trimmed mean

The 10% trimmed mean for the speed of light data is 27.43.

Clearly, the trimmed mean is less affected by the outliers and has a higher breakdown point.

Then a trimmed mean is calculated by dropping the highest and lowest score.

In the previous example the trimmed mean would be obtained from the smaller set:

In fact, the mean, median and trimmed mean are all special cases of M-estimators.

The score given to each boxer would be taken from 3 out of 5 judges either by similar score or trimmed mean.

The analysis was performed in R and 10,000 bootstrap samples were used for each of the raw and trimmed means.

Whilst the trimmed mean performs well relative to the mean in this example, better robust estimates are available.

A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median.

For instance, the 5% trimmed mean is obtained by taking the mean of the 2.5% to 97.5% range.

The distribution of the mean is clearly much wider than that of the 10% trimmed mean (the plots are on the same scale).

Notice that if we replace the lowest observation, -44, by -1000, the mean becomes 11.73, whereas the 10% trimmed mean is still 27.43.

The trimmed mean scores are then translated into a factored mark by multiplying by a factor that depends on the discipline, competition segment, and level.

Trimmed means that the highest rises and declines in prices are trimmed by a certain percentage, attributing to a more accurate measurement on core inflation.

In calculations of a trimmed mean, a fixed percentage of data is dropped from each end of an ordered data, thus eliminating the outliers.

Other alternatives include trimming and Winsorising, as in the trimmed mean and the Winsorized mean.

Also note that whereas the distribution of the trimmed mean appears to be close to normal, the distribution of the raw mean is quite skewed to the left.

The BBA throws out the highest 4 and lowest 4 responses, and averages the remaining middle 10, yielding a 23% trimmed mean.

When the percentage of points to discard does not yield a whole number, the trimmed mean may be defined by interpolation, generally linear interpolation, between the nearest whole numbers.

In the United States the Dallas Federal Reserve computes a trimmed mean PCE price index, which separates "noise" and "signal".

The X% trimmed mean has breakdown point of X%, for the chosen level of X. Huber (1981) and Maronna et al. (2006) contain more details.

The Cleveland Federal Reserve computes a Median CPI and a 16% trimmed mean CPI.

The trimmed mean is a simple robust estimator of location that deletes a certain percentage of observations (10% here) from each end of the data, then computes the mean in the usual way.

The Libor benchmark interest rate is calculated as a trimmed mean: given 18 response, the top 4 and bottom 4 are discarded, and the remaining 10 are averaged (yielding trim factor of ).

Each sample was scaled to a target intensity of 1000 using the "all probe sets" scaling option, this option scales the trimmed mean target intensity to the specified value [ 11 ] .