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Questions tagged [central-tendency]

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3
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0answers
22 views

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 ...
2
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0answers
15 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 ...
1
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1answer
61 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). ...
1
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1answer
35 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?
2
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0answers
21 views

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 ...
8
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1answer
111 views

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 ...
0
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1answer
17 views

Examples of high/low central tendency and volatily

There are two important measures for any data set. Its central tendency and its variability. These provide measures of expectation and variability/volatility, respectively. Can there be examples of: ...
1
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2answers
343 views

What is the mode in a multimodal data set?

Given the data set {10,10,14,14,15,15,17,17,27,27,30,30} is the mode {10,14,15,17,27,30} or is there no mode?
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0answers
137 views

Bimodal distribution dispersion

what is the correct way to study the variability of a data set when all the observations are distributed like a bimodal distribution? For instance, here I identified the two modes as central index. ...
4
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1answer
196 views

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 ...
1
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1answer
51 views

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 ...
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0answers
50 views

Difference between Medoid and Centroid [duplicate]

For a certain dataset, I am finding the k closest points in my dataset to the centroid of the dataset. Are these k points the k medoids or are medoids something completely different. If so, is there ...
0
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1answer
475 views

For persons aged 25 and over in the US would the average or the median be higher for income?

Question: For persons aged 25 and over in the US would the average or the median be higher for income? I'm not sure how to answer this. If I assume that the ...
0
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1answer
82 views

Is mean or median a better way to find central tendency of a season of television?

What is better to use for calculating the score of a season of television: the mean or the median? I will say from the outset that my question may be somewhat subjective. That being said, my question ...
1
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0answers
54 views

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-...
0
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0answers
16 views

What happens when the lower values in a series are repeatedly replaced by the mean of the series?

I want to know that if we take a set of numbers, calculate the mean, then raise the value of numbers lesser than the mean to be equal to the mean and repeat this process, then do all my numbers become ...
6
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1answer
2k views

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 ...
12
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4answers
56k 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,...