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.

Filter by
Sorted by
Tagged with
2 votes
2 answers
82 views

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}{\...
user avatar
0 votes
0 answers
33 views

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 ...
user avatar
  • 841
1 vote
0 answers
17 views

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. ...
user avatar
  • 147
1 vote
1 answer
46 views

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: ...
user avatar
0 votes
0 answers
36 views

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 ...
user avatar
  • 101
0 votes
1 answer
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 ...
user avatar
2 votes
1 answer
23 views

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 ...
user avatar
  • 37
0 votes
0 answers
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 ...
user avatar
0 votes
2 answers
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 ...
user avatar
1 vote
0 answers
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 ...
user avatar
  • 17
0 votes
0 answers
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
user avatar
1 vote
1 answer
15 views

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 ...
user avatar
  • 284
-1 votes
1 answer
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 ...
user avatar
  • 17
8 votes
3 answers
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, ...
user avatar
  • 85
2 votes
0 answers
23 views

What order of power mean best estimates the median of a gamma distribution?

Suppose we have a gamma-distributed random variable $X$ whose shape/scale parameters are known to be $\alpha$ and $\beta$. What order $p$ for the sample power mean $\hat M_p[X]$ minimizes $$ (\mathcal{...
user avatar
  • 3,546
0 votes
0 answers
9 views

Which type of quantiles are safest to report in R?

With this topic in mind: If there is no censoring, can be the naive 3rd quantile different from the one calculated with from the Kaplan-Meier? I'm wondering which one is the safest option. Of course I ...
user avatar
1 vote
1 answer
30 views

If there is no censoring, can be the naive 3rd quantile different from the one calculated with from the Kaplan-Meier?

I know, that the median survival time calculated from the Kaplan-Meier estimator is equal to the "naive" descriptive median of the survival time when no censoring in data occurs. Does it ...
user avatar
0 votes
0 answers
19 views

finding central tendency

The following table presents frequency distribution of teachers of 1 year: Rank ----------Frequency Professor ------------7 Assoc Professor ------4 Asst Professor--------3 Instructor -----------5 ...
user avatar
  • 1
0 votes
0 answers
45 views

Error propagation for the median of time-series

Let's assume that we have a set of different measurements from an instrument of a parameter of a parameter P that changes with time during a time period t. Let's also assume that the measurements ...
user avatar
8 votes
1 answer
252 views

Median of the squared difference from the median of a Cauchy random variable

Motivation One of the classic challenges with Cauchy random variables is that their moments are not finite, and I even recently learned that Cauchy principal values of even moments of Cauchy random ...
user avatar
  • 3,546
1 vote
0 answers
36 views

On the naming of two different median estimators

Assume that $X \sim \mathcal{E}(\lambda)$ is, for example, exponential with $\lambda > 0$. Given a data sample $X_1, \ldots, X_n$, assume that I want to estimate the median of $X$. Consider these ...
user avatar
  • 632
0 votes
0 answers
20 views

Is there a 1 sample t test equivalent for the median? [duplicate]

I want to check whether the MEDIAN of a sample is statistically significantly different from 0. What test could I use to do this? I know that a 1 sample t test would do this for the mean... Thank you
user avatar
  • 1
28 votes
2 answers
3k views

Can mean be less than half of median if all numbers are non-negative?

I feel like I might be missing something dumb, but in a set of non-negative numbers, is it possible for the mean to be less than half of the median? Example: there are 999 numbers and we are told that ...
user avatar
  • 383
5 votes
1 answer
644 views

Show that, for any real numbers a and b such that m ≤ a ≤ b or m ≥ a ≥ b, E|Y − a| ≤ E|Y − b| ,where Y be a random variable with finite expectation

Let $Y$ be a random variable with finite expectation, and $m$ be a median of $Y;$ i.e., $P(Y \le m) \ge 1/2$ and $P(Y \ge m) \ge 1/2.$ Show that, for any real numbers $a$ and $b$ such that $m\le a \le ...
user avatar
1 vote
1 answer
23 views

Possible pitfalls/accuracy issues using a weighted average of a median

I am trying to aggregate data for testing for multiple data sets. It is unrealistic to load the entire data set (which is composed of multiple subsets of varying length) into memory to calculate a ...
user avatar
0 votes
0 answers
34 views

Nonparametric hypothesis test for ratio of medians

I have 4 distributions: A1, A2, B1, and B2. I would like to test whether there is a significant difference between median(A1)/median(A2) and median(B1)/median(B2). While I can calculate propagated ...
user avatar
  • 1
0 votes
0 answers
92 views

Sample Geometric Mean and Sample Median of a Log-Normal Random Variable

The Wikipedia article for the log-normal distribution states that the geometric mean and median of a log-normal random variable are equal. However, when I simulate log normal data with a small N, ...
user avatar
  • 43
1 vote
1 answer
17 views

Median for grouped/ungrouped data [duplicate]

If I am given a series of, let's say, 50 observations, of a continuous data, for example, the height of some group of people: 165.23 cm, 134.28 cm, and so on, and I want to find the box plot, I need ...
user avatar
4 votes
2 answers
127 views

How to test statistical difference given only median and IQR?

If I only know the medians and IQRs from samples (along with the number of samples of each population) drawn from two distributions, how to test the medians of the two distributions are different or ...
user avatar
1 vote
1 answer
60 views

mean + 95 % confidence intervall versus boxplots

I am wondring about the use of boxplots versus mean with 95 % in a figure? A boxplot will give you median and you can add a notch to show the 95 % CI for the median so it is quick and easy to compare ...
user avatar
  • 11
1 vote
2 answers
43 views

Representation of population data mean/median (similar to BMI/age curve)

I want to represent my data (n=150 samples with a curve of value over time, similar to BMI representations in figure). Possibilities are either mean/std and median/percentiles. The question are: Can ...
user avatar
0 votes
0 answers
14 views

Standard error for the median value of estimated means

I apologize in advance if this is a very basic question, but I can't find a straight answer so far. I have a country level dataset that contains the means and standard errors of a health indicator ...
user avatar
0 votes
0 answers
11 views

Interpretation of LAD under model misspecification

Suppose we have $n$ i.i.d. draws of $y_i$ and $x_i$ and consider a linear equation: $$y_i =\beta_0 +\beta_1x_{1i}+...+\beta_kx_{ki}+u_i =x_i'\beta+u_i $$ A common assumption in OLS is $E[y|x]=x_i'\...
user avatar
0 votes
0 answers
16 views

How to test how accurate the quantile returned by quantregForest is?

Here is the example code from quantregForest. ...
user avatar
2 votes
4 answers
539 views

Why don't we automatically have outliers when mean and median differ strongly?

Assume you have a data set with information on income of all students in the lecture. The mean value is 1500\$. The median value is however only 800\$. Which of the following conclusions is wrong? The ...
user avatar
0 votes
0 answers
17 views

How to aggregate time-bucketed values across a set

I am trying to perform some analysis over a dataset of multiple projects. This dataset has multiple months of data for every single project. Because projects occur at different times and have ...
user avatar
  • 111
4 votes
0 answers
35 views

The use of a pseudo variance $\int_{-\infty}^\infty \text{sign}(x) (x-\mu)^2 f(x) dx$ in place of $\int_{-\infty}^\infty (x-\mu)^2 f(x) dx$

Difference between odd central moments and even central moments When we compute $n$-th central moments $$\mu_n = \int_{-\infty}^\infty (x-\mu)^nf(x) dx$$ then there is a difference in interpretation ...
user avatar
1 vote
0 answers
24 views

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 ...
user avatar
  • 11
8 votes
1 answer
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 ...
user avatar
  • 183
0 votes
0 answers
18 views

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 ...
user avatar
0 votes
1 answer
28 views

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. ...
user avatar
1 vote
0 answers
39 views

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 ...
user avatar
  • 32.4k
0 votes
1 answer
31 views

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 ...
user avatar
9 votes
10 answers
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"...
user avatar
  • 5,884
2 votes
1 answer
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" ...
user avatar
  • 21
1 vote
1 answer
35 views

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 ...
user avatar
1 vote
1 answer
22 views

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 ...
user avatar
  • 2,280
0 votes
0 answers
8 views

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 ...
user avatar
0 votes
0 answers
42 views

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) ...
user avatar
10 votes
2 answers
298 views

What are the properties of the distribution of medians from samples of a set of integers?

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 ...
user avatar

1
2 3 4 5
14