Statistical Analysis Stack Exchange
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Questions tagged [trimmed-mean]

A k-trimmed mean is a mean where the largest and smallest k% of the observations are removed before the mean is calculated.

A trimmed mean is a mean where a given percentage of the data from the largest and smallest observations are removed before the mean is calculated.

It is more robust than an ordinary mean; for example, a 25% trimmed mean (the average of the data between the upper and lower quartiles, sometimes called the interquartile mean) is able to tolerate up to 25% arbitrary contamination.

A median is (asymptotically) a 50% trimmed mean.

One alternative to a trimmed mean is a Winsorized mean.

Reference: Wikipedia - Trimmed mean

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What are the relative merits of Winsorizing vs. Trimming data?

Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values. I always see both methods discussed as a viable option to lessen…
Brian
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How can I interpret a plot of trimming percentage vs. trimmed mean?

For part of a homework question, I was asked to calculate the trimmed mean for a dataset by deleting the smallest and largest observation, and to interpret the result. The trimmed mean was lower than the untrimmed mean. My interpretation was that…
wchargin
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Downweight outliers in mean

I have a bunch of points $x_i$ and would like to calculate a kind of weighted mean that deemphasizes outliers. My first idea was to weight each point by $1/ (x_i - \mu)^2$. However, the problem is that this includes the mean $\mu$ already. I could…
jdm
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Trimmed mean vs median

I have a data set with all the calls made to an emergency service and the response times of the ambulance department. They admitted that there are some mistakes with the response times as there are cases where they didn't start recording (so the…
Duarte_RV
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Given independence, is the median of a product equal to the product of the medians?

Question: Assume $X$ and $Y$ are independent random variables. Is $Median(XY) = Median(X) \cdot Median(Y)$? If so, how would one prove this? If not, what conditions would be sufficient for this relationship to hold? Additional question: Does the…
Colin T Bowers
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How to calculate the truncated or trimmed mean?

How can I calculate the truncated or trimmed mean? Let's say truncated by 10%? I can imagine how to do it if you have 10 entries or so, but how can I do it for a lot of entries?
Queops
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For what distribution is a trimmed mean the maximum likelihood estimator?

The sample mean is the maximum likelihood estimator of $\mu$ for a normal distribution $\text{Normal}(\mu,\sigma)$. The sample median is the maximum likelihood estimator of $m$ for a Laplace distribution $\text{Laplace}(m,s)$ (also called the…
Rasmus Bååth
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Sampling distribution of sample trimmed (truncated) mean

It is elementary probability theory that the sample mean of an i.i.d. sample follows normal distribution, if the background distribution is normal. But what about the trimmed mean? Is there any result on its distribution for an i.i.d. sample of size…
Tamas Ferenci
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Mean has lower standard error than 5% trimmed mean?

I'm investigating using a trimmed mean to measure the location of various distributions. The distributions sometimes are heavily contaminated and sometimes not. Usually they follow something similar to a log-normal or possibly mixed log-normal…
Antonio2100
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An X% trimmed mean means?

Rand Wilcox in Fundamentals Of Statistical Methods, 1st. edition, gives a formula which says that for a 20% trimmed mean, you would trim away 20% of one end of the ranked data, and 20% of the other end, making 40% trimmed away in total. But…
HumbleOrange
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Mean vs. Trimmed mean in the normal distribution

In a simple experiment with the normal distribution in R I ran 500 iterations of a simulated normal distribution with N=100 each. For each iteration from the 500 iterations, I calculated both the mean and the trimmed mean with 20% trim (from each…
Mickey
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use and misuse of Winsorization

I am doing research on Winsorization (and trimming), which has been broadly applied in many fields, but I think many researchers didn't do it in a "rigorous" way. Or maybe even worse, they misuse it. So I am wondering if there is a well-defined,…
Master Shi
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Why are Winsorized random variables independent?

While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent. However it is said that "by re-writing the trimmed mean as the average of…
rapaio
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Is it allowed to use a 5% trimmed mean for analyzing data from a creativity task (quantity of ideas)?

For my research I conducted a creativity test and measured the quantity of ideas subjects had. Some people are extreme outliers as they have a lot of ideas or only 1 or 2 ideas. Intuitively I wanted to 5% trim my data to obtain a more robust…
user670186
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How to interpret output from least trimmed squares estimate and compare it to OLS?

I have to compute and compare the least squares method on a model to the least trimmed method. The LS model results were: Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -39.9197 11.8960 -3.356 0.00375 **…
stacy
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