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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1answer
21 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
72 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 ...
9
votes
3answers
190 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
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1answer
14 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 ...
0
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1answer
16 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?
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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 ...
2
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2answers
141 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 ...
0
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1answer
18 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
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2answers
36 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 ...
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0answers
28 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 ...
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5answers
28 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
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0answers
18 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
0answers
12 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 ...
4
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2answers
42 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: ...
0
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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 ...
3
votes
1answer
24 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
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1answer
70 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
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1answer
64 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
51 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
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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 ...
0
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0answers
36 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
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0answers
19 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 ...
1
vote
1answer
40 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} ...
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0answers
29 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 ...
0
votes
2answers
51 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
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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
22 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
86 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
47 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
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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 ...
1
vote
2answers
46 views

Distribution with two (or more) medians

Is there any example with a distribution with two or more medians? I was reading about the median on wikipedia: https://en.wikipedia.org/wiki/Median and here it says that there may be more than one ...
2
votes
1answer
41 views

Average weighted by inverse distance to median equal to median?

Problem Statement I have a set of $N$ ordered elements such that $x = \{x_1, x_2, ..., x_q, x_p, ..., x_N\}$ where $x_q \le x_m \le x_p$ and $x_m$ is the median of the set $x$. I define a particular ...
0
votes
1answer
141 views

calculate minimum of max value of set of numbers

Suppose to have a set of numbers: $$S:=\{ 1,2,3,9,10,56,58,60\}$$ How can i group this number like this: group 1:$\{1,2,3,9,10\}$ group 2:$\{56,58,60\}$ and then take "56" as minimum value of ...
1
vote
2answers
38 views

Need help proving this geometry problem.

My friend asked me one question yesterday.It is as follows. Let there be two triangles ABD and ACD.D is a point on base BC such that BD=CD(given).Also,clearly side AD is common.Now we know median ...
3
votes
1answer
32 views

Median of waiting time for $k$-th ace from bridge cards

I can't figure out how to get median of a waiting time from the exercise 36 from W. Feller's book An Introduction to Probability Theory and Its Applications Vol.1 (bold in the quote): ...
0
votes
1answer
142 views

How to find median from a probability distribution?

Having trouble on something that should be really, really easy. I need to find the median of the following probability distribution...but according to the website I linked below...I'm doing it ...
0
votes
0answers
20 views

Median of n normal distributions

I have the following problem: I would like to know the distribution of $\mathrm{Med}[X1,\ldots,Xn]$, where $X1,\ldots,Xn$ are standard normal distributions $N(0,1)$. I know that one should consider ...
2
votes
4answers
250 views

Prove that the co-ordinates of the centroid of a triangle is an average of that of vertices

For a given triangle [ABC], how do I prove that the co-ordinates of the Centroid $O_{xy}$ (intersection of the medians) is the average of the individual vertices? $O_x = \left(\frac {A_x + B_x + ...
1
vote
1answer
37 views

Non-Whole Median Numbers in Real Data [duplicate]

According to this CDC report, the median number of reported sexual partners for females aged 15-44 is 3.2, and for males 5.1. Tables on pages 19 and 20 report these statistics for a variety of ...
0
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0answers
11 views

What is the behavior of the spatial median in high-dimensional spaces?

I am a photographer who is investigating a technique known as image stacking, in which multiple images of the same subject are combined to reduce noise (by CLT). Commonly used techniques are mean and ...
1
vote
2answers
4k 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, ...
0
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0answers
15 views

what's the best way to find a central tendency and filter outliners for this given problem?

I'm faced with the following problem: I have a group of Nodes which belong in the same network. They are constantly talking with one another providing services to one another. Suppose nodeA asks for ...
0
votes
1answer
75 views

The validity of dividing an average cost by an average duration?

Let's say you wanted to calculate, for example, the average (i.e. mean) cost per day for a hotel to accommodate a tourist. If only aggregate cost data is available, is dividing the average cumulative ...
0
votes
2answers
50 views

Is it possible to find Median of set contains string value as well as Null value?

I am doing one calculation on Median and AFSIK about Median, it can be calculated by a "set of Finite set of Numbers". Now if a set has following value as: A = {3,4.56, 2, 11, JAMES, , Joy, 54, 9} ...
2
votes
1answer
73 views

What is the median of the pdf $f(x) = e ^{-x}$?

I got its integral to get the CDF, which is equal to $-e^{-x}$, and I equate it to 0.5, but I'm stuck since I was getting an answer of ln(-0.5) which is a math error.
0
votes
1answer
38 views

Uniqueness of Spatial Median

https://projecteuclid.org/download/pdf_1/euclid.aos/1176350511 Can You help me understand why there is less-than sign in the proof? ...
1
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0answers
40 views

Runtime of recursive algorithm - Master's Theorem

I wrote a computer program that solves a question, and I am interested in knowing what is the runtime. My aim is for $O(\log n)$, and I'd like someone more experienced (and smarter?) to review my ...
2
votes
1answer
32 views

Equivalent events in proof of Central Limit Theorem for Sample Median

Let $X_1,X_2,\ldots,X_n$ be i.i.d. random variables with cdf $F$ on $\mathbb{R}$ and $M_n$ be the sample median. The proof starts off with defining for any $a\in\mathbb{R}$, $S_n = \#\text{ of ...
0
votes
1answer
111 views

Is it possible for the median to be left to the mean in the Gamma distribution?

Many textbooks teach a rule of thumb stating that the mean is right of the median under right skew, and left of the median under left skew but this is not always true. According to wikipedia, there ...