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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11 views

Plotting raw data, but running statistics on log-transformed data

My data is non-normal, I want to show my raw data, in a scientific journal, by median +/- mad, to show the true nature of the data. However, if log-transformed, the data is normal. Can I then ...
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19 views

Bar plot with median +/- median absolute deviation in scientific publication

I know bar plots usually represents mean +/- sem, but if the data is non-normal, is it ok to bar plot median +/- mad? I don't like box plots. Suggestison?
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15 views

How to project video viewcount based on historicals?

My goal is to create a formula that can give an indication of how a YouTube channel's video will perform in the first 30 days of its lifespan and eliminate viral video / "lightening in a bottle" ...
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1answer
29 views

When to report proportions and when to report median + IQR for ordinal variable

A colleague brought to my attention documentation for a standardised questionnaire which recommended using the median and interquartile range to describe summary variables created by combining ...
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34 views

Find interquartile range of these data

Take these data: 5, 8, 9, 14 R says the interquartile range is 3: ...
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1answer
146 views

Do mean, variance and median exist for a continuous random variable with continuous PDF over the real axis and a well defined CDF?

For a continuous random variable with continuous PDF over the real axis and well defined CDF, are the mean, variance, and median always well defined? Mean and variance do not always exist, e.g. for a ...
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2answers
183 views

Why is the geometric median called the $L_1$ estimator?

My question is simply, why is the geometric median called the $L_1$ estimator? This always reminds of $L_p$ spaces but the distance being minimized in the geometric median's definition isn't $L_1$ but ...
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1answer
21 views

Estimating costs with extreme values

I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values? By extreme values I mean I have a large portion of my costs being zero and a small ...
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35 views

What are the exact assumptions of Mood's Median Test?

I have checked with various sources, but I'm still puzzled: 1) What are the exact assumptions of Mood's Median Test? 2) Is homogenity of variance needed for both groups or is the same shape criterion ...
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2answers
103 views

Estimating the time for completing a sequence of actions

In short: suppose I have observations for times taken to do some action. I want to estimate, how long will it take to complete a sequence of actions. The estimate should minimize the mean absolute ...
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2answers
44 views

Obtaining error bars for a difference

I have a pair of data sets, and I want to know whether the medians of these two sets differ significantly. I've calculated the median of each set and subtracted them from each other. How can I ...
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0answers
16 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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50 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
42 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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35 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 ...
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1answer
106 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
51 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
142 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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24 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 ...
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1answer
42 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 ...
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1answer
63 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
1k 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 ...
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1answer
79 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
58 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
54 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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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
99 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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2answers
106 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
40 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
930 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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60 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
143 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
144 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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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
155 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
39 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
1k 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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35 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
109 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
225 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
211 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
178 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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135 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
437 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
335 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 ...
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1answer
452 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
434 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
133 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 ...