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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Mean,Median and Mode [on hold]

Responses to a survey question about eye color are coded as 1 (for brown), 2 (for blue), 3 (for green), 4 (for hazel), and 5 (for any other color). Does it make sense to find the mean, median, or ...
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71 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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31 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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20 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
382 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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1answer
30 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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144 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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38 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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2answers
248 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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4 views

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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29 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
34 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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1answer
49 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
106 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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0answers
67 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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1answer
55 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
135 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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23 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
111 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
41 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
78 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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23 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
695 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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1answer
128 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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602 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
57 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
113 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
91 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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1answer
629 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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18 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 ...
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1k views

Quarter is to quartile as half is to…?

Is there one word to describe the sections of data on either side of the median? I'd guess "half", but it seems like there ought be something better...
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Is the mean smaller than the median

The mean and the median selling prices of single-family homes were reported to be \$163,900 and \$210,900. The report was not clear about which was which. \$163,900 is the mean and \$210,900 is the ...
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Which statistical test should I use to compare the median values between two groups in my study?

I am doing a retrospective study comparing the effect of medication adherence on the length of a patient's illness. One group of patients took their medication compliantly, and I want to compare the ...
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1answer
111 views

How to test the median of a population?

I have a sample of 250 units. The distribution is asymmetric. I want to test a hypothesis that the median of the population is different from 3.5, so I think a one-sample test would be appropriate. I ...
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1answer
49 views

Question about the the median and the mode in skewed distributions

In intro statistics textbooks, the mode is typically described as least susceptible to skewness, followed by the median, which is in turn followed by the mean. The difference between the median and ...
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74 views

Extension of Median to big data integer distributions?

I am analysing big samples of integer values. Because they come from a non-symmetrical distribution (high positive skew), I prefer to use the median to characterise central tendency, not the mean. ...
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23 views

Repeat measures regress

I have a question about using regression for repeat measures analysis. I have a design in which each participant viewed 4 sets of pictures. 2 sets were positive and 2 were negative. There were 2 ...
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93 views

Bootstrapped BCa confidence interval of median (R package simpleboot) does not correspond with Wilcox.test p value

I am using R to compare the medians of two groups. Each individual has received a score of between 0 and 100. Both distributions are very skewed. The median of group A (n=33) is 87.8 (IQR 75.1, 100.0) ...
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46 views

Finding the median distribution of many distributions?

I have many customers. Each generates his own distribution of shopping times. Each customer thus has their own empirical distribution of shopping times. If I want to get a sense of the average ...
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Are there non-trivial settings where the MAD statistic has a closed-form density?

The MAD statistic of an iid sample $(x_1,\ldots,x_n)$ is defined as the median of the absolute deviation from the median: $$ ...
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960 views

Does mean = median imply that a unimodal distribution is symmetric?

For a unimodal distribution, if mean = median then is it sufficient to say that distribution is symmetric? Wikipedia says in relationship between mean and median: "If the distribution is ...
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1answer
62 views

Comparing medians from two groups

Hi: I have a survey where respondents were asked to rank a series of statements in terms of how much they agreed with them. There were seven statements. So, for each of seven statements, each ...
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1answer
70 views

MAD formula for outlier detection

Does anyone know what is the name of this formula? $$M_i = \displaystyle\frac{0.6745(x_i - \hat{x})}{\mathrm{MAD}}$$ where $\textrm{MAD}$ is the median absolute deviation and $\hat{x}$ is the median ...
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1answer
325 views

When if ever is a median statistic a sufficient statistic?

I came across a remark on The Chemical Statistician that a sample median could often be a choice for a sufficient statistic but, besides the obvious case of one or two observations where it equals the ...
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1answer
69 views

Inconsistent outcomes of boostraped hypothesis tests on max and median

I am trying to make an hypothesis test using bootstrapping. I compute a quantity Q from a sample set (the exact calculation should not be relevant, but let's say ...
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1answer
418 views

What are the pros and cons of using median imputation to handle missing value?

I have to choose between median or mean imputation to handle missing values. I feel median imputation will work better because it is a number that is already present in the data set and is less ...
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92 views

Confidence intervals for median

I have a distribution of samples with a small number of values in each one (less than $10$). I have calculated the median for each sample, which I want to compare with a model and obtain the ...
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44 views

Statistical nomenclature: what family does “head” and “tail” - in the sense of data runs belong

If I look at mean, variance, skew and kurtosis they are nth moments. If I look at percentiles, quartiles, and medians they are order statistics. Both work together to make a textbook summary. The ...