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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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
713 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
10 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, ...
0
votes
0answers
7 views

Calculate popularity (frequency) of an item sold from multidimensional array [on hold]

I have an array extracted from my database online where i store id status: sold / not sold time: day that the item sold or not price sold and the output example is given below ...
3
votes
2answers
39 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, & ...
2
votes
2answers
21 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 ...
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 ...
2
votes
1answer
36 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
73 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
199 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
18 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
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
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
votes
2answers
42 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
32 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
20 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
30 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 ...
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 ...
3
votes
1answer
25 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
93 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
76 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
54 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 ...
0
votes
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
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 ...
9
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 ...
1
vote
1answer
41 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 ...
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
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
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
92 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
48 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
138 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
434 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 ...
2
votes
1answer
42 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 ...
1
vote
2answers
52 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 ...
0
votes
1answer
154 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 ...
0
votes
2answers
512 views

In a distribution that is skewed by a few extreme outliers, what would be the best choice for a measure of central tendency?

According to my Professor, the answer to this question is the MEDIAN. However, wouldn't MODE be a better measure of central tendency? The mode is almost never affected by extreme outliers..please help ...
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): ...