Questions tagged [median]
For questions about the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.
544 questions
6 votes
1 answer
620 views
Median wealth after repeated iterations of multiplicative game?
I start with \$1. After one iteration of a game, one of the following $m$ outcomes occurs: With probability $p_1$, my wealth multiplies by $r_1$; With probability $p_2$, my wealth multiplies by $r_2$;...
- 163
3 votes
1 answer
122 views
Is the variance of the sample median of iid variables at most the variance of each variable?
Let $X_1,\dotsc,X_n$ be iid random variables with variance $\sigma^2 < \infty$. Let $M$ be the median of $X_1,\dotsc,X_n$. If it helps, assume that $n$ is odd (but more generally, I consider the ...
- 53
0 votes
0 answers
34 views
Extended median of triples
Given $n\ge 1$ triples $(x_1,y_1,z_1),\dots,(x_n,y_n,z_n)$ such that $x_i+y_i+z_i = 1$ and $x_i,y_i,z_i\ge 0$ for all $i$, we can compute their "extended median" as follows. Find a value $t$ ...
- 2,003
1 vote
2 answers
94 views
Find median of five positive integer data
Given five positive integer data $n_1,n_2,n_3,n_4,n_5$. Average of five data given is equal to 8. Now, we omitted two data and the average is equal to 6. Can we determine the range of median of five ...
- 2,988
1 vote
1 answer
95 views
Prove the geometric relation in a convex quadrilateral with midpoints of diagonals
In the figure, $ABCD$ is a convex quadrilateral and E and F are respectively the midpoints of diagonals $AC$ and $BD$. Prove that: $$AB^2 + BC^2 + CD^2 + DA^2 = AC^2 + BD^2 + (4*EF^2)$$ (Hint: Use ...
- 71
0 votes
0 answers
38 views
Geometric median alternative definition, as maximum of distances less than the median-distance
When using a Brute-force algorithm to calculate the Geometric Median, step by step, we are facing with a list a sums of distances. When we include, in the same list, a column with the number of ...
- 96
-1 votes
1 answer
34 views
Is the median of an inner product of two i.i.d. random vectors non-negative? [closed]
We have two independent random vectors $X$, $Y \in \mathbb{R}^d$ with the same distribution $F$. Is it then true that $$ \mathsf{P}\left( \left\langle X, Y \right\rangle \geq 0 \right) \geq 1/2? $$
- 791
1 vote
1 answer
75 views
I stumbled on a bruteforcing median algorithm. Can anyone tell me why it works and is there a name for this equation?
I recently stumbled on an algorithm while trying to write a program to estimate a median without sorting, a randomized group of non-repeating numbers with a known number of elements. Performance is ...
- 11