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

learn more… | top users | synonyms

0
votes
0answers
25 views

Probability of $n$ numbers picked from set to have greater mean than set

If we have (N) varying non-negative numbers , with a mean equal to X, and a median less than X, if we pick (n) unique numbers from the set, what is the formula for the probability that the mean of ...
1
vote
1answer
18 views

Formula for the weighted median

I am looking for mathematical notation (not computer code) for the following simple scenario: I have three numbers: 6, 7 and 2. I wish to find the weighted median where the weights are say, 20, 10, ...
1
vote
1answer
4k views

How do I find percentiles of data sets (Even vs odd)?

Given the following data set with an even number of values: $100, 100, 105, 113, 129, 132, 146, 152, 176, 200$ The value representing the 30th percentile, using the formula n(p/100) where n = sample ...
-1
votes
2answers
33 views

Statistics. How to find the median of two other medians?

I got median of 226 and another median of 304. Now the question is how to find the overall median? Averaging them is not the correct answer.
1
vote
0answers
14 views

Geometric median (or Fertmat-Webber problem), including continuous case

For a finite set $X\subset \mathbb R^n$ the geometric median is defined as the point in $\mathbb R^n$ for which the sum of distances to all points of $X$ attains its minimum. Here is a wiki article: ...
1
vote
0answers
21 views

Area of triangle constructed from the medians of other triangle

We have triangle ABC of area P. Is it possible to compute the area of a triangle with sides "made" from medians of the triangle ABC in terms of P I'm looking for some hints maybe,
0
votes
1answer
31 views

non-linearity of median - proof

I'd like to show counterexamples for: a. $med(X+Y) = med(X) + med(Y)$ b. $med(aX+b) = a\cdot med(X) + b$. Showing that "a" is not correct: Let $X, Y$ be independent random variables with ...
1
vote
1answer
15 views

Relationship between subset medians and the median

Suppose we have a set of data $A = \{a_1, a_2, \dots, a_n\}$ and $B = \{b_1, b_2, \dots, b_n \}$. So there are $2n$ elements in total. Further suppose the median of $A$ and $B$ is $a$ and $b$, ...
2
votes
2answers
152 views

Why can/should we use 5 instead of 10?

Problem: A pharmacy has a uniform annual demand for 200 bottles of a certain antibiotic. It costs \$10 per year for a storage place for one bottle, and $40 to place an order. How many times during ...
1
vote
1answer
717 views

Given x is an exponential random variable, find median & probability

For the median, I believe that I should integrate the function, ∫x0λe−λtdt=1−e−λx Then I need 1−e−λm=.5 for m, which is equivalent to e−λm=.5. m=ln(2)/λ =>m=ln(2)/.2
0
votes
0answers
12 views

How to estimate the duration of the path?

Let $G=<V,E>$ $p$ - sequence of vertices and edges For each edge $(u,v)\in E$ there is information about the transition time from $u$ to $v$ represented as a set of values $T=\{t_0, t_1, ... ...
1
vote
2answers
5k views

A set having the same mean, median, mode, and range

Is it possible to have a set with the same mean, median, mode, and range? If not, how can the following question be solved: Set $H$ contains five positive integers such that the mean, median, ...
3
votes
2answers
43 views

Finding the median given the PDF $f(x) = cx^2$.

I'm new to stats and I facing problems in finding the median of a PDF. I have to find the median of this PDF $$ f(x) = \begin{cases} cx^2, & \text{if 0 $\le$ $x$ $\le$ 3} \\ 0, & \text{...
2
votes
2answers
23 views

Calculating new median if one of the observations from original calculation is removed

find new average if removing one element from current average Hey guys, found an old question that I would like to build on if possible, would appreciate your help. To piggyback on this old ...
2
votes
1answer
42 views

Does three medians determine a triangle?

If given three medians, is there only one triangle that has these three medians? How do I prove that?
0
votes
1answer
22 views

Is this the correct way of calculating the median?

I just completed the June $2009$ mei stats paper. On the mark scheme for question $5ii$ it shows the median being calculated using $600$, shouldn't it be $600+1$? I thought the median was calculated ...
3
votes
1answer
74 views

Median of a multinomial variable

Let $k\in\mathbb N^+$ be a positive integer. Consider a set of i.i.d. random variables $X_1,X_2,\ldots, X_n$, each of which is distributed uniformly over $\{1,2,\ldots,2k+1\}$. For $i\in \{1,2,\...
9
votes
3answers
203 views

How to win Matt Parker's jackpot - finding the median of the following distribution

In a recent video the legendary Matt Parker claimed he kept flipping a two-sided (fair) coin untill he scored a sequence of ten consecutive 'switch flips', i.e. letting $T$ denote a tail and $H$ a ...
0
votes
1answer
19 views

Proof of sample mean and median

Show that $$\overline{X}=arg_{a\in\mathbb{R}}min \sum_{i=1}^n (x_i-a)^2$$ $$m=arg_{a\in\mathbb{R}}min \sum_{i=1}^n |x_i-a|$$ where $m$ is the median Is there any way to prove it? I tried to ...
0
votes
1answer
17 views

Determination of the lengths of the medians of a triangle.

The lengths of the sides $AB, BC$ and $CA$ of a $\triangle ABC$ are respectively $√14, √26$ and $√56$. What are the lengths of the medians of the triangle?
0
votes
0answers
8 views

Another name for mode frequency

Is there another term for the number of times the mode number occurs in a list/array of numbers or 'the frequency of the mode' in a list/array of numbers? Apologies if this has been asked before - I ...
0
votes
1answer
19 views

Multiple, One (?), or No Medians for discrete

I am a bit confused on how medians are calculated for discrete distributions. I understand that there can be multiple medians or none at all. Can there be one median for a discrete distribution? Can ...
0
votes
2answers
44 views

finding median with cumulative distribution function (absolute value)

I am currently working on distribution with density function $$f(x)=\begin{cases} \frac{2}{5}|x-2|,& \text{0 ≤ x ≤ 3} \\\\0 & \text{otherwise}\end{cases}$$ I have found that cumulative ...
1
vote
0answers
35 views

Median of medians vs. single median

I have 10 sets. Each set corresponds to a user. Each set contains a different amount of floating point numbers. Each such number corresponds to a response time (of a user). Now I would like to ...
3
votes
1answer
27 views

What is the third quartile when there are no data above the median?

I'm a programmer, so apologies if this is a bad question. I'm writing some code that needs to detect outliers. I am currently calculating first and third quartiles. In a sample set of data, I have ...
0
votes
0answers
22 views

Median of the sample median equal to the median of the distribution?

I'm taking a course in mathematical statistics this semester. I don't know how much consensus there is among mathematicians about notations and definitions, so I'll just define the essentials. Let me ...
0
votes
5answers
33 views

Find a set A of five numbers that satisifies average(A) = 10 and median(A) = 9

Problem Find a set A of five numbers that satisifies mean(A) = 10 and median(A) = 9. Progress The only method I can think of here is brute force, which hasn't yielded any results for me yet. I ...
0
votes
0answers
13 views

error on the median

I have a set of values ${x_i}, i=1, \dots ,N$ of which I calculate the median M. I was wondering how I could calculate the error on this estimation. On the net I found that it can be calculated as $1....
4
votes
2answers
43 views

Maximise difference between mean and median

I have a set of numbers and I want to maximise the difference between the mean and the median by removing a given number of elements. For instance I have the following set: ...
1
vote
1answer
19k views

Finding the median value on a probability density function

Quick question here that I cannot find in my textbook or online. I have a probability density function as follows: $\begin{cases} 0.04x & 0 \le x < 5 \\ 0.4 - 0.04x & 5 \le x < 10 \\ ...
0
votes
0answers
23 views

Is the intuition correct?

Let $X$ be a random variable such that $E|X|<\infty$ and $$P\left(X\ge\frac{1}{2}+x\right)=P\left(X\le\frac{1}{2}-x\right)\ \forall x\in \mathbb{R}.$$ Then $E(X)=\frac{1}{2}$ and Median($X$)$=\...
3
votes
1answer
28 views

Median of Medians

Given a set A with median Am = 10 and set B with median Bm = 20 is it true that the median of the combined set C is $10 \le$ Cm$\le 20$ ? My first thought was that this wasn't true so I tried to find ...
0
votes
1answer
118 views

calculation of median of grouped data

While calculating the median of grouped data of total frequency $N$, in order to find the median class which value should be taken into consideration to match against cumulative frequency : $\frac N2$ ...
0
votes
1answer
109 views

Ratios of median/mean and standard deviation/IQR in a normal distribution

I have some queries on the following question For a normal distribution, find the ratios of: (a) $\frac {\mbox{median}}{\mbox{mean}}$ (b) $\frac {\mbox{standard deviation}}{\mbox{interquartile ...
3
votes
1answer
60 views

How can I draw the skewed normal distribution curve

If its of real importance, I am trying to plot the data on gnuplot. I have the following of some experimental data, obtained by ...
0
votes
0answers
15 views

median of bivariate truncated lognormal

$(X,Y)$ are bivariate lognormal random variables with mean $(\mu_1,\mu_2)$ and $\Sigma$ as the variance-covairance matrix, truncated to be in $[a_1, a_2]\times[a_1,a_2]$ where $a_1>0$ and $a_2<\...
1
vote
0answers
40 views

In biweight midvariance, why would the median absolute deviation (MAD) be multiplied by the 0.75 standard normal quantile?

The biweight midvariance $\zeta^2$ is a measure of scale that is more robust to non-normal distributions. It is defined as follows by [1] in three steps. For observations $X_i$, $i = 1,2,\cdots,n$, ...
0
votes
0answers
21 views

Is there a generally unbiased estimator for the quantiles of a distribution?

1) Is there a generally unbiased estimator for the quantiles of a distribution? If not - I would be glad for an explanation (proof?) of why not. 2) Also (if not), is there a specific family of ...
10
votes
5answers
6k views

The median minimizes the sum of absolute deviations

Suppose we have a set $S$ of real numbers. Show that $$\sum_{s\in S}|s-x| $$ is minimal if $x$ is equal to the median. This is a sample exam question of one of the exams that I need to take and ...
2
votes
1answer
45 views

minimizing the sum of weighted absolute distance

Let $x_1, \ldots, x_n \in \mathbb{R}^d$ denote $n$ points in $d$-dimensional Euclidean space, and $w_1, \ldots, w_n \in \mathbb{R}_{\geq 0}$ any non-negative weights. $\arg\min_{\mu \in \mathbb{R}^d} ...
2
votes
0answers
30 views

Continuity of Median

There are three arbitrary random variables on $\mathbb{R}$: $X$, $Y$, $Z$. The median is defined as $\mathrm{Me}(X) = \mathrm{sup} \left\{t: F_X(t) \le \frac12\right\}$ (so it's hopefully always ...
5
votes
0answers
198 views

How to show that this function respects the strict ordering of its input.

Suppose you have a vector $\pmb x=\{x_i\}_{i=1}^n$ where each entry is drawn from a continuous distribution and $n$ is even. Then, denote $i^*=\{1\leq j\neq i\leq n:|x_i-x_{j}|=\mbox{med}_j|x_i-x_j|\}...
0
votes
2answers
52 views

High school Math: Finding the Median

I have a problem trying to understand the following two questions: In question 1, the median is found at the 50% of the total group. However, this strategy doesn't work for question 2. Why?
0
votes
1answer
22 views

How to find the median element when each element has three scores?

I know how to find the median with a list of one element but what to do with a list like this one: \begin{array}{|l|cr} & math & info & gestion\\ \hline Nelim & 0 & 4 & 0\\ ...
0
votes
1answer
23 views

Should I use interpolation when finding median, and quartiles?

I am a S1 maths (Edexcel) AS student in the UK. My question: Say we have a stem-and-leaf diagram with 26 values. We want to find the lower quartile. To get the marks for our specification, we need to ...
1
vote
1answer
103 views

Prove the median of a uniform distributions is $\frac{1}{2}(a+b)$

Let X~U(a,b) with a and b in the real line, such that b>a with X's pdf given by $$f_X(x)=\frac{1}{b-a}\mathbb{1}(a<x< b)$$ Show the median of X's distribution is given by $$m=\frac{1}{2}(b+a)$$ ...
4
votes
2answers
51 views

Geometric Median Problem with a twist

Given two vectors $x, y$ in $\mathbb{R}^n$ and scalar $\alpha$, what is the value of $\alpha$ that minimizes $||\alpha x - y ||_1$? Give an algorithm to find the minimum. I've tried couple of ...
0
votes
1answer
49 views

Show that $\mathbb{E}~|\xi - \mathrm{med}(\xi)| \leq \mathbb{E}~|\xi - \mathbb{E}(\xi)| $ [duplicate]

Assuming $\mu$ is the median of random variable $\xi$, prove, that, $$\mathbb{E}~|\xi - \mu| \leq \mathbb{E}~|\xi - \mathbb{E}\xi| $$ The case when $\mu = \mathbb{E}\xi $ is trivial, but I have ...
3
votes
2answers
140 views

The minimum of the sum

I was trying to prove some theorem on my way. So the problem was: Theorem: Let $x_1, x_2, ..., x_n$ be the rising sorted sequence of numbers. The $ \sum_{k=1}^n |x_k-a|$ reaches it minimum if $...
0
votes
2answers
442 views

question on five number summary & quantile.

i know that in five number summary : 25% of a data set lies between Min & 1st quartile. 50% of a data set lies between Min & 2nd quartile, that is, Median. 75% of a data set lies between ...