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1answer
34 views

Why is the median the value that minimizes the sum of absolute deviations?

Apparently, the mean is the value that minimizes the sum of the squares of deviations, and this made sense to me because the sum of the squared differences can be represented as an equation: (a - ...
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3answers
50 views

Median $\neq$ Expectation

Do you have an example of real random variable such that its median is very different from its expectation? I mean it is obvious that they are differents. Thank you
2
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2answers
52 views

Median vs. Mean

Problem: Consider the following model: $y_i = \mu + \epsilon_i$, $i = 1,...,n$ Let the mean $\mu$ be estimated by minimizing the criterion $\sum|\mu - y_i|$ over $\mu$. Show that $m = ...
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1answer
14 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 ...
2
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1answer
17 views

Bounds on median of random walks

If $k$ random $n$-step $\pm 1$ walks start at 0, and the $i$th walk ends at position $X_i$, how big is $\text{median}_i \, |X_i|$? Is there a bound along the lines of $\text{P}(\text{median}_i \, ...
0
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2answers
37 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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2answers
50 views

Probability Question Random Variable Median

I have not idea where to start with this question can someone point me in the right direction...
1
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1answer
160 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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2answers
85 views

Find Weight for minimum Manhattan Distance

Let's say, I have three points $(1, 4)$, $(4, 3)$ and $(5, 2)$. I need to find weight $w_1$ and $w_2$ so that the point $(1, 4)$ be the centroid of the points in ...
1
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1answer
41 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
54 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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2answers
168 views

Functions minimized at the median of their arguments

I am doing research on problems of location of a public facility on a network which lead me to the following question. Is there an interesting way to characterize the class of functions $f : ...
1
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2answers
37 views

Determine random variable such as Med[X]=a and E[X]=b.

Let $a<b$ (a,b real numbers). Determine a random variable $X$ such as $Med[X]=a$ and $E[X]=b$. Hmmm how does one find $E[X]$ and $Med[X]$ if we don't have the probability distribution? The only ...
0
votes
1answer
26 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 ...
1
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1answer
93 views

Distance between mean and median

I want to solve the following problem in T.Tao's random matrix theory book. Let $X$ be a random variable with finite second momment. A median $M(X)$ of $X$ saisfies ...
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2answers
76 views

What is the median in this gre question?

This is gre preparation question of data interpretation, Distribution of test score among students(Score range -> total % of students) 0-65 -> 16 65-69 -> 37 70-79 -> 25 80-89 -> 14 ...
2
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1answer
33 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
327 views

Asymptotic correlation between sample mean and sample median

Suppose $X_1,X_2,\cdots$ are i.i.d. $N(\mu,1)$. Show that the asymptotic correlation between sample mean and sample median (after suitably centering and renormalization) is $\sqrt{\frac{2}{\pi}}$.
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1answer
45 views

Median based on number of entries instead of values

I’m writing a computer program that provides some useful statistical information about files. Calculating the mean is trivial, and the mode at least has a simple definition, but the median is proving ...
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2answers
180 views

Why do Mean, Median, Mode, and Range present in school lessons?

I studied in East Europe and post Soviet mathematical education program have no Median, Mode, and Range terms. Mean (or average) on other hand was studied (with root mean square and sometimes with ...
2
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0answers
35 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 ...
1
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1answer
71 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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0answers
31 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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1answer
104 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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2answers
3k 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?
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0answers
68 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 ...
1
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1answer
1k views

Compute number of comparisons in quicksort pivoting on median or third

With a few friends we read the Algorithm Design Manual from Skiena. One of his (chapter 4) exercises asks for the number of comparisons that the quicksort algorithm does (comparing an element to the ...
1
vote
1answer
319 views

Algorithm to separate an array of numbers into “low”, “medium” and “high” ranges

this is my first post on Math-Exchange. I'm a programmer, and I work with object-oriented algorithms, but when things gets too "algebraic" I get stuck. So I thought I'd ask over here. I need to ...
0
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1answer
3k 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: $$0.04x \space 0 \le x < 5$$ $$ 0.4 - 0.04x \space 5 \le x < 10 $$ $$ 0 ...
0
votes
1answer
79 views

Fractional part of Median always .5 or .0

If we find the mid value of two integer number,it's decimal part would always contain .5 or .0 exactly For Example: (5+10)/2=7 .5 (6+2)/2=4 .0 But,in some coding challenge they asked to calculate ...
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1answer
1k views

Find the median of the exponential random variable with parameter λ

The median of a random variable X is a number µ that satisfies Find the median of the exponential random variable with parameter λ.
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2answers
452 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 ...
1
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1answer
156 views

Calculate Statistics (Check if the answers are correct)

Calculate the statistics below using the following data on a sample of the variable $X$: Data ($X$ sample) = $\{9, -1, 7, 0, -2, 5, 4, 9, 5 \}$ Using the sample data, calculate: Mean; Median; ...
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1answer
550 views

median of a uniform distribution [0,1]

I need to find the distribution of the median from the given distribution, where n is known to be odd. The formula given in class for this is: $n=2m+1$ where $m\in\mathbb{N}$ ...
0
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1answer
551 views

Find median of 2 sorted arrays with different lengths

I'm trying to solve the below problem for my assignment but I have no clue how to find the time algorithm. If I have two arrays of same even length then I get, $T(n) = T(n/2) + \theta(n)$ but what ...
0
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1answer
170 views

Sample-based median calculation

Is there any technique to find the median of a large data set using sampling (or maybe randomized algorithms)?
2
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4answers
987 views

what's the name of the theorem:median of right-triangle hypotenuse is always half of it

This question is related to one of my previous questions. The answer to that question included a theorem: "The median on the hypotenuse of a right triangle equals one-half the hypotenuse". When I ...
1
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1answer
1k views

Median of medians algorithm

I am referring to the algorithm presented here used to find a good pivot: http://en.wikipedia.org/wiki/Selection_algorithm#Linear_general_selection_algorithm_-_Median_of_Medians_algorithm My ...
0
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1answer
359 views

Calculate average angle after crossing 360 degrees

For a piece of code I am writing to smooth out movements I need to calculate the average angle over the past 5 recorded angles given (used to give directionality to an object) This can be achieved ...
1
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1answer
162 views

How to compute ideal investment leverage ratio based upon volatility? [closed]

I want to compute the ideal investment leverage ratio based upon an investment's volatility. For example, if I had an investment that with 50% likelihood quadruples your investment on a given day ...
7
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1answer
488 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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2answers
53 views

Find factor of sample elements given the median

I have a sample $S(x)$ containing $n$ elements: $$S(x)=\{ s_1 x, s_2 x, \ldots, s_n x \},\qquad s_i \in \mathbb{R}, x\in \mathbb{R^{+}}$$ Every element in the sample is multiplied by $x$. Now ...