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Questions tagged [median]

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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Generate weighted median from activity per timespan

I have a set of data where I have a number of observations over the course of a year per individual. Generally speaking, I want to know the average activeness of the individuals that participated in ...
P.Weyh's user avatar
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6 votes
2 answers
324 views

Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript

I'd like to generate realistic sample data in javascript for monetary donations. I've chosen to model them as following the log normal distribution. I think a fairly intuitive way for a lay person to ...
michaelmcandrew's user avatar
2 votes
1 answer
55 views

mean of medians consistently differs from median

Disclaimer: my first question here. Background of the problem: I want to compare two distributions (n1 ~ 500 and n2 ~ 700), not normal and with different variances, but roughly unimodal. I decided to ...
Paul S's user avatar
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2 votes
0 answers
41 views

Are there known bounds for the median of a negative binomial distribution based on its parameters?

This seems like an innocent enough question to me, but I could not find a satisfactory answer when I did some digging. The binomial distribution has a closed form median and the Poisson distribution ...
ricewhitlam's user avatar
3 votes
2 answers
183 views

Distribution of medians of triplicate samples taken from Gaussian distribution

My Monte Carlo simulation seems to show that the standard deviation of the medians of triplicate samples taken from the Gaussian distribution approaches 2/3 of the SD of the original distribution. ...
Maciej Tomczak's user avatar
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Mean Index of deprivation score

I've created a python function which can return a subset of the 2019 Index of Multiple Deprivation scores representing the LSOA areas within a defined radius of a certain latitude and longitude. Here'...
elksie5000's user avatar
2 votes
3 answers
83 views

Does sample size affect the value of median?

I have two groups of A and B. Group A consists of 11 people and group B of 35 people. The results of one behavioral outcome measure is higher for the group B while logically it should be the other way ...
Lily's user avatar
  • 41
9 votes
3 answers
408 views

When does positive skew imply median<mean?

For a random variable $X$, the skew is defined as $S(X):={\frac {E\overline{X}^3}{(E\overline{X}^2)^{3/2}}}$, where $\overline{X}=X-EX$. It is often claimed that positive (resp. negative) skew implies ...
2 votes
0 answers
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Decision theory when distributions don't have a first moment? [closed]

Lets say that we are presented with two gambling opportunities and would like to decide between them in a decision-theoretic framework. For gamble 1, the cost is $1$ and the payoff is $X_1$ where $X_1 ...
QMath's user avatar
  • 451
1 vote
1 answer
35 views

How to calculate the median from a set of data where some of the data is sampled over unequal intervals of time?

Suppose you are measuring how much money you spend each calendar week (Monday to Sunday) over the course of March 2024 and the results are as follows: Date range Money spent ($) 03/01 to 03/03 0 03/...
SSS's user avatar
  • 13
11 votes
1 answer
960 views

Deviation between Mean and Median

If I have a mean of 15 and median of 10, is there a term for the difference between these? Can you use this difference of 5 for anything valuable statistically?
greenguy's user avatar
  • 111
8 votes
3 answers
1k views

Median of a set with even number of elements

Consider the following sample of numbers: 9,18,11,14,15,17,10,69,11,13 Since there are 10 elements, the median of the set would be (13+14)/2 = 13.5 However, is it wrong to say that median is one of 13 ...
user avatar
4 votes
1 answer
109 views

Probability mass function of sample median (Bootstrap)

Consider a sample $X_1,X_2,...X_n\overset{\text{iid}}{\sim}F$. Let $T_n=F_n^{-1}(1/2)$ be the sample median where, $F^{-1}(x)=\inf\{t:F(t)\ge x\}$ and $F_n(y)=\frac{1}{n}\sum_{i=1}^n\mathbb{I}(X_i\le ...
reyna's user avatar
  • 385
-2 votes
2 answers
89 views

using mode or median

A survey is conducted among high school students, consisting of 30 questions designed to evaluate their levels of social media addiction. The responses to these questions are aggregated to calculate a ...
Sundown Brownbear's user avatar
2 votes
1 answer
30 views

Can ANOVAs or Student tests be conducted on any summary statistic at the individual level?

I am wondering if ANOVAs or Student tests can be performed on any summary statistic of performance at the individual level without any effect on type 1 and type 2 error. For example, consider a simple ...
user1363251's user avatar
1 vote
1 answer
68 views

How is median of the difference calculated in Mann Whitney U test (TOST)?

I'm running wilcox_TOST in R and below is the result. If Mann Whitney U test is equal to Wilcoxon Rank Sum Test and considering what this test does (e.g., ranking the data and summing the ranks etc.,) ...
Lily's user avatar
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4 votes
1 answer
68 views

What is the hypothesis test I've used, or what should I change to fit a "common" one?

I've had discussions with several professors, as well as scouring the internet (and chatgpt), trying to improve the description of the methods I've used, or to look for better ones. I'm hoping a wider ...
Adam Jones's user avatar
1 vote
0 answers
71 views

Converting median absolute deviation to standard deviation

I'm working on some medical research and I'm wondering what is the most straightforward method to convert median and median absolute deviation (MAD) to mean and standard deviation. If anyone has any ...
Yomna's user avatar
  • 21
4 votes
3 answers
756 views

Mann Whitney test problem

I have data from 4 populations : A (n=16), B (n=16), C (n=14) and D (n=16). Data from A and B are not normally distributed. Data from C and D are normally distributed. All data passed the Levene's ...
Steph Pauline's user avatar
0 votes
0 answers
49 views

Should data be centered at $1$ before applying Box-Cox transformation?

Let's suppose that we perform Box-Cox transformation in R for the following data ...
Adam Bogdański's user avatar
2 votes
1 answer
72 views

How to consider independent samples in a mixed-design experiment?

I collected data from an experiment with a mixed-design, specifically a 2x3x4 mixed-design, where the factors are populations (2 levels), conditions for the first population (3 levels), and conditions ...
Andrea Gulli's user avatar
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0 answers
54 views

Compare median time between different groups and years

I want to investigate whether there is a difference in median waiting time between different groups in different year. I'll try to explain as best I can. My data looks like this: Year Country Waiting ...
Jam.Wil's user avatar
  • 77
0 votes
0 answers
36 views

One-sided test for the difference of medians in two independent samples

I have two independent samples 1 and 2, and want to test a null hypothesis that the median of sample 2 is lower or equal to the median of sample 1. Is there a non-parametric test for that?
quant_dev's user avatar
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1 vote
1 answer
51 views

Can r.m One-way ANOVA be used to compare differences between groups, if those groups are made up of median values?

Essentially, I'm trying to see whether a drug affects a latency measure. I have $n=10$ mice, each with $15$ individual latency recordings (in seconds) per drug dose (repeated measures design). Most of ...
louiseinger's user avatar
1 vote
1 answer
68 views

Descriptive Statistics for Zero-Inflated Dataset

Just as titled, I'm curious as to what should you choose to represent a measure of central tendency for a zero-inflated vector or such. My background says go "mean" if normally distributed, &...
Derf's user avatar
  • 295
2 votes
3 answers
373 views

Expected value and variance of median

Suppose $Y|\Lambda\sim U(0,\lambda)$ with $\Lambda \sim U(0,1)$. If there is sample with size $n$ of $Y$ (To simplify, assume $n$ is odd, so $n=2m-1$). How do I calculate the expected value of median (...
skewr's user avatar
  • 23
2 votes
0 answers
32 views

Adjustment for confounders

I have some epidemiological data, relating to the prevalence of obesity at UK local authority level. For the purpose of exploration I want to derive the median obesity prevalence. However, I need to ...
j.rahilly_UCL's user avatar
4 votes
1 answer
534 views

Is it acceptable to take the mean of a bunch of median values?

I use a Bayesian latent variable model to construct a time series cross-sectional measure of corruption for all countries in the world from 1960 to 2010. For each country-year observation, I obtain a ...
w5698's user avatar
  • 151
0 votes
1 answer
232 views

Can I calculate median survival time and its confidence interval using the Kaplan-Meier curve? I don't have available raw data

I am conducting a meta-analysis to compare the differences between Group A and Group B by measuring the pooled Hazard Ratios (HRs) for the median Progression-Free Survival (PFS) and Overall Survival (...
HAHA's user avatar
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6 votes
3 answers
2k views

"Weighted Median": statistical properties and connection to the sample variance

Suppose we only have the following information: A set of sample means : $\bar{x_1}$, $\bar{x_2}$ ... $\bar{x_k}$ The sample size used to calculated each sample mean: $n_1$, $n_2$ ....$n_k$ The ...
stats_noob's user avatar
7 votes
2 answers
814 views

Can any quantity be bootstrapped?

Suppose we have the median incomes of 150 different countries (in each country, the median income was calculated on a sample of people) - we don't have the individual incomes of each person in these ...
stats_noob's user avatar
2 votes
0 answers
91 views

Mean of Medians? Median of Means?

This is a question I have wondered about for a long time and have never been able to find a full mathematical explanation behind this. Suppose there are 100 countries. As an experiment: We give Person ...
stats_noob's user avatar
2 votes
2 answers
121 views

How do I compare my data with the general population data in SPSS

My purpose is to compare my data with the general population data derived from a published report. I can only extract mean, median, 5th, 95th and 97.5th percentiles from it. Also, My data is non-...
user392974's user avatar
2 votes
2 answers
409 views

Is distance from the median instead of from the mean in standard deviation calculation meaningful in case of data with outliers?

I'm borrowing from the idea of Mean of absolute deviation around the median (https://en.wikipedia.org/wiki/Average_absolute_deviation#Mean_absolute_deviation_around_the_median). Would calculating ...
hihik's user avatar
  • 21
2 votes
2 answers
2k views

How to set the age range, median, and mean age

Thank you for reading my question. I used the clustering method to classify the age of the houses. This graph show the clustered results. I should to get the age range, mean age, and median age for ...
user21268575's user avatar
1 vote
1 answer
46 views

Scaled median shift between two observation when median is close to zero

I'm coming for a computer science background and statistics is not my forte, please bear with me. I have two revisions $R_1$ and $R_2$ each consisting of around 10000 processes $T_i$ (involving some ...
Pouya's user avatar
  • 111
2 votes
0 answers
81 views

Where is the number "0.963" in the paper "Why Isn't Everyone a Bayesian?" by Bradley Efron coming from? [duplicate]

This paper by Bradley Efron (also available here) concerning Bayesian vs. frequentist interpretation of probability contains an example I don't quite understand. It's on page two in the right column ...
Ludwig Neste's user avatar
0 votes
1 answer
229 views

In R Limma's `normalizeMedianValues` function, why is its operations preceded with a log transformation followed by an exponential transformation?

In the function normalizeMedianValues in the package limma, column counts are normalised such that their column medians are ...
SpikyClip's user avatar
1 vote
1 answer
647 views

How can I compare median survival times statistically based on Kaplan Meier curves/Log-rank test

I have a few question concerning the log-rank test and would be glad if anyone can answer these: First of all I am wondering which benefits one has when plotting KM curves of two groups if one already ...
user avatar
0 votes
1 answer
194 views

What is the correct interpretation of the Log-Rank test (Kaplan Meier Curves)

I am wondering how to correctly interpret Kaplan Meier Curves, the log-rank test respectively. I calculated a log-rank test to compare two survival curves and got an insignificant p-value from this. ...
user avatar
0 votes
2 answers
204 views

Logistic Regression: Median Imputing vs Mean Imputing

Missing values need to be imputed when performing logistic regression. Missing values are often imputed by the median. The mean is the BLUE (best linear unbiased estimator). But Median is robust to ...
PalimPalim's user avatar
0 votes
1 answer
54 views

Salesman Auditor problem: Which mean and median is correct? What is preferred?

Trip Days Expenses Expenses per day 1 0.5 13.50 27 2 2.0 12.00 6 3 3.5 17.50 5 4 1.0 9.00 9 5 9.0 27.00 3 6 0.5 9.00 18 7 8.5 17.00 2 Total 25.0 105.00 70 Question: The following data ...
A32589's user avatar
  • 3
3 votes
1 answer
193 views

How to transform t-statistic into a statistic using median and IQR?

I want to calculate similarity between various samples, but I'm limited to only knowing the IQR and medians. I came across a similar problem here but the top answer states that the newly proposed ...
Tadsz's user avatar
  • 31
2 votes
1 answer
255 views

How to calculate median and median absolute deviation of data with a function applied?

I have a set of data X containing members xi (these are pixel values). I need to calculate the median and MAD of f(X), where f is a color space transform from linear RGB to sRGB (i.e. f(x) = x^(1/2.2))...
Adrian K-B.'s user avatar
0 votes
0 answers
21 views

Overall Average greater than Individual Category averages

I am calculating Gender Pay gap using gross salaries for employees. I'm doing two things to be specific: Calculate Overall Gender pay gap for all the employees. (Taking all male/female employees to ...
Mikaal's user avatar
  • 1
9 votes
1 answer
950 views

When is the median-of-means estimator better than the standard mean?

The median-of-means estimator is often given as an alternative way to, given a sequence of IID random variables $X_1,...,X_N$, estimate the expectation value $\mathbb{E}[X]$ (see e.g. these pdf notes ...
glS's user avatar
  • 383
1 vote
0 answers
72 views

Why does one interested in modelling the distribution of median of random samples?

I was reading this article which introduce the families of distribution for the median of an random sample. However, the writer did not state the reason why one is interested in modelling the ...
fletcherwrw's user avatar
2 votes
1 answer
326 views

Why am I not able to correctly calculate the median survival time for the Weibull distribution?

The survival function for the Weibull distribution is: $S(t) = exp(-\lambda t^\alpha)$, $\lambda$ = scale parameter, $\alpha$ = shape parameter If I wanted to calculate the median survival time, I ...
Dan W's user avatar
  • 303
3 votes
1 answer
200 views

Why is the pseudomedian better than the median in a Wilcoxon test?

The wilcox.test function in R calculates the pseudomedian and a confidence interval when conf.int=TRUE. In this question, ...
kidokin's user avatar
  • 157
0 votes
0 answers
154 views

Kruskal-Wallis Test - medians are same but result is significant?

I have run a Kruskal Wallis test in my dataset and have a significant overall result (p<<0.001). However, since the medians for my categories are the same, I can't work out the direction of the ...
nina's user avatar
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