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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2answers
287 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 ...
3
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1answer
25 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
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1answer
29 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 ...
1
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1answer
464 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
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0answers
17 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 ...
1
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1answer
37 views

How to understand the Repeated Median Estimator (Siegel 1982)?

I guess I did not understand the formula of the repeated median estimator introduced by Siegel (1982): This is the formula: If I got the following time series for instance: ...
7
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1answer
897 views

Median of the F-distribution

Is the median of the F-distribution with m and n degrees of freedom decreasing in n, for any m? From experiments it looks like it might be, but I have been unable to prove it.
2
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4answers
35 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
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1answer
23 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
5 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
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1answer
269 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 ...
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2answers
116 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
11 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 ...
2
votes
1answer
251 views

How to compute ideal investment leverage ratio to maximize median return? [closed]

If I had an investment that with 50% likelihood quadruples your investment on a given day and you lose it all also with 50% likelihood, what percent of your money should you invest each day to ...
0
votes
1answer
23 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 ...
3
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4answers
223 views

Median $\neq$ expectation

Do you have an example of real random variable such that its median is remarkably different from its expectation? I'd like an example where it is obvious that they are different.
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2answers
25 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
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1answer
35 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
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1answer
11k 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 \\ ...
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2answers
89 views

Where should I use median instead of average?

Is there a general law, or rule of thumb, or rationale, when to use median and when average? Although I know the difference and how they are computed, when I try to translate to simple English I ...
0
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1answer
32 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? ...
2
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2answers
2k views

Given a mean, median and sum how to find how many elements more than mean?

Given a mean, median and total sum, how can you calculate how many elements in the collection will be more than a mean value? Here is an example; I have a stack of poles. The total hight of all the ...
4
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4answers
749 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 I ...
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0answers
29 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
26 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
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1answer
37 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 ...
0
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1answer
37 views

Design an algorithm - Median, computer science

I was wondering if this question belongs here or on StackOverflow, but it is a question of mathematical nature so this seems more appropriate. We have an array $S$ of $n$ different numbers ...
1
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1answer
16 views

Find the reason of median

The median salary of Mr Pang's company is $10000$. Mr Pang therefore thinks that nobody in the company earns more than $20000$. Is this conclusion drawn appropriate? If not,why?
0
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2answers
77 views

How to find the median of three numbers, if one of them appears twice?

How do you determine the median of three numbers where two of the numbers are duplicated? For example, $(6,6,3)$.
5
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1answer
123 views

Why hasn't the median function made the mean (effectively) obsolete?

I've learned in my AP statistics class that means can really only be used on nearly-normal distributions, but I know that many studies, experiments, etc. don't always give that perfect normal curve ...
3
votes
2answers
78 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
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2answers
33 views

SD from Mean and Median

Given the mean and median of a dataset, is it possible to compute the standard deviation of the dataset?
0
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1answer
37 views

$E|X-m|$ is minimised at $m$=median

For a continuous random variable $X$, I want to show that $E|X-m|$ is minimum implies $m$ is the median of the distribution. Assume that the distribution function is $F$ and the density function is ...
0
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1answer
35 views

Create a Data Set Given Median and Mean

Its a very simple problem to a homework question that I can easily solve, but if time-willing I like to go about it a more elegant way. So lets say you need to create a set of 5 numbers whose median ...
1
vote
1answer
46 views

Problem with similarity of triangles and median.

I have the next problem: In the next image, MN // AB, PN = NC, QM = 8, BM = 6 and MC = 9. Calculate PM. First I tried to find similarities in the triangles formed by the parallel sides, ABC and ...
1
vote
3answers
53 views

What is the general formula for calculating the median?

How can I rewrite the equation $\mu = \frac{1}{N}\sum _{i=1}^Nx_i$, if I don't want to find the mean, but the median of all $x_i$, $i=1,\dots,N$?
2
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2answers
395 views

Why add the number 1 to find the median number

Example 1: There are 45 numbers 45 plus 1 is 46, then divide by 2 and you get 23 So the median is the 23rd number in the sorted list. Example2: There are 66 numbers 66 plus 1 is 67, then divide ...
1
vote
2answers
61 views

Finding median of union of two sorted (ordered) lists

We are given two sorted list of numbers $a_1, a_2, \ldots, a_n$ and $b_1, b_2, \ldots, b_n$. Question is, how to find a median for list $a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_n$. Algorithm should ...
1
vote
3answers
9k views

How to calculate the median of a continuous random variable

$X$ is a continuous random variable with probability density function $f(x)= \dfrac{2x}{15}$ where $1≤x≤4$. What is the median of X?
0
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0answers
17 views

Confidence level using unknown median

This is a general question. Lets say we are giving a sample space n. The sample space has an unknown median The order statistics of each person, $**X_{i}**$ in sample space is measured (lets say ...
0
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0answers
21 views

CONFIDENCE LEVEL for Median Interval

A firm wants to estimate the unknown median, m , of the height of their employees. Random Simple Size = 90 $X_{i}$ is the order statistics of the Sample Size X where height of each employee was ...
1
vote
2answers
69 views

Defining median for discrete distribution

In probability theory, a median of a probability distribution is a number $M$ such that the CDF of this distribution $F_\xi(x)$ satisfies $F_\xi(M)=\frac{1}{2} \tag1$ This works for continuous ...
2
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2answers
38 views

Proving that median of list $[x_1,x_2,…,x_n]$ minimises the sum $\sum_{i=1}^{i=n} |x_i-m|$ where $m$ is some number [duplicate]

The problem is in the title. Here is a detailed description: Let's say we have list $[x_i]_{i=1}^{i=n}$ where $x_i\in\Bbb{N}$. I want to pick such $m\in\Bbb{N}$ which minimises the sum ...
0
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1answer
22 views

Can you further explain or clarify the proof of this?

I am trying to prove that $AG = 2(GD)$, given $AD, BE$ and $CF$ are 3 medians meeting at point $G$ of a triangle $ABC$. I found this website that seems to show what I want to prove: ...
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0answers
8 views

Fill chart using known final answers [duplicate]

so all I know is that: n=100. i have 5 departments within the numbers: 0-1000. md = 500. avg =490. lower decile=200. upper quarter=600. I really don't know how to use the formulas of each if I don't ...
0
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1answer
54 views

Median of truncated / limited normal distribution

The peoples weight is normally distributed $\mathcal{N}(0,\,1)$ The $\mu \; , \; \sigma \; and \; \sigma^2$ are known. How can i calculate the median weight of people if everyone who weights less ...
0
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1answer
73 views

What information guarantees a ranking in the 90th percentile is greater than a ranking in the 70th percentile?

Consider the following facts: Person A's salary is in the 90th percentile in Company A. Person B's salary is in the 70th percentile in Company B. The question is: What piece of information is ...
3
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1answer
70 views

Squence of order statistic converges to median?

Suppose that $(X_1,...,X_N)$ be $N$ iid samples from uniform distribution. Let $X_{(n)}$ be $n$-th order statistic. It sounds natural that $X_{N/2}$ converges to the median, $1/2$. (interpret $N/2$ as ...
0
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1answer
207 views

Analysis of IQ scores given mean, median, sd, quartiles

The statistics below provides a summary of IQ scores of 100 children Mean: 100 Median: 102 Standard Deviation: 10 First Quartile: 84 Third Quartile: 110 About 50 of the children in this sample have ...
4
votes
2answers
4k views

Prove that the sample median is an unbiased estimator

My book says that sample median of a normal distribution is an unbiased estimator of its mean, by virtue of the symmetry of normal distribution. Please advice how can this be proved.