Questions tagged [central-tendency]
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33
questions
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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
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 ...
5
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1answer
91 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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49 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 ...
0
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1answer
264 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
...
1
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1answer
40 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
40 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
100 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 ...
2
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0answers
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 ...
0
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1answer
160 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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2answers
1k 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}...
1
vote
1answer
96 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 ...
1
vote
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 (...
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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 ...
3
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0answers
63 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 ...
3
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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 ...
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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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1answer
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?
2
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0answers
52 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
377 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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1answer
32 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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0answers
273 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. ...
6
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1answer
313 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 ...
2
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1answer
97 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
1k 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
959 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
votes
1answer
274 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
131 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-...
5
votes
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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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,...
