Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [central-tendency]

36 questions
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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, median and mode) by explaining that the mean is…
Alexis
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Why start with measures of central tendency?

In teaching descriptive statistics, measures of central tendency come up early on, e.g. before measures of spread. For me it is natural enough to learn about central tendency, or location, of the data before learning many other properties, but this…
Richard Hardy
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Is there a "central distribution" for distributions for which the CLT doesn't apply?

The central limit theorems state roughly that under a certain set of properties of a sampling process, the distribution of a statistic from that sample will converge in distribution to the normal distribution. As the canonical example, let me take…
user56834
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Mid-range via minimax

Warning: crossposted at Mathematics SE. Given vector ${\rm a} \in \Bbb R^n$, $$\begin{array}{ll} \displaystyle\arg\min_{x \in {\Bbb R}} & \left\| x {\Bbb 1}_n - {\rm a} \right\|_2^2\end{array} = \frac1n {\Bbb 1}_n^\top {\rm a} \tag{mean}$$ is the…
Rodrigo de Azevedo
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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 and samples the quantities mean, mode and median…
Michael R. Chernick
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Adding Cumulative Means and Variances

I would like to get cumulative data about opioid use after surgery on day 2 of use. I have the mean, SD for day 1 and for day 2. My understanding for the means is I can add them together. When it comes to the SD I know I need to convert them to the…
Vicki Archer
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Is mode a measure of central tendency?

I am just starting out with my stat basics and that’s where I came across measures of central tendency. In one of the books measure of central tendency is defined as a measure which yield information regarding the central or the middle part of a…
Gugaa Srikanth
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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 the central tendency of that distribution. The…
andrewH
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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 truncated mean, but it's a soft approach to dealing with…
Electric-Gecko
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"Media" as a measure of central tendency

I've just read a meta-analysis that used 'media' as a measure of central tendency: "The media of skin side events related to PPE was 75.13%". I've never come across the use of "media" like this before- is this a typo, a variation on median, or is…
Elaine
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Practical use of median?

Someone recently asked me the business use of various measures of central tendencies. Although the usage of mean and mode is intuitive and easily seen, I could not think of one intuitive use of median. What is median used for?
Srishti Jain
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What is a term to describe data where the mode represents a large proportion of all observations?

Below are some histograms of continuous variables, where 20-50% of all observations fall on the mode. Are there any terms to describe data that exhibit this unusual concentration of observations on the mode?
logworthy
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Generalization of median, mean for L_p spaces for p different than 1,2

I find it fascinating that the mean and median both minimizing the a measure of error of a point estimate. The median $m_1$ is any (non-unique) $m \in \mathbb R$ which minimizes the $L_1$ norm $\int |f - m|$. Likewise, the mean $m_2$ minimizes…
user71216
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Best plausible estimate of parameter of hypergeometric distribution

Consider the Urn problem where a hypothetical urn contains a finite number of $m$ balls, $r$ of which are black and $m-r$ are white. We take a random sample without replacement of $n$ balls and observe $k$ are black. The distribution of $K$ follows…
Richard Border
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central tendency as minimized variance

I'm reading John Kruschke's Doing Bayesian Data Analysis: A Tutorial with R and BUGS, in which it says that we define the central tendency of a distribution as the value $M$ that minimizes the long-run expected distance between it and all the other…
MissMonicaE
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