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1answer
28 views

Distribution of sample median for a discrete random variable

Say I have a set $S = \{x_1, \dots, x_m\}$, where $1 \le x_i \le n$, all distinct, with median $M$. I take a sample $T$ of size $t$ from $S$, with replacement. I call $Y$ the median of $T$. What is ...
1
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2answers
451 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 ...
2
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1answer
23 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 ...
7
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1answer
579 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.
1
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1answer
264 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
20 views

Median value resulting in negative number

I know the that the formula for finding the median of grouped data that is: $$\mathrm{Median} = L_m + \left [ \frac { \frac{n}{2} - F_{m-1} }{f_m} \right ] \times c$$ And I also know what the ...
0
votes
1answer
19 views

Finding the median of the largest gap of a sequence of numbers in a set/vector

Im working on a programming function, but I cant seem to get this equation right. Im hoping someone can help point me in the right direction here. Say you have a set of numbers: 1, 10, 15, 25 All ...
2
votes
2answers
67 views

How can I calculate the median value?

$$f(a,b) = a^b$$ Where $0\le a \le1$ and $0\le b \le1$ and either $a\ne0$ or $b\ne0$ How can I calculate the median value of $f$ ? I can estimate it to be about 0.76536 by taking values along the ...
0
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1answer
30 views

How do I “recalculate” a median number?

I'm not sure how to explain the question, so I'll do it by an example. The median age in some country is 41.7. 50% is younger than 41.7, 50% is older. How would I calculate the percentage of the ...
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0answers
46 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.
1
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1answer
34 views

What is weighted median?

I heard median of any number of data. Suppose we have a data [13,23,23,23,54] The median of this data is is 23. How we calculate the weighted median of same data (as mentioned above). ** ...
1
vote
1answer
28 views

How to prove the property of the Lemoine point of a triangle?

From Wolfram MathWorld, I know there is a Lemoine point of triangle, also called symmedian point, the sum of squared distances of this point to all the three sides is algebraically minimum. How to ...
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2answers
75 views

Formulation and computation of “the” unique median of an even-sized list

Consider an even-sized set of numbers $X = \{x_k\}$, such as $X = \{1, 2, 7, 10\}$. The median $m$ is defined as: $$m = \mathrm{arg \min_x} \sum_k \lvert x_k - x\rvert^1$$ Any $m \in [2, 7]$ is a ...
0
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1answer
21 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?
1
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2answers
41 views

Median of i.i.d. uniform random variables on the interval $[-1/2, 1/2]$

Let $X_1, X_2, \ldots , X_{999}$ be independent and identically distributed random variables on the interval $[-1/2, 1/2]$. Let $X_{500}$ be the empirical median; that is, $X_{500} = X_k$ for some ...
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0answers
16 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 ...
2
votes
2answers
67 views

Prove that this segment bisects another

The circle touches the trapezoid $GFEC$ at the points $C$, $D$ and $E$. The point $A$ is the center of the circle. The rest of the information can be seen in the diagrams below. What we have to ...
1
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1answer
103 views

Median of Medians in 2D Array/Matrix

This is a bit of a mathematics problem, and a MATLAB problem. In MATLAB, if I call median(M), where M is an ...
0
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1answer
75 views

Conclusions to be drawn from mean, median, stdev, and range

From a sample of size n = 100, the following descriptive measures were calculated: median=23, mean=20, standard deviation=5, range=35; 75 sample values are between 10 and 30; and 99 sample values are ...
2
votes
1answer
268 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
59 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
63 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 = ...
0
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1answer
59 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 ...
0
votes
1answer
18 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
votes
1answer
29 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
77 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
54 views

Probability Question Random Variable Median

I have not idea where to start with this question can someone point me in the right direction...
0
votes
1answer
35 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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2answers
102 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
vote
1answer
48 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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2answers
4k 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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2answers
185 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 : ...
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2answers
38 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 ...
1
vote
1answer
153 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 ...
5
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1answer
392 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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2answers
92 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
votes
1answer
35 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 ...
1
vote
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
197 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
38 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
vote
1answer
92 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 $M_2$.
2
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0answers
36 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 ...
1
vote
1answer
2k 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 ...
0
votes
1answer
124 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
81 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
vote
1answer
604 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
votes
1answer
4k 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
90 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
2k 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
706 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 ...