# Questions tagged [median]

For questions about the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

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### Median of a Poisson-Binomial distribution

Let $Z$ be a random variable following a Poisson-Binomial distribution with parameters $(p_1, \dots, p_n)$ such that $\sum_{i=1}^{n}p_i > \frac{n}{2}$. Consider the following two properties: -If $n$...
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### Number of possible histograms of a test given that the median is 60

There is the following problem I'm having a hard time coming up with a Sigma-less solution to: If $360$ have taken a test, and grades can range from $0-100$ (inclusive), how many possible histograms ...
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1 vote
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### Inequality with medians

It is well known that in any triangle $\triangle ABC$ with side lengths $a,b,c$ and medians $m_a,m_b,m_c$ inequality $$\frac{3}{4}(a+b+c)<m_a+m_b+m_c<a+b+c$$ holds. ...
1 vote
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### A possible error in a math question of 2022 Brazil's ENEM, a equivalent to US's SAT

This is a rather simple question, and it may seem like a physics question, but it actually belongs to a math test. I'll translate it into English first and then reproduce the Portuguese version. "...
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### Median of Mixed Random Variable [closed]

I have the following CDF $$F_X(x) = \begin{cases} 0 & x < 0 \\ 1 - p e^{-x} & x \geq 0 \end{cases}$$ I found $\mathcal{X} = \{ 0\} \hspace{0.1cm} \cup (0,\infty)$ with $P(X = 0) = 1-p$ ...
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### Finding the distribution of the median of three independent random variables

Problem: Let $Y_1$, $Y_2$ and $Y_3$ be independent and uniformly distributed over the interval $(0,1)$. Let $Y_0$ be the median of the three variables. Find the probability density for $Y_0$. Answer: ...
• 4,064
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### Medians from rows of numbers

You have three rows of numbers, $(a_1,a_2,a_3), (b_1,b_2,b_3), (c_1,c_2,c_3)$, each in the range $[0,1]$ and summing up to $1$. If the medians of the three columns are $m_1,m_2,m_3$ with sum $m$, you ...
1 vote
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### The Medians of Lipschitz Functions on $(X,d,\mu)$ (Existence and Uniqueness)

Let $\varphi:(X,d,\mu)\to \Bbb R$ be a Lipschitz function, where $\mu$ is a probability measure on the metric space $(X,d)$. The median $m_\varphi$ of $\varphi$ is defined as the real number such that ...
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### median of multivariate Gaussian

I have the following basic question. I am interested in the spatial median of mutlivariate Gaussian random variable. Let $d$ be the dimension and let $\mathcal{N}(\mu,I_d)$ denote the multivariate ...
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### Finding the median value, am I missing something?

If I'm not missing anything, please tell me. This is my understanding of the definition of a statistical mean: Using the definition: The median is the middle value that separates the lower and higher ...
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### Maximum Likelihood Estimation of median for an exponential distribution

Given data x1, ... xn i.i.d. with exponential distribution and unknown parameter λ, determine maximum likelihood estimation of θ given the observed data where theta is the median of the distribution. ...
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### Robustness of Geometric Median to Change of k Points

Let $N \in \mathbb{N}$ be a constant. Let $B_d(1)$ denote the ball of radius one in $\mathbb{R}^d$. Let $(a_1,\dots,a_N)\in (B_d(1))^N$ and $(b_1,\dots,b_N)\in (B_d(1))^N$ be two sets of N data ...
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1 vote
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### Finding the median value from a PDF

Suppose that the time in days until hospital discharge for a certain patient population follows a density $f(x) = (0.5)\exp(-x/2)$ for $x > 0$. What is the median discharge time in days? I reason ...
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### Global minimum is attained at the median [duplicate]

I have the following homework problem. Let $(x_1,x_2,\ldots,x_n)$ be an increasing sample of size $n$. Show that the function $$f: x\mapsto \sum_{k=1}^n |x_k-x|$$ obtains a global minimum at the ...
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