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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Recalculating mean, median, std dev and confidence interval after updating sample

I am working on an application which gets rolling samples of World of Warcraft auctions every two hours. The auctions contain, among other data: item ID (will be used to group auctions before ...
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19 views

Weighted median

I'd like to compute a median of measurements taken from a population with 3 subgroups, A, B, and C. I'd like to the median to be "weighted", in the sense that each of the groups should have equal ...
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12 views

How to take median of medians when not all are weighted the same

I've got an arbitrary list of U.S. counties, with a median income score for each one. I need the median income of all of those counties together. (I could settle for an average if need be.) I've ...
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28 views

Impute with the Mean or Median? Instrumental Variables

I am using instrumental variables and I have missing data. In r, I don't believe you can use the MICE package with the AER package. Therefore, I am going to impute with either the mean or median ...
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20 views

Possible to estimate distribution around mean given #samples, mean, highest and lowest?

For a project for which there are multiple bidders, the following is known: Number of bidders: 24 Mean bid: 104 Highest bid: 356 Lowest bid: 20 Given the above, is it possible (however roughly) ...
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67 views

If I have means and medians, is there a way to average them?

Please consider these data points as an example of many more, they represent single studies with multiple samples which have been done during the last decades. ...
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37 views

Different Central Tendency Measures for Describing Groups or Individuals

Background: I have records with various metrics for many users. I want to develop a profile for each and also group similar users using clustering. Question: When developing a profile for each user, ...
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1answer
35 views

Weighted median of a portfolio

I need to calculate weighted median return for a portfolio (using MATLAB). There is information available online: MATLAB Central/rates&weights and Excel/note 4+4+4+7+7/5 logic How would you ...
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8 views

can one approximate median of non central t- location scale distribution

Generally one can approximate the median to be the non central parameter. I want full proof of the same. can you please give me any journal paper link, in which this has been proved.
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28 views

Calculation of median: Why are means of ranks not used for it?

in order to calculate the median, I have to sort the data in a ascending/descending order. Each value gets a rank so that I can (for uneven samples) look up the value that rank X = (n + 1)/2 has, ...
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31 views

Interpreting contradicting results T-Test vs. Mann-Whitney test (2 independent samples)

I want to test if two indepent experimental groups are sign. different in terms of one outcome variable, but face the following questions: Basic setup 2 groups with 200 observations each Outcome ...
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306 views

What is the median of the school grades A A B B ?

If the sample was $S_1=\{1,2,3,4\} \subset \mathbb R $ the median is 2.5 because 50% of the sample is $>=$ 2.5 and 50% of the sample is $<=$ 2.5. The median obviously does not need to be ...
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22 views

What is the median of the Dirichlet Distribution?

The Dirichlet is a multivariate generalisation of the Beta distribution, and Wikipedia states that the median of the Beta distribution is the inverse of the incomplete Beta function evaluated at ...
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31 views

CSV file with several values, get median in groups of ten [closed]

I have a csv file with 4000 lines and 270 columns. So I want to read each column and take the median of groups of 10 elements. How do I do this in Python on a fast way, taking into account the number ...
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886 views

Percentile vs quantile vs quartile

What is the difference between the three terms below? percentile quantile quartile
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1answer
60 views

Estimating median survival times from Kaplan-Meier plot inspection

I've gone through the various questions relating to Kaplan-Meier plots and survival estimates, but I haven't really been able to find anything to help with this specific scenario. Sometimes, when ...
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26 views

Alerting framework for incoming traffic using mean or standard deviation

Currently I put hourly traffic (total number of input requests) of my website in a MySQL table. I keep data for the last 90 days. I want to check every hour, lets say 6th hour, that whether the ...
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42 views

Categorizing a continuous predictor?

If you had to split a continuous (independent) variable ranging from 0 to 9 and reflecting the number of x (e.g. number of cigarettes smoked), would you rather do: Median split (but then also ...
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72 views

Median-computation (“grouped median”). Problem with gmedian-computation in SPSS

In my basic-statistics course I wanted to delve deeper into the problem of the (grouped) median-computation and did some computations using SPSS. The protocol seems to indicate either a different ...
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3answers
105 views

How to compare the distributions of two variables

The attached figure plots the distributions of two variables. I want to demonstrate statistically how closely the the two distributions match each other. What is the best way of doing this?
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1answer
39 views

How to quantify the difference of each value with respect to the median of a list of values

I have a list of 7 numbers in the range [0-1]. I have a median of all of them. I would like to quantify how much different each number is from the median. Probably it is a stupid question but how can ...
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1answer
37 views

Representative transaction KPIs - what method to chose (average, median…) / how?

In my dataset i have about 30k of transactional data. For analysis, I want to show the end user some important KPIs: Average of transactions with loyalty cards Average turnover of these transactions ...
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1answer
412 views

Is the median a “metric” or a “topological” property?

I apologize for the slight abuse of terminology; I hope it will become clear what I mean below. Consider a random variable $X$. Both the mean and the median can be characterized by an optimality ...
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42 views

How to choose the observation with the median value when there are an even number of observations?

Obviously, in most circumstances, you would just take the mean of the two middle values. However, imagine a dataset of 100 countries. You want to know which country has the median household income. ...
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164 views

Why is it so uncommon to report confidence intervals for medians?

Why is it so uncommon to find confidence intervals reported in papers from applied sciences? I work mostly on Computer Science, but often read papers from (Social) Psychology, Sociology and Urban ...
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47 views

Cauchy MLE Reliability of Asymptotic Results

I have the following regression model $$ p_i = x'_i\beta +s \varepsilon_i $$ with sample size $n \approx 150$ and 4 independent variables. I have reason to believe and $\varepsilon_i$ is distributed ...
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300 views

Approximate mean from .25, .5, .75 percentiles

If I have median (.5 percentiles), and the .25 and .75 percentiles, what is the best guess of the mean? If the .25 and .75 percentiles are in the middle of a probability mass with weight .5 (.25 on ...
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Medians of logged fold changes.

So I have a set of measurements from several studies consisting of fold changes between log2-transformed values between two groups, each calculated using the formula ...
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54 views

Mood's median test - an apparent paradox

I have collected some data about systolic blood pressure in kids. Altogether, I have collected 500 measurements of blood pressure - 300 measurements for girls and 200 measurements for boys. The ...
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1answer
45 views

Is it possible to compute the mean/median of an variable by a contingency table?

A contingency table contains the frequencies of two discretized variables. To be more specific, the discretization is done by splitting the spectrum of a signal into equal width intervals. Is it then ...
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69 views

What does it mean if the median or average of sums is greater than sum of those of addends?

I'm analyzing the distribution of network latency. The median upload time (U) is 0.5s. The median download (D) time is 2s. However, the median total time (for each data point, T = U + D) is 4s. What ...
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2answers
186 views

Which is better, replacement by mean and replacement by median?

I'm doing a project that involves replacing missing values in a set of data (first time doing this). This is involves using to methods "replacement by mean" and "replacement by median" to fill in the ...
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140 views

Reporting Mann Whitney test rejecting the null hypothesis, but samples have equal medians

I'm using the Mann Whitney test to verify if two population samples are equal. If the p-value is less than alpha (in this case, 0.05) I reject the null hypothesis and use the median of each population ...
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1answer
31 views

Random variables, inequalities involving them and medians thereof (II)

I have a continuous function $A$ for which it holds that: $$x\in S\implies A(x)<0$$ $$x\in T\implies A(x)>0$$ Of course, $S$ and $T$ don't intersect. Now consider two continuous ...
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57 views

Random variables, inequalities involving them and medians thereof

I have three facts which I know to be true and I am wondering if together they logically imply a fourth one (or not!). Consider $F_x$ and $G_y$ two continuous, uni-modal distributions on ...
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2answers
170 views

Which notation should be used for the mean, SD, and median: mean±SD or mean (SD)?

I usually use mean±SD notation for reporting values. I know that many people use mean (SD) notation and I understand why. Right now in the document I am writing I am also reporting medians but I ...
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34 views

Q1: Median Split and Q2: repeated measures multiple regression analysis

Question 1: I have performed a pretest in order to analyse which products are considered to be hedonic or utilitarian based upon characteristics. These characteristics were rated with a Likert scale. ...
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1answer
128 views

Two different definitions of a median

I read from the book "Introduction to the Practice of Statistics", The International Seventh Edition, page 31 that "The $\textbf{median $M$}$ is the midpoint of a distribution. Half the observations ...
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1answer
49 views

Why is the CI in the median larger then the CI in the mean?

if I generate sample of normally distributed values (N=100, Mean of 10, STD 2.5) Then I calculate the mean with confidence intervals and the median with confidence intervals of the sample I get: A ...
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1answer
462 views

How to calculate the median age of a population?

I want to calculate the median age of a population. Consider the following example data (downloaded from Statistics Canada's CANSIM database, Table 051-0001): ...
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28 views

Using geometric mean to take median of an even number of data points

When taking the median of a data set consisting of an even number of data points, generally the arithmetic mean of the two middle points is taken. Suppose a set of data points has a suspected ...
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1answer
2k views

How to find average and median age from an aggregated frequency table

I am using excel and I am trying to find both the average age and median age. I have two columns. 1 for the category and the other for the number of people in each category. ...
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173 views

When would we use tantiles and the medial, rather than quantiles and the median?

I can't find definitions for either tantile or medial on Wikipedia or Wolfram Mathworld, but the following explanation is given in Bílková, D. and Mala, I. (2012), "Application of the L-moment method ...
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Calculating the highest of overlapping sets

My data set looks like the following: I have information about a large number of devices. For each device, I also have the data consumed by an application per day. Note however, all the devices ...
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732 views

Is the median a type of mean, for some generalization of “mean”?

The concept of "mean" roams far wider than the traditional arithmetic mean; does it stretch so far as to include the median? By analogy, $$ \text{raw data} \overset{\text{id}}{\longrightarrow} ...
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1answer
59 views

Continuous random variable and median problem

The definition of median, $m$, for a continuous random variable $X$ is $$P(X\leq m)=P(X\geq m)=\int_{-\infty}^m f(x)\text{d}x=\int_{m}^{\infty}f(x)\text{d}x=\frac{1}{2}$$ where $f(x)$ is the pdf of ...
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1answer
185 views

For what (symmetric) distributions is sample mean a more efficient estimator than sample median?

I have labored under the belief that the sample median is more robust measure of central tendency than the sample mean, since it ignores outliers. I was therefore surprised to learn (in the answer to ...
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2answers
244 views

Reporting Results of Mann-Whitney U Test - Means vs Medians

I had a question yesterday that I got a bunch of great responses on. I have, hopefully, a quicker question here. There is a debate in the literature regarding reporting means vs medians in a ...
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666 views

Which converges faster, mean or median?

If I draw i.i.d. variables from N(0,1), will the mean or the median converge faster? How much faster? To be more specific, let $x_1, x_2, \ldots $ be a sequence of i.i.d. variables drawn from ...
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21 views

Accuracy of approximation to sample median

Suppose we sample $n$ real numbers uniformly on $[a, b]$. We wish to find the sample median, but we will approximate it as follows: randomly choose a subset of the sample of size $k$ with uniform ...