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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15 views

Regression of a dataset using median

I have a dataset containing (x,y) information from the years 1985–2013. The x data is the pick number and the y data is performance. Each year has 60 (x,y) data points. When looking at my data for ...
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46 views

Standard error on median for exponential distribution

I am trying to find the standard error on the median, $\sigma_\tilde{x}$, for a sample, $X_i$, of a population whose pdf could be modelled as $\lambda e^{-\lambda x} $ if normalized. To make sure we ...
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19 views

Symmetry of a distribution

I have received a sample, summarized by a frequency table with groups (i.e. 1-7, 7-10, 10-13, 13-16, etc...) I calculated the mean and median, both were around 15, the mean was 15.3, the median 15.6. ...
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1answer
34 views

Estimate median from mean, std dev, and/or range

I have easy access to the the mean, standard deviation and min/max values for a variable. I also have the number of elements used to compute those values. The data is real numbers with an absolute ...
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28 views

confidence interval using median

I have a model where time is the response variable. I'd like to generate confidence intervals for the estimates. I have established that the error in the estimation is roughly normally distributed (it ...
2
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1answer
80 views

Online estimation of quartiles without storing observations

I need to compute quartiles (Q1,median and Q3) in real-time on a large set of data without storing the observations. I first tried the P square algorithm (Jain/Chlamtac) but I was no satisfied ...
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1answer
49 views

How to get the median of Z=f(x,y)?

Defining $Z=f(x,y)$ in interval $[q,1][q,1]$,$x,y$ are all i.i.d. uniform. I know that, if $f(x,y)$ is non-increasing or non-decreasing for both $x$ and $y$, the median of $z$ is $f((1-q)/2,(1-q)/2)$. ...
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1answer
100 views

One sample median test: Wilcoxon, sign test or chi squared

I would like to understand the differences between these tests for one sample median test and when to use each of them. I have been searching information and this is what I got so far: Sign test ...
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16 views

One-sample median test:: Signrank seems unsuitable

I have some data on successive bets made by customers. I want to see whether there is a statistically significant change in bet stake with each subsequent bet. The data is skewed, so I have ...
0
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1answer
34 views

How to calculate median absolute deviation in a cross validation scenario?

In a cross validation scenario "leave one out" I want to measure how the estimated continuous variable fits with the observed variable. I learned from Wikipedia that the Median absolute deviation ...
3
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1answer
53 views

Multistage sampling for Population Median

Has there been any research done on how to estimate the population median using multistage sampling? Simple random sampling is not possible in my case I would really like to use something like ...
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4answers
963 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 ...
3
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1answer
73 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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1answer
43 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
49 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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0answers
16 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
71 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 ...
2
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2answers
96 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
34 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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2answers
598 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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0answers
57 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 ...
6
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1answer
126 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
132 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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0answers
32 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
130 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
36 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
842 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
86 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
170 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
197 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
62 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
171 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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126 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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378 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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1answer
327 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, as ...
5
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1answer
384 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
350 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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121 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
3k 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)? ...
5
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3answers
239 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 ...
5
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2answers
311 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
2k 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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2answers
196 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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104 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 ...
0
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1answer
85 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
235 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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3answers
140 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 ...