# 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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### Using the Median to Estimate a Parameter

I am trying to use the Median to estimate the value for the parameter $a$ in the following PMF. \begin{equation} \label{eq1:givenpdf} \mathbb{P}\left[X=\frac{a}{n}\right] = \frac{36}{5}\frac{n^2}{\...
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### Is it fine to present Median and IQR for normally distributed data?

I have data with more than 25 variables. Some of them are normally distributed and others are not. Instead of checking each variables for normal distribution and presenting ...
1 vote
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### Median survival time in individual models separated by a variable vs a single model with covariate

Suppose I wish to find the median survival time of each sex in lung data. ...
1 vote
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### qrule mathematic interpolation in quantile estimation in R survey package

I've been having difficulty understanding the code for qrule_math in the survey package. This document here says this about it: ...
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### Skewed distributions: choosing the median or average

Goal: To determine whether to use the median or average (or a weighted combination of the two) from a data set based on whether ...
42 views

### Interpretation of kruskal wallis test results

Hello I have run a kruskal wallis test to compare the median between three groups as in this picture below: I know what median value and p value are but: IQR is the spread of data but what is used ...
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### Interquartile ranges of 2 groups in meta analysis

I am performing a meta analysis of mutliple trials (Intervention vs. Placebo) and wanted to describe the baseline characteristics in a table. Some trials report continous variables as medians and ...
26 views

### Difference between geometric distribution expectation and 1 - failure with Binomial

I'm trying to understand a simple problem: How many times you'd need to roll two dice to get two ones in a single roll. One way I see this is as a problem the geometric distribution describes. You ...
137 views

### The variance of the weighted median and optimal weights

The median $\tilde{\mu}$ of a sample in many ways is analogous to the sample mean $\mu$. Both are an estimate for the population median or mean respectively, and both approach a Gaussian distribution ...
1 vote
127 views

### Standard deviation on Bimodal data

Standard deviation, whilst it is often used on normal distributions, is it a useful statistic on global temperature, both daily and yearly, given that weight of the data is towards the ends of the ...
14 views

### Should I use Mean or Median? [duplicate]

I am analyzing a set of data (results) that does not follow Normal distribution or any known distribution. In this case, is it better to use (mean) or (median) to describe the result? Thanks
1 vote
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### weighted median result is integer

I am computing the weighted median for a dataset using the R reldist package. The input data are integers but my result is an integer number too. Should't my result ...
201 views

### Statistics to use on Bimodal data

What summary statistics, mean, median, standard deviation, etc. should be used on a skewed, bimodal, dataset and why? These are almost U shaped in a histogram layout with a slight preference for lower ...
534 views

### Is it possible to calculate median value and interquatile range for a set of numbers containing a range or inequalities?

I am trying to make simple median and IQR calculations that involve numbers (in percentages) appearing in a range and inequalities in addition to whole numbers. My sample dataset looks like this: 5, ...
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1 vote
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### What can you infer from being always above the median and the mean?

In the context of a national competition, what can you infer from being always above the median and the mean in all modules? Say, that all marks are normally distributed, does it always mean that for ...
151 views

### Median of the sum vs. sum of the median for Gaussian variables

This is a problem I stumbled upon in my research. Consider $n$ Gaussian random variables $x_i \sim \mathcal{N} (\mu_i, \sigma_i^2)$, each with its own mean $\mu_i$ and variance $\sigma_i^2$. Can we ...
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### Comparing Star Ratings

Data Illustration NOTE: I do not have a stats background. I'm pretty sure I'll use some terminology incorrectly. I have come across several approaches via Python/SQL that I would like to confirm as ...
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### Standard deviation estimator without outliers

I have samples that are distributed like this: I want to calculate the standard deviation (or similar) of the main peak without the outliers. Of course I can do this just applying a cut at, say, -5µ. ...
1 vote
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### Symmetric distribution with defined mean: is the median always unbiased for the mean?

Let $X_1,\cdots,X_n\overset{iid}{\sim} F_X(x)$ be a random sample from a symmetric distribution with a defined mean. If need be, assume that $n$ is odd and that $F_X(x)$ is continuous. Is it always ...
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### How to propagate standard error of medians

I am interested in median-to-median propagation of standard error: The values in my variable (say, $Y$) are all medians (of something, say, $X$), and are each associated with a standard error. Next, I ...
3k views

### Why is the Median Less Sensitive to Extreme Values Compared to the Mean?

I am sure we have all heard the following argument stated in some way or the other: For a given set of measurements (e.g. heights of students), the mean of these measurements is more "prone"...
102 views

### What is the meaning of using median instead of mean to calculate sample variance?

I am reading the source code of MAGeCK 0.5.9.5 which is a popular software for analyzing CRISPR knockout screen data. In its mageckMathFunc.py, it calculates "mean" and "variance" ...
1 vote
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### Proper way to compute stats of multiple box plots

If I have 10 sample distributions that I've calculated the box plots for, what is the proper way to summarize that into a single box plot? I should add that the sample distributions are not drawn from ...
1 vote
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### Mean being systematically different (unbiasedness) vs median being systematically different

I am going to get a finite sample (size $2n+1$) of data from some process which is not symmetric about the median. I want to use either the mean or the median as a summary statistic. If I choose the ...
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### Comparing average user order value between marketing channels - Do you average at the user level first or just at the channel level, or both?

I feel like this might be obvious, but I'm having trouble figuring out how to approach this. I have order-level data for various users that came from multiple marketing channels. I want to compare the ...
### How to find the median of Bernoulli trials and $\bar{X} = (X_1 + X_2 + X_3)/3$?
Assume $X_{1}, X_{2}$ and $X_{3}$ are independent Bernoulli trials with $p=0.5 .$ Let $\bar{X}=\left(X_{1}+X_{2}+X_{3}\right) / 3$ and $M=\operatorname{median}\left(X_{1}, X_{2}, X_{3}\right)$. (a) ...
Given a set of integers $S = \{1, 2, 3, ..., n\}$ I draw uniformly at random without repetition $m$ integers a large number of times ($1 \leq m \leq n$). For each of these samples (each of size $m$) I ...