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Questions tagged [central-tendency]

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Descriptive Statistics for Zero-Inflated Dataset

Just as titled, I'm curious as to what should you choose to represent a measure of central tendency for a zero-inflated vector or such. My background says go "mean" if normally distributed, &...
Derf's user avatar
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4 views

How do I minimize the difference between development and production data after normalization relative to measures of central tendency?

I think that normalization of data is performed assuming that the samples you train on are "representative" of real-world or "production" data. This means I have to constantly ...
Joachim Rives's user avatar
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13 views

What is the best way to average a data set that mostly lies in extremes

I apologise that the question in the title is a little ambiguous but it is hard to word in a single sentence. Say I have a set of data, but it is found that a data point is either quite low or quite ...
user avatar
2 votes
1 answer
437 views

Is winsorizing limited to the usage of a certain percentile cutoff?

The Context My dataset consists of 68 groups, each with 4 data points inside it. As means of a robustness test, I am looking to see how the type of average/mean I use impacts the analysis that I will ...
Son18's user avatar
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1 answer
2k views

Statistics to use on Bimodal data

What summary statistics, mean, median, standard deviation, etc. should be used on a skewed, bimodal, dataset and why? These are almost U shaped in a histogram layout with a slight preference for lower ...
RLH's user avatar
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If we numerically code the categories of an ordinal variable, then can we determine its mean as in Likert scale?

Can anyone clear my doubts about 2 things. Doubt1)A dataset of Ordinal type having 2 modes, then does it mean that such dataset have 2 central locations ? Doubt2)As We know that we can not determine ...
hornet's user avatar
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0 answers
24 views

finding central tendency

The following table presents frequency distribution of teachers of 1 year: Rank ----------Frequency Professor ------------7 Assoc Professor ------4 Asst Professor--------3 Instructor -----------5 ...
hornet's user avatar
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3 votes
0 answers
932 views

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 ...
Vicki Archer's user avatar
2 votes
1 answer
48 views

"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&...
Elaine's user avatar
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1 answer
62 views

Mode for equal consecutive frequencies

I'd like to calculate the mode for the frequency distribution table: ...
hasan's user avatar
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1 vote
1 answer
276 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 ...
Positron12's user avatar
5 votes
1 answer
173 views

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} = \...
Rodrigo de Azevedo's user avatar
1 vote
0 answers
365 views

Why is it said that centroids and geometric medians correspond to L2 and L1 central tendencies?

I'm reading an article on Wikipedia about central tendency and I'm confused about why it states that centroids correspond to L2 central tendencies and geometric medians L1. For samples $x_i$, The ...
relatively_random's user avatar
1 vote
1 answer
5k views

Central Tendency of 5-point Likert Scale

I have a Likert Scale (1-5) for rating of a product. So, the question is as follows: Q: How would you are our platforms web experience? Poor Fair Good Very good ...
Alix Blaine's user avatar
1 vote
1 answer
198 views

Statistics of Frequency given Time Intervals

We are analyzing some heart rate algorithms to understand their accuracy. We are interested in calculating statistics for the heart rate in beats-per-minute. The input data is beat-to-beat interval (...
Hephaestus's user avatar
2 votes
2 answers
61 views

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....
Srishti Jain's user avatar
1 vote
1 answer
421 views

Is expected value different in meaning from central tendency? Isn't both about "typical values"?

I was taught, that for any distribution having the 1st raw moment defined, the "expected value" is equal to it and it's also the arithmetic mean. "Expected value" sounds to me like "typical value". ...
Goala's user avatar
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Central Tendency Examples?

Can someone give me separate cases of empirical distributions where: mean does not accurately describe the central tendency. median does not accurately describe the central tendency. mode does not ...
NoName's user avatar
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14 views

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 ...
logworthy's user avatar
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5 votes
3 answers
1k views

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 ...
Gugaa Srikanth's user avatar
3 votes
2 answers
4k views

Ratio of median to mean

Is the ratio of the median to the mean of a distribution used for any descriptors e.g. measure of skewness?
Beerhunter's user avatar
0 votes
2 answers
63 views

Checking of Measurement in Grouped Data

My teacher uses the formula below when looking for the median and mode of a grouped data. $$ median = L_m + c\frac{\frac{n}{2} - F_{m-1}}{f_m} \\ mode = L_m +c\frac{f_m - f_{m-1}}{2f_m-f_{m-1}-f_{m+1}...
log's user avatar
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2 votes
1 answer
262 views

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 ...
Eric Kim's user avatar
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2 votes
1 answer
214 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 (...
Eric Kim's user avatar
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1 answer
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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 ...
guazalli's user avatar
3 votes
0 answers
73 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 ...
andrewH's user avatar
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3 votes
1 answer
83 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 ...
Electric-Gecko's user avatar
1 vote
1 answer
726 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). ...
Olga Mil's user avatar
3 votes
2 answers
988 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?
Determinant's user avatar
2 votes
0 answers
91 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 ...
user71216's user avatar
7 votes
1 answer
1k 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 ...
Richard Hardy's user avatar
0 votes
1 answer
77 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: ...
Eduardo J. Sanchez's user avatar
1 vote
2 answers
2k 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?
Mohamed Helmy's user avatar
1 vote
0 answers
366 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. ...
ThugMazzola's user avatar
7 votes
1 answer
533 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 ...
user56834's user avatar
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2 votes
1 answer
190 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 ...
Richard Border's user avatar
1 vote
0 answers
2k 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 ...
J. Doe's user avatar
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1 vote
1 answer
2k 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 ...
baxx's user avatar
  • 946
0 votes
1 answer
700 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 ...
Darien Springer's user avatar
2 votes
0 answers
204 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-...
MissMonicaE's user avatar
5 votes
1 answer
3k 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 ...
Michael R. Chernick's user avatar
23 votes
4 answers
69k 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,...
Alexis's user avatar
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