# Questions tagged [central-tendency]

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### Determine item level variance of single test administrations as well as of an entire sample of administrations

I am decades out of school and need help determining the correct statistic / concept to use for my use case. My agency (human services) uses a specific functional test to determine how well clients ...
1answer
24 views

### Calculating the trimmed mean as an estimator

My book provides the following steps to calculate the $100 \alpha$ percent trimmed mean for a sample data of $n$ measurments: 1-Order the measurments. 2-Discard the smallest $100\alpha$ percent and ...
1answer
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### Central Tendency of Cauchy distribution

How do you measure the central tendency of a cauchy distribution? I'm aware that the mean is not a good measure of the central location for cauchy. Can I use median? I've been searching with the key ...
1answer
103 views

### Highest Density Interval for the measure of central tendency

When samples are skewed, mean is not a good estimation of central tendency. But instead, median is a better choice. For cauchy distribution, I heard that there's a completely different estimator (...
1answer
560 views

### What is the relationship between: the first raw moment, location, expected value, mean in general, arithmetic mean for any sensible distribution? [closed]

I am a bit confused by the several sources telling that: the first raw moment is by definition the arithmetic mean expected value of any random variable is exactly the arithmetic mean The expected ...
0answers
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### Measures of central tendency for right-skewed size distributions

Suppose we are looking at a right-skewed size distribution such as the distributions of income, casualty losses, or flood sizes, and we want to look at some alternative measures to jointly represent ...
1answer
46 views

### Is there a term to refer to a weighted mean that's weighted by a function of percentile (using a kernel)?

I came-up with a type of central tendency which is a weighted mean. The weighting is based on percentile, with values closer to the median having a higher weight. It's similar to the idea of a ...
1answer
329 views

### Distribution of the inverse square of a non-standard normal random variable multiplied by a constant

It's a somewhat complicated situation and sorry about my phrasing, but it's my first time here. Suppose I have random normal variable $X$ ~ $N( \mu, \sigma^2)$, which represents some true effect(s). ...
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126 views

### Measure of dispersion around the mode

I usually associate the standard deviation with the mean and the IQR with the median. Is there a measure of dispersion typically associated with the mode?
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### What is central tendency?

I have seen many questions on CV that deal with central tendency. It seems to be a nebulous topic. Definitions include values of a distribution that are most common. For probability distributions ...
4answers
62k views

### Should the mean be used when data are skewed?

Often introductory applied statistics texts distinguish the mean from the median (often in the the context of descriptive statistics and motivating the summarization of central tendency using the mean,...