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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
26 views

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 ...
MMH's user avatar
  • 638
0 votes
0 answers
57 views

Characterize a function given the average and the median

How to (1) obtain some examples for an $f$ function and/or (2) characterize the whole set of $f$ functions which has the following properties given $m$ ($\leftarrow$ the median) that $0 < m < ...
Bálint Sass's user avatar
2 votes
1 answer
45 views

Deducing an incorrect statement when the mean and median are given

$~a,~b,~c,~d$ are positive integers such that $a~<~b~<~c~<~d$ If mean and median of $~a, ~b, ~c,~d$ are $35$ and $39$ respectively, then which one of the following statements cannot be true? ...
Darshit Sharma's user avatar
8 votes
1 answer
180 views

How to approximate the median of the numbers in the first $n$ rows of Pascal's triangle?

How can we approximate the median of the numbers in the first $n$ rows of Pascal's triangle? (The top row is the $0$th row.) Using Excel, I made a graph of the natural log of the median against $n$, ...
Dan's user avatar
  • 16.5k
0 votes
1 answer
31 views

Finding value of m, where m is the bound of a pdf such that it gives the median value.

I have come across this question whilst doing my homework and would like to clarify on the value of m. The median of a continous random variable is given below. $\int_{-\infty}^{m}f(x)dx = \frac{1}{2}$...
Catt's user avatar
  • 53
2 votes
0 answers
165 views

distance between coordinate-wise median and geometric median

Let $N \in \mathbb{N}$ be a constant. Let $B_d(1)$ denote the ball of radius one in $\mathbb{R}^d$. For $i \in \{1,\dots,N\}$, let $a^{(i)}$ be a vector in $B_d(1)$. Define the geometric median of $a^...
MMH's user avatar
  • 638
7 votes
2 answers
258 views

If $a_1=1, a_n=|\cot a_{n-1}|$, then what is $\lim\limits_{n\to\infty}\text{median}\{a_1,a_2,\dots,a_n\}$?

I made up the following sequence: $a_1=1, a_n=|\cot a_{n-1}|$. What is $\lim\limits_{n\to\infty}\text{median}\{a_1,a_2,\dots,a_n\}$ ? My thoughts Here is the graph of $a_n$ against $n$, for $1\le n \...
Dan's user avatar
  • 16.5k
0 votes
0 answers
11 views

What is the term for median but use the geometric mean instead of arithmetic mean if there are an even number of values?

"Geometric median" seems like the obvious choice for "median (but for even number of values, take the geometric mean of the central two values instead of the arithmetic mean)", but ...
DanielM's user avatar
3 votes
1 answer
107 views

Is it possible to determine sides in a triangle given angle of median and opposite side length?

Questions In the triangle $ABC$ below we know the values of $\alpha$, $\beta$ and $\vert BD\vert$ in addition to knowing that AD is the median in the triangle, i.e. $\vert BD\vert = \vert DC\vert$. Is ...
GraftCraft's user avatar
4 votes
2 answers
211 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 ...
stats_noob's user avatar
  • 2,358
0 votes
0 answers
33 views

Finding the median

I have a following problem to solve: Let X be a random variable equal to a greater dice number when throwing two symmetric dices with values from 1 to 6. What is the median of X? I'm not quite sure if ...
Karol Wyrębkiewicz's user avatar
0 votes
0 answers
39 views

Can we find the probability using the mean and median ? If it is possible, how can we calculate it?

Lucas is a student who did a math competition against 2875 other people. His rank in his results will allow him to have a school. Everybody has distinct ranks. The nearest of 1 is better. The result ...
Jotadiolyne Dicci's user avatar
0 votes
0 answers
22 views

mean median and maximum product question

The mean and the median of nine distinct positive integers is 30. If the nine integers are such that their product is maximum, what is the product of the smallest and the largest integers? My attempt: ...
CountDOOKU's user avatar
  • 1,021
0 votes
0 answers
13 views

Statistical indexes order in an asymmetrical distribution

I was wondering what's the order between mode, median, arithmetic mean, geometric mean and harmonic mean in a distribution with positive skewness and in another with negative skewness. Which are the ...
Davide Barcella's user avatar
0 votes
0 answers
27 views

Median definition

Definition 6.1.1 (Median): We say that $c$ is a median of a random variable $X$ if $\mathbb{P}(X≥m)≥ 1/2$ and $\mathbb{P}(X≤m)≥ 1/2$. (The simplest way this can happen is if the CDF of $X$ hits $1=2$ ...
Saif's user avatar
  • 1
1 vote
1 answer
76 views

Consider equilateral triangle ABC and points D and E such that $BD = \frac{BC} 3$. If DF is perepndicular on AD, F belongs to AC, prove that EF = AD.

Consider equilateral triangle ABC and points D and E such that $BD = \frac{BC} 3$, DE belongs to (BC), and E is the midpoint of (AD). If DF is perepndicular on AD, F belongs to AC, prove that EF = AD. ...
user avatar
0 votes
0 answers
24 views

Looking for a distribution that mean and median are different.

I am looking for a distribution whose mean and median are different, preferably a distribution that share some properties with Gaussian distribution. I kinda know that there is something called skewed ...
Mq Hu's user avatar
  • 56
0 votes
1 answer
60 views

Expectation of median of independent and identically distributed exponential random variables

Suppose there are $n=2k+1$ independent and identically distributed exponential random variables with rate parameter $\lambda.$ Find $\mathbb{E}[median(X_1,\cdots,X_n)]?$ To do so, I found the density ...
sunspots's user avatar
  • 752
0 votes
1 answer
82 views

Probability of the median of three independent outcomes

I have come across a statistics problem that I want to solve but I don't know where to begin. The problem is the following What is the probability that the median of three random numbers between 60 ...
Keudn's user avatar
  • 11
0 votes
1 answer
40 views

If the median of $X$ is greater than the median of $Y$ then $\Bbb P(X>Y) \geq \frac14$

The median value of a random variable $X$ is $m$ if $\Bbb P (X \geq m) \geq \frac12$ and $\Bbb P (X \leq m) \geq \frac12$. Let $X$ and $Y$ be independent real random variables. Show that if the median ...
Ava Kate Lich's user avatar
1 vote
4 answers
215 views

HELP Let ABC an isosceles right triangle with ABC = 90°. Consider the point P on AB such that $\frac{PA}{PB}=2$. Show that $PA\cdot BP=BQ\cdot BG$.

Let ABC be an isosceles right triangle with ABC = 90°, M and N the midpoints of sides BC and AC, and G is BN intersected by AM. Consider the point P on AB such that $\frac{BM}{BP}=2$. If BN intersects ...
user avatar
1 vote
0 answers
50 views

Maximum Likelihood Estimation (absolute value)

Im currently struggling on a problem. Let X1, . . . , Xn be a random sample of a random variable that has a pdf: $$f(x)=\frac{1}{2}\cdot e^{-\left |x-\theta \right |}, \infty <x<\infty $$ And ...
Jacob Larsson's user avatar
1 vote
2 answers
101 views

HELPP... Prove the equivalence: ACB = 30 only if BD = 2*MD

Please help mee!!!!!! In triangle $ABC$, $BAC=90^\circ$, $M$ is its middle $ [BC]$ and $BD\perp AM$, $D\in(AC)$. Prove the equivalence: :: $$ ACB = 30^\circ \iff BD = 2\cdot MD $$ You can see my ...
user avatar
0 votes
1 answer
103 views

Finding the median of the total number of die rolls

Question A fair die is to be rolled repeatedly until a six comes up. Find the median of the total number of rolls given that five comes up on the first roll. My working Clearly, this follows a ...
Ethan Mark's user avatar
  • 2,147
2 votes
0 answers
186 views

Median of three numbers... but not the typical way

Let's say I have three numbers $a$, $b$, and $c$. To find the median of these three numbers, you order them from least to greatest, then take the second (middle) number. For example, if the numbers ...
Tyrcnex's user avatar
  • 572
0 votes
0 answers
35 views

Are median filters nonexpansive operators?

Let $m:\mathbb{R}^n \rightarrow \mathbb{R}^n$ be the median filter associated with the family of windows defined by the rule $$ W(i) = \{ j \in \{1,2, \dots, n\} : \max \{ 1,i-k\} \le j \le \min\{i+k,...
mlbj's user avatar
  • 128
0 votes
2 answers
56 views

Why must the population mean equal the population median if the density function is symmetric about the median?

Suppose we have $X_1,X_2,...X_n\overset{\text{iid}}{\sim}f(x-\mu)$ where, $f$ is symmetric about $0$. So, $\mu=$ median of $X$ and (if it exists) mean of $X$. Since, $f(x)$ is symmetric around $0$, $...
zaira's user avatar
  • 1,989
0 votes
0 answers
51 views

Combining two Left Skewed Distributions?

Let's say I have two groups of students, Group A & Group B. We are going to test the groups with an examination paper, but on separate days. One group will complete the test on Monday, the other ...
the man's user avatar
  • 2,336
1 vote
1 answer
60 views

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 ...
Stanley Yu's user avatar
0 votes
1 answer
52 views

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 ...
modeltheory's user avatar
0 votes
1 answer
79 views

How to Find the Median of a Probability Distribution Function?

I am interested in learning about how to find out the Median (https://en.wikipedia.org/wiki/Median) for some "generic" Probability Distribution Function (https://en.wikipedia.org/wiki/...
stats_noob's user avatar
  • 2,358
0 votes
1 answer
17 views

Calculating list size from original and altered average when x is removed. [closed]

The average of x number of values is 66, and when a certain 77 is removed from these values, the average drops to 62. Find x, or the number of values that when averaged give 66, and when 77 is removed ...
rummy rummyrum's user avatar
1 vote
1 answer
323 views

Median of medians algorithm [closed]

My question is I don't understand how we determine the constant in T(T(n/3), T(n/5)). For example, we divide elements into 9 groups and get a formula like this T(n) <= T(n/9) + T(7n/9) + O(n) I don'...
Rustam's user avatar
  • 13
1 vote
1 answer
82 views

Area of a triangle $\triangle ABC$

Let be $\triangle ABC$ a triangle with its area of $48\text{cm}^{2}$. $M$ is the mid of $[BC]$ and $P$ is the mid of $AM$. We know that $BP \cap AC = \left\{N\right\}$. The question is: how to compute ...
Iuli's user avatar
  • 6,770
0 votes
0 answers
35 views

Given a set of many 2d lines, computing the median line for multiple x positions?

I have a set of 2-dimensional lines, defined by $y = a_i x + b_i$ for $i$ in range 1 to n. I also have a separate set of query x positions $x_j$ for j in range 1 to m. I need to compute the median ...
Lalaland's user avatar
  • 175
1 vote
1 answer
148 views

Convergence of median and convergence in distribution

Let $X_n$ be a sequence of real random variables such that $X_n \rightarrow^{d} X$, that is, $X_n$ converges in distribution to $X$. Suppose that $X$ has a cummulative distribution function, $F$, ...
CantorEuler1996's user avatar
1 vote
1 answer
56 views

Prove that $\text{P}(\max\limits_{1\leq k\leq n}|X_k-m_k|\geq t)\leq 2\text{P}(\max\limits_{1\leq k\leq n}|X_k-X_k^{'}|\geq t)$

Let $\{X_k:1\leq k\leq n\}$ and $\{X_k^{'}:1\leq k\leq n\}$ be two independent sequences of random variables (i.e the two sequences are independent,but the variables in the same sequence are not ...
qmww987's user avatar
  • 849
0 votes
0 answers
22 views

By comparing boxplots, how to tell which sample is more likely to have outliers?

For example, from three boxplots, like these how could I tell which one is more likely to have outliers? By outliers, I mean values below $Q1 - 1.5 * (Q3-Q1)$ or above $Q3 + 1.5 * (Q3-Q1)$
Jonas's user avatar
  • 13
-1 votes
1 answer
52 views

Median and Mode from grouped frequencies

I'm currently learning about grouped frequencies and I was wondering how we could determine the Median and Mode from grouped frequencies. We don't know the precise values so we can only determine and ...
James Chadwick's user avatar
1 vote
1 answer
88 views

Is the median of CDFs again a CDF?

I am working on the following barycenter problem: Suppose we are given $N$ probability measures on $\mathbb{R}$ with cumulative distribution functions $F_1,\dots,F_N$ and we are interested in the ...
ad28a's user avatar
  • 45
3 votes
1 answer
151 views

Generalization of mean and median

It is well known that a median of a distribution $\mu$ can be defined as an $m$ such that $$m\in\operatorname*{arg\,min}_{c\in\mathbb{R}}\mathbb{E}_{X\sim\mu}[|X-c|].$$ Similarly, the mean of a ...
Tyler6's user avatar
  • 1,197
2 votes
1 answer
20 views

Efficient way to verify if pair of numbers are medians of partition of sets

Given a multi-set of multi-sets $\mathcal{S} = \{S_1, \ldots,S_i, \ldots, S_n \}, S_i \subset \mathbb{R}$. Denote powerset of $\mathcal{S}$ as $\mathbb{P}(\mathcal{S})$. My question is, given a pair $(...
peng yu's user avatar
  • 1,273
1 vote
1 answer
24 views

How to think about changes to the median

I've been asked the following question, and, while it is obviously pretty simple, I've got myself in a tangle overthinking it. The question is: "Imagine that you have data from a web server, ...
Dan Öz's user avatar
  • 477
1 vote
3 answers
715 views

Assuming a random variable X has a strictly decreasing pdf, prove that its mean is strictly greater than its median

Got asked this question in an interview. More generally, I would like to understand for which distributions is the mean greater than the median and vice versa. For example, it is known that for ...
Filip Batur Stipic's user avatar
1 vote
1 answer
69 views

$o_p(1)$ property of sample median estimator

$\textbf{Motivation:}$ Van der Vaart - Asymptotic statistics [Example 5.11] $\textbf{Setup:}$ Suppose I have $i.i.d$ random variables $X_1,...,X_n$. Define the sample median $\hat\theta_n(\omega)$ as ...
dante's user avatar
  • 353
1 vote
0 answers
46 views

How to prove that the median of a set cannot surpass a given value by contradiction?

I hope you're having a good day, I'm very new to statistics, and I'm having trouble with this question: "The average age of 100 people is 30 years. Prove by contradiction that the median of the ...
MHDFrags's user avatar
0 votes
0 answers
27 views

Median values in probability distribution where two median values can possibly occur?

I have a relatively basic question, I will keep it short, sharp and shiny. In a probability distribution lets suppose $P_1 =0.5, P_2 = 0.0, P_3 =0.5$ All three outcomes share a slice of the median ...
Dat Boi's user avatar
  • 19
1 vote
2 answers
96 views

How do I find the median of this continous random variable?

The question given was to find the median of $X$ given $f(x)=1.1e^{-1.1x}$ Random variable is $X≥0$ I have no issue working out the median of probability density functions with parameters like $1≤X≤5$ ...
oxy's user avatar
  • 13
0 votes
1 answer
89 views

Can a median value occur twice?

From a practice exam: From the set $$\{7, 12, 5, 16, 23, 44, 18, 9, Z\},$$ which of the following values $Z$ be equal to if it is the median of the set? Choose from: $14, 11, 12, 17, 21.$ $14$ was ...
John Harvey's user avatar
4 votes
0 answers
83 views

Bounds on $k$-medians

For a metric space $(X,d)$, given $N$ points $S=(s_1,\dotsc,s_N) \subset X^N$, a $k$-median is a multiset of centers $K=\{c_1,\dotsc,c_k\} \subset X$, $k\leq N$, that minimizes $$ f_S(K) \equiv \sum_{...
adfriedman's user avatar
  • 3,596

1
2 3 4 5
11