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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Probability Question Random Variable Median

I have not idea where to start with this question can someone point me in the right direction...
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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} ...
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2answers
288 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 ...
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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): ...
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1answer
56 views

Does the median tend to the lower limit of the median class?

The median for a continous distribution is given by $M= L +\dfrac{(N/2-C)\cdot I}{f}$ where $M$ is median, $L$ is lower limit of median class, $N$ is the total frequency, $C$ is the cumulative ...
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1answer
51 views

Ordering of positive integers

Three positive integers: m. n and q, their average is 10, median is m+6. what is the greatest possible value of Q ? I understand how to find the solution which I am outlying below. My question is ...
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1answer
38 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: ...
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1answer
274 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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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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1answer
82 views

Means and Median of Probability

The question is: pennies come in rolls of 50. Out of the 200 rolls a bank is storing, 12 have all Canadian pennies: the remaining 188 rolls contain at least one American penny. In the 200 rolls, about ...
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1answer
161 views

Prove That The Composite Median Of Two Groups Lies Between Separate Medians of The Groups

Let $M_1$ be the median of $n_1$ observations and $M_2$ be the median of $n_2$ observations. Show that $M$, the median of$(n_1+n_2)$ observations combined, lies within $M_1$ and $M_2$.
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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 ...
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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 ...
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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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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 ...
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1answer
24 views

Median of limited normal distributions

If $$x + \mathcal{N}(0,\,1) = 6$$ $$y + \mathcal{N}(0,\,1) = 7.5$$ $$\left|{y-x}\right| < 1$$ then what is the median of $y$? I'm expecting it to be $< 7.5$. If it is not, then why doesn't the ...
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1answer
70 views

Give a randomized algorithm to find the median that has an expected number of comparisons = 2n + o(n)

Any help would be very much appreciated. I'm aware of 2 types of algorithms: "Median of the medians" and one using guards like here: http://www.cs.nthu.edu.tw/~wkhon/random12/lecture/lecture9.pdf ...
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1answer
68 views

calculating the median in iWorks Numbers from a dictionary of values

I need to calculate the median among some numbers which I have in iWorks numbers. Since I have to do this several times (a few hundreds) I really cannot do it by hand. The numbers reach me (from the ...
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1answer
258 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 ...
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0answers
54 views

Generalizing the mode and mean like the quantile

The mode, median, and means of a series of number ($x_1,x_2,...,x_N$) can be roughly thought of as the points that minimize the $p$-norm of the sequence for $p\in \{0,1,2\}$. The median is ...
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0answers
51 views

What are the properties of median-unbiased estimators?

On Wikipedia it says that " A median-unbiased estimator minimizes the risk with respect to the absolute-deviation loss function, as observed by Laplace." How to prove this? Note that I asked on Cross ...
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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 ...
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0answers
82 views

A point minimizing total great circle distance to a given set of points on a hemisphere

If you have a set of points on a hemisphere, how do you find a point on that hemisphere that has the minimum total great circle distance to the points in the set.
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0answers
60 views

Error propagation of the median absolute deviation.

I wonder if there is a way to estimate error propagation of the mad (=median absolute deviation) for the difference between two median distributions, similar to how you estimate error propagation for ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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0answers
36 views

Distribution estimate from a sample or just a probability theory task

Here is the task: I have a sample of replies to my e-mail from my mail box. A sample is taken over a period of 90 days, 1000 e-mails and replies if any. (We only consider a pair of {my original ...
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0answers
129 views

How to generate a random number including mathematical dispersion?

I need to generate not completely random number that would be influenced by functional dependency. Current solution I was looking was to give an algorithm value of statistical dispersion or spread ...