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What is a truncated mean used for?
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both.
Why is a trimmed mean more resistant than the mean?
Less Common Measures of Center The trimmed mean is the mean after the lowest 10% of the values and the highest 10% of the values have been removed. The trimmed mean has the benefit over the regular mean that the extreme values have been cast out and so the trimmed mean is more resistant to change than the mean.
What does it mean if a trimmed mean is resistant?
The 90% trimmed mean is the mean of the values after truncating the lowest and highest 5% of the values. Mosteller and Tukey (see Reference section below) define two types of robustness: resistance means that changing a small part, even by a large amount, of the data does not cause a large change in the estimate.
Will a data set will always have exactly one mode?
A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set. The mode can be the same value as the mean and/or median, but this is usually not the case.
What is the meaning of a truncated mean?
Truncated mean. A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both.
Which is the correct definition of a trimmed mean?
A trimmed mean is stated as a mean trimmed by x%, where x is the sum of the percentage of observations removed from both the upper and lower bounds. The trimming points are often arbitrary in that they follow rules of thumb rather than some optimized method of setting those thresholds. A trimmed mean is also known as a truncated mean.
Why is a truncated mean a good estimator?
The truncated mean is a useful estimator because it is less sensitive to outliers than the mean but will still give a reasonable estimate of central tendency or mean for many statistical models. In this regard it is referred to as a robust estimator.
Which is better a truncated mean or a median mean?
The truncated mean uses more information from the distribution or sample than the median, but unless the underlying distribution is symmetric, the truncated mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median.