For questions about the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.
Questions tagged [median]
515 questions
8
votes
1 answer
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).
** http://en.wikipedia.org/wiki/Weighted_median (this is i…
Ashmi
- 81
6
votes
1 answer
Why does the median minimize 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:
$$ (a - x)^2 + (b - x)^2 + (c - x)^2 + \cdots $$
This…
5
votes
1 answer
What is the equivalent of "centre of mass" or "centre of gravity" for medians?
After cutting a scotch egg into two to share, a friend and I wondered, "How many different ingredients can a solid mixture have, such that there exists a plane that splits the mixture into two halves, each having the same amount of each…
Gnubie
- 445
3
votes
2 answers
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 poles is 1472 in. The mean height is 64in and…
Nair
- 135
3
votes
2 answers
Is the median a function?
Suppose I have a list of values $S$ containing $$x_1, x_2,...,x_n$$ where each $x_i \in \Bbb R$. Suppose I order them from smallest to largest $$x_{(1)}, x_{(2)},...,x_{(n)}$$
Is there a function or an optimization problem that achieves this? Or is…
Stan Shunpike
- 4,921
3
votes
1 answer
What is the median of the pdf $f(x) = e ^{-x}$?
I got its integral to get the CDF, which is equal to $-e^{-x}$, and I equate it to 0.5, but I'm stuck since I was getting an answer of ln(-0.5) which is a math error.
Heyho
- 31
2
votes
1 answer
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 this: when can I and when can I not assume q is the…
jessica
- 1,002
2
votes
1 answer
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 $M_2$.
Ron
- 91
2
votes
1 answer
Median of the subsets of a finite set of real numbers
Starting from this$^1$ question, using Mathematica I did the following.
Generated a sequence of $n$ random distinct "real" numbers.
Computed the median of the $2^n$ subsets (conventionally $\emptyset$ has a median zero) and deleted duplicates.
The…
Raffaele
- 26,371
1
vote
1 answer
Finding the (not) median from a histogram
This question is related to How to find median from a histogram?
A common problem is to estimate a median from a histogram, where 50% of the numbers are below the median, and 50% are above.
I would like to do this, but for some fraction other than…
Rocketmagnet
- 213
1
vote
1 answer
Change Value of the Median Without Using the Original Set of Numbers
Is it possible to change the value of the median based only on its value, without knowing the original set of numbers?
Example:
Consider the set $\{1, 1, 1, 5, 6\}$. The median value is $1$.
Now forget the set. I want to modify the median value by…
1
vote
0 answers
Median of sum of identially distrbuted copies of random variables
Let $X_1,Y_1$ be two arbitrary random variables, with distribution functions $P(X_1=x)= P_X(x), P(Y_1=y)= P_Y(y)$, and let $X_2,Y_2$ be random variables with the same distribution respectively, i.e., $P(X_2=x)= P_X(x), P(Y_2=y)= P_Y(y)$. However, we…
kvphxga
- 679
1
vote
1 answer
Find the reason of median
The median salary of Mr Pang's company is $10000$. Mr Pang therefore thinks that nobody in the company earns more than $20000$. Is this conclusion drawn appropriate? If not,why?
Alexander
- 11
0
votes
0 answers
What is the term for median but use the geometric mean instead of arithmetic mean if there are an even number of values?
"Geometric median" seems like the obvious choice for "median (but for even number of values, take the geometric mean of the central two values instead of the arithmetic mean)", but this seems to have a different meaning. Is there a term for this…
DanielM
- 1
0
votes
1 answer
median of unions of multiple set.
Suppose there are four sets $A, B, C, D$ with each having median $a < b < c < d$.
And the median of any two union. $a< median (A\cup B) < b $.
But I'm wondering would a similar behavior hold for more than 2 set ?
e.g. would $median (A \cup B \cup C)…
peng yu
- 1,271