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 ...
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1answer
16 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 ...
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84 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} = \...
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34 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 ...
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1answer
92 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 ...
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1answer
37 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 (...
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2answers
35 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....
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1answer
77 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". ...
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25 views

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 ...
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11 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 ...
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55 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 ...
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929 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?
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27 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}...
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67 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 ...
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1answer
101 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 (...
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1answer
342 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 ...
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62 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 ...
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1answer
41 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 ...
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1answer
276 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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1answer
98 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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50 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 ...
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1answer
281 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 ...
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29 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: ...
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2answers
1k 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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258 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. ...
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1answer
299 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 ...
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1answer
86 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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917 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 ...
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1answer
897 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 ...
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1answer
231 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 ...
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121 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-...
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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 ...
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61k 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,...