either as dB C or L C. Unweighted sound pressure level is called "linear sound pressure level" and is often written as dB L or just L. Some sound measuring instruments use the letter "Z" as an indication of linear SPL. [13]
Weighted means are commonly used in statistics to compensate for the presence of bias.For a quantity measured multiple independent times with variance, the best estimate of the signal is obtained by averaging all the measurements with weight = /, and the resulting variance is smaller than each of the independent measurements = /.