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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3
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4answers
513 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 ...
4
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1answer
2k 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 ...
1
vote
2answers
44 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 ...
1
vote
2answers
45 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 ...