The median is the value below which half the data or probability distribution lies - when the sample size is odd, the median is the 'middle' value of an ordered sample.

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55 views

Simulate the distribution of the median

I have done part(a); now I need to do part(b): I want to simulate the distribution of the median $M$ using R. I don't know how to work it out. And for part(c), do I need to use R as well? This is ...
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25 views

What is the sample-size range for which the median should be preferred to the mean as a measure of central tendency? And why?

I have firing-rate data for neurons ranging from 40-60 in number for various experimental groups. I've seen both mean and median being used in the literature, but without much explanation for the ...
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2answers
36 views

Paired t-test of medians

I need to run an inferential test on some large data where the individual data points have a heavily skewed distribution. I'm considering doing a paired t-test across a number of days comparing the ...
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14 views

Should I take mean or median to compare short-term and long-term observation?

I have a finite set A of discrete values and I have a packet flow (computer networking) where each packet is assigned with a value from A. I want to determine if it is possible to predict the ...
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1answer
35 views

K-medians, formula to compute the median

If you are running K-medians, and your distance metric is the L1 norm, how do you derive that the center of each centroid is the median of the data points assigned to it? Second, how do you compute ...
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73 views

Prior Gamma distribution: Select appropriate alpha given beta and median

I am trying to programatically select a prior distribution from the Gamma family of distributions. The primary criteria that I need to satisfy is that the median of the distribution should be a given ...
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1answer
24 views

What can be inferred when multivariable ordinary least squares and quantile (median) regression yield differing results?

There lies information in a discrepancy of the (unconditional) mean and median. For example, if the median is larger than the mean, the distribution must be left-skewed. Does this kind of inference ...
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412 views

In left skewed data, what is the relationship between mean and median?

I found this question on the open MOOC from Stanford, however the answer is not present. I think the median $\leq$ mean. Is this the case?
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52 views

Determine number of runs is significant at 5% level of significance

I have the following question to answer: The total thickness X of the four pads of 36 half-ring (H-R) mounts for aircraft engines, taken periodically from the production line, were found to be ...
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1answer
108 views

Prove that distribution of sample median (for even sample) is symmetric

Let $\mathbf{X}=(X_1,X_2,\ldots,X_{2k})$ be a sample from normal distribution $\mathcal{N}(0,1)$. Prove that distribution of sample median (for even sample) is symmetric around 0. $me(\mathbf{X}) = ...
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2answers
110 views

Given independence, is the median of a product equal to the product of the medians?

Question: Assume $X$ and $Y$ are independent random variables. Is $Median(XY) = Median(X) \cdot Median(Y)$? If so, how would one prove this? If not, what conditions would be sufficient for this ...
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29 views

Creating a model to interpret numerical scores

Good morning/afternoon everyone, first of all thanks to all of you for the valuable insights provided. I will be oulining here my current challenge, trying to provide as much detail as possible. ...
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1answer
108 views

Why are statistical properties of mode and median difficult to determine?

I have read a book saying that statistical properties of the mode and the median are difficult to determine compared to the mean. I am not entirely sure why is so. Is it correct that because the mean ...
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1answer
26 views

Interpolating median for uncensored survival data

This question is specific to a text. I am reading "Statistical Methods for Survival Data Analysis" by Lee and Wang. On p. 70 in the 4th edition (and p. 66 in the 3rd) the authors show a linear ...
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3answers
242 views

Hypothesis test for difference in medians among more than two samples

Question The test scores of three groups of people are saved as separate vectors in R. ...
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0answers
33 views

Estimating the mean with least median of squares

I have a set of real numbers $x_{1}...x_{n}$ and would like to estimate their mean (let's call it y) so that $median(x_{i}-y)^{2}$ is minimal. Is there an algorithm and a correctness proof for ...
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1answer
58 views

Is median better than mean for reporting on website speed

Whilst I understand why median can be a better metric than mean in certain circumstances (e.g. you're creating/marketing a ...
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2answers
125 views

How to get the median of a row in SPSS? [closed]

I have a data in SPSS structured like this: student_number age study_for q1 q2 q3 q4 q5 q6 q7 q8 (<-- these are columns) There are students with numbers from 1 to 67. For each of those students I ...
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2answers
170 views

When is the median more affected by sampling error than the mean?

I'm writing a paper on making probability estimates, and it's been asserted to me that I should take the median of the estimates given by my participants, rather than the mean. I've been told I should ...
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1answer
57 views

How to estimate errors on a sample with very few data points

I have a very simple question to ask, but I can't figure this on my own. I have two samples: sample A with only three data points, and sample B with hundreds of points. For each sample I measure the ...
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1answer
147 views

Outlier detection using Medial Rule

I have a data set captured every minute. Using Tukey's test for outlier detection (i.e., if number points above Q2+2.3IQR is above 10% of total distribution) then I mark the one minute window as ...
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0answers
112 views

Median bootstrap

I ran a data set containing ages through SAS npar1way first, but a reviewer wanted standard errors, so that motivated a smooth bootstrap. Since I could not use survyselect, I had to code a data step. ...
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0answers
285 views

How to split up variable equally (50/50) above and below the median in Stata?

So I am trying to assign 1 to numbers above the median and 0 to those below the median using the generate command. The problem is that I have a bunch of numbers ...
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234 views

Does a median-unbiased estimator minimize mean absolute deviance?

This is a follow-up but also a different question of my previous one. I read on wikipedia that " A median-unbiased estimator minimizes the risk with respect to the absolute-deviation loss function, ...
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1answer
281 views

When to use sample median as an estimator for the median of a lognormal distribution?

I myself would always use geometric mean to estimate a lognormal median. However, in the industry world, sometimes using the sample median gives better results. The question thus is, is there a cutoff ...
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2answers
228 views

Test whether data set approximates normal distribution using mean and median

I am of the knowledge that to test whether a data set approximates a normal distribution, the median and the mean should be approximately equal. So my question is to what degree should the difference ...
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0answers
103 views

Mean or median as the measure of central tendency for data spanning three orders of magnitude

Here is a data set I am working with. I basically have a total of 1082 different data segments of $y$ vs. $x$ all plotted here on a log scale in bright blue in the background. Now what I need to do ...
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40 views

Inferring low p values and medians

For my set of data, I have a very low p-value (< 2.2 e-16) and a median of -1. I'm new to statistics and I really am not sure what to make of this data and how to interpret it. Note: The p-value ...
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3answers
2k views

Standard error of the median

Is the following formula right if I want to measure the standard error of the median in case of a small sample with non normal distribution (I'm using python)? ...
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3answers
206 views

Percentiles of a distribution

I'm measuring error on the median of my data using bootstrapping. I would like to obtain I sigma error bars on my data, so I'm measuring the 16th and 84th percentiles of my data. Should I divide these ...
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2answers
242 views

Median + MAD for skewed data

I am trying to figure out what happens if you apply Hampel's outlier detection technique based on the median and the MAD to data that is skewed. Apparently, the advantage of Hampel's method over ...
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0answers
1k views

How to report results from Friedman's test including post-hoc results

I have performed comparison of repeated measures for a group using Friedman’s test (K-related-samples test) and additional post-hoc analysis with Wilcoxon signed-rank test and Bonferroni correction. I ...
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195 views

Why does this criterion characterize the median of a continuous random variable?

If $X$ is a continuous random variable, then let $$\min_a{\mathbb{E}\:| X - a |} = \mathbb{E}\: | X - m |$$ Why is $m$ the median of $X$?
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97 views

Distributed Median

What is the most optimum method to calculate the median in a distributed setting? I want to optimize with respect to data transmission i.e. an algorithm that finds the median across data spread across ...
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1answer
75 views

Use median for clustering, instead of average value

I have a List of Files on which I run some statistical methods to get a rating between 0 and 1. Now i need to cluster the files for similarities. The easiest way i thought that would be is to use the ...
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1answer
226 views

Expectation of the sample median for symmetric distributions

Is the sample median an unbiased estimator of the population mean when the distribution is symmetric?
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131 views

Sampled median's accuracy

I'm working on a problem where I need to calculate the median for a very large data set (for instance, 100M values) that has a log-normal distribution. Because of the data set's size, we were ...
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1answer
49 views

What number minimises RMSD between itself and randomly generated numbers?

Let us assume that we have a random number generator given by its probability density function. Now, we need to use this distribution to generate a number that has the following property. It minimises ...
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1answer
297 views

Comparing distributions as opposed to medians?

Assume a hypothetical scenario of two events. During event 1, I observe a set of values $[X_1, X_2,X_3,...,X_n]$. A physical phenomena occurs and this triggers event 2 for a short period of time and I ...
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44 views

Comparing tests for staging cancer

I am comparing 4 different tests for the evaluation/identification of cancer. One is a continuous variable yielding cut-off values based on both the mean and the median of 5 consecutive measurements ...
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1answer
237 views

Median Averaging and Error Analysis

I am not sure if i should be asking this on the Mathematics of Physics Stack Exchange site. I am taking data for a physics research application and have a question about using median vs. mean ...
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131 views

Software for median polishing

Is there any easy-to-use software for Tukey median-polishing rows and columns with lots of missing values?
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584 views

How to calculate median of distributed data?

How to find the median (or approximate median) of n chunks of values. The values in each chunk can be assumed to have been sorted if it helps. In addition, the existence of a histogram for each chunk ...
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4answers
1k views

Central limit theorem for sample medians

If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a ...
5
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1answer
578 views

Measure of variation around Median

Are there terms for measures of variation around the median? I know that we use "variance" for means of data but how can variance be defined for the median? Is there a similar statistic for median?
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1answer
585 views

What are the multidimensional versions of median

What are the multidimensional versions of the median and what are their pros and cons? I confess this doesn't have a single answer, but I think it is a useful question to ask and will be a benefit to ...
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3answers
1k views

Variance of sample median

Given a sample of n units out of a population of N, population median can be estimated by the sample median. How can we get the variance of this estimator?
2
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1answer
125 views

When are tertiary splits un/justified?

I'm studying neuroscience and have a question about presenting some data. I would like to know if tertiary splits are acceptable when the variable in question is normally or not normally distributed. ...
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2answers
136 views

Advanced procedures using the Median statistic

With the risk of asking a duplicate question (to be fair, I looked at 10 pages): Could you name and explain some advanced procedures which make use of the median statistic? Background: I am ...
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1answer
126 views

Calculate one median for data from five experimental repetitions

I have an experiment that produces a few thousand data points which I then have repeated 5 times. Now I wonder how to calculate one single median to summarize all of them. I could combine the data ...