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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0
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2answers
19 views

Is it possible to find Median of set contains string value as well as Null value?

I am doing one calculation on Median and AFSIK about Median, it can be calculated by a "set of Finite set of Numbers". Now if a set has following value as: A = {3,4.56, 2, 11, JAMES, , Joy, 54, 9} ...
2
votes
1answer
25 views

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.
7
votes
1answer
860 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.
0
votes
1answer
10k 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: $\begin{cases} 0.04x & 0 \le x < 5 \\ 0.4 - 0.04x & 5 \le x < 10 \\ ...
1
vote
2answers
59 views

Where should I use median instead of average?

Is there a general law, or rule of thumb, or rationale, when to use median and when average? Although I know the difference and how they are computed, when I try to translate to simple English I ...
1
vote
1answer
448 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
0
votes
1answer
27 views

Uniqueness of Spatial Median

https://projecteuclid.org/download/pdf_1/euclid.aos/1176350511 Can You help me understand why there is less-than sign in the proof? ...
2
votes
2answers
2k 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 ...
4
votes
4answers
600 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 ...
1
vote
0answers
22 views

Runtime of recursive algorithm - Master's Theorem

I wrote a computer program that solves a question, and I am interested in knowing what is the runtime. My aim is for $O(\log n)$, and I'd like someone more experienced (and smarter?) to review my ...
2
votes
1answer
22 views

Equivalent events in proof of Central Limit Theorem for Sample Median

Let $X_1,X_2,\ldots,X_n$ be i.i.d. random variables with cdf $F$ on $\mathbb{R}$ and $M_n$ be the sample median. The proof starts off with defining for any $a\in\mathbb{R}$, $S_n = \#\text{ of ...
0
votes
1answer
36 views

Is it possible for the median to be left to the mean in the Gamma distribution?

Many textbooks teach a rule of thumb stating that the mean is right of the median under right skew, and left of the median under left skew but this is not always true. According to wikipedia, there ...
0
votes
1answer
31 views

Design an algorithm - Median, computer science

I was wondering if this question belongs here or on StackOverflow, but it is a question of mathematical nature so this seems more appropriate. We have an array $S$ of $n$ different numbers ...
1
vote
1answer
16 views

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?
0
votes
2answers
40 views

How to find the median of three numbers, if one of them appears twice?

How do you determine the median of three numbers where two of the numbers are duplicated? For example, $(6,6,3)$.
5
votes
1answer
106 views

Why hasn't the median function made the mean (effectively) obsolete?

I've learned in my AP statistics class that means can really only be used on nearly-normal distributions, but I know that many studies, experiments, etc. don't always give that perfect normal curve ...
3
votes
2answers
68 views

The minimum of the sum

I was trying to prove some theorem on my way. So the problem was: Theorem: Let $x_1, x_2, ..., x_n$ be the rising sorted sequence of numbers. The $ \sum_{k=1}^n |x_k-a|$ reaches it minimum if ...
0
votes
2answers
32 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
vote
0answers
22 views

How to understand the Repeated Median Estimator (Siegel 1982)?

I guess I did not understand the formula of the repeated median estimator introduced by Siegel (1982): This is the formula: If I got the following time series for instance: ...
0
votes
1answer
34 views

$E|X-m|$ is minimised at $m$=median

For a continuous random variable $X$, I want to show that $E|X-m|$ is minimum implies $m$ is the median of the distribution. Assume that the distribution function is $F$ and the density function is ...
0
votes
1answer
30 views

Create a Data Set Given Median and Mean

Its a very simple problem to a homework question that I can easily solve, but if time-willing I like to go about it a more elegant way. So lets say you need to create a set of 5 numbers whose median ...
1
vote
1answer
32 views

Problem with similarity of triangles and median.

I have the next problem: In the next image, MN // AB, PN = NC, QM = 8, BM = 6 and MC = 9. Calculate PM. First I tried to find similarities in the triangles formed by the parallel sides, ABC and ...
1
vote
3answers
42 views

What is the general formula for calculating the median?

How can I rewrite the equation $\mu = \frac{1}{N}\sum _{i=1}^Nx_i$, if I don't want to find the mean, but the median of all $x_i$, $i=1,\dots,N$?
2
votes
2answers
195 views

Why add the number 1 to find the median number

Example 1: There are 45 numbers 45 plus 1 is 46, then divide by 2 and you get 23 So the median is the 23rd number in the sorted list. Example2: There are 66 numbers 66 plus 1 is 67, then divide ...
1
vote
2answers
55 views

Finding median of union of two sorted (ordered) lists

We are given two sorted list of numbers $a_1, a_2, \ldots, a_n$ and $b_1, b_2, \ldots, b_n$. Question is, how to find a median for list $a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_n$. Algorithm should ...
1
vote
3answers
8k 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?
1
vote
0answers
127 views

How do I find percentiles of data sets (Even vs odd)?

Given the following data set with an even number of values: $100, 100, 105, 113, 129, 132, 146, 152, 176, 200$ The value representing the 30th percentile, using the formula n(p/100) where n = sample ...
0
votes
0answers
13 views

Confidence level using unknown median

This is a general question. Lets say we are giving a sample space n. The sample space has an unknown median The order statistics of each person, $**X_{i}**$ in sample space is measured (lets say ...
0
votes
0answers
16 views

CONFIDENCE LEVEL for Median Interval

A firm wants to estimate the unknown median, m , of the height of their employees. Random Simple Size = 90 $X_{i}$ is the order statistics of the Sample Size X where height of each employee was ...
1
vote
2answers
51 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 ...
2
votes
2answers
33 views

Proving that median of list $[x_1,x_2,…,x_n]$ minimises the sum $\sum_{i=1}^{i=n} |x_i-m|$ where $m$ is some number [duplicate]

The problem is in the title. Here is a detailed description: Let's say we have list $[x_i]_{i=1}^{i=n}$ where $x_i\in\Bbb{N}$. I want to pick such $m\in\Bbb{N}$ which minimises the sum ...
0
votes
1answer
19 views

Can you further explain or clarify the proof of this?

I am trying to prove that $AG = 2(GD)$, given $AD, BE$ and $CF$ are 3 medians meeting at point $G$ of a triangle $ABC$. I found this website that seems to show what I want to prove: ...
0
votes
0answers
8 views

Fill chart using known final answers [duplicate]

so all I know is that: n=100. i have 5 departments within the numbers: 0-1000. md = 500. avg =490. lower decile=200. upper quarter=600. I really don't know how to use the formulas of each if I don't ...
0
votes
1answer
47 views

Median of truncated / limited normal distribution

The peoples weight is normally distributed $\mathcal{N}(0,\,1)$ The $\mu \; , \; \sigma \; and \; \sigma^2$ are known. How can i calculate the median weight of people if everyone who weights less ...
0
votes
1answer
59 views

What information guarantees a ranking in the 90th percentile is greater than a ranking in the 70th percentile?

Consider the following facts: Person A's salary is in the 90th percentile in Company A. Person B's salary is in the 70th percentile in Company B. The question is: What piece of information is ...
3
votes
1answer
61 views

Squence of order statistic converges to median?

Suppose that $(X_1,...,X_N)$ be $N$ iid samples from uniform distribution. Let $X_{(n)}$ be $n$-th order statistic. It sounds natural that $X_{N/2}$ converges to the median, $1/2$. (interpret $N/2$ as ...
0
votes
1answer
174 views

Analysis of IQ scores given mean, median, sd, quartiles

The statistics below provides a summary of IQ scores of 100 children Mean: 100 Median: 102 Standard Deviation: 10 First Quartile: 84 Third Quartile: 110 About 50 of the children in this sample have ...
4
votes
2answers
3k views

Prove that the sample median is an unbiased estimator

My book says that sample median of a normal distribution is an unbiased estimator of its mean, by virtue of the symmetry of normal distribution. Please advice how can this be proved.
0
votes
1answer
112 views

How to plot median with 10% and 90% percentiles

I have to make a plot of same data (I do it in Matlab). On the x-axis the time (in seconds) and on the y-axis the response time (in ms). Now I have to do it with "Median with 10% and 90% ...
0
votes
1answer
21 views

Calculation of median

I want to calculate the median of several variables. The detail is as follow: For example, a, b and c are all random number from uniform distribution in certain range (different between each other). ...
0
votes
1answer
252 views

Finding the most likely serve speed of a tennis player

U.S. Open Tennis Championship a statistician keeps track of every serve that player hits. The statistician reported that the mean serve speed of a particular player was 95 miles per hour. Suppose ...
1
vote
1answer
3k views

What is weighted median? [duplicate]

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
votes
2answers
47 views

Finding Median in a distribution

What does it mean by "find all medians"? I thought there could only be one median. Also, how would you approach solving this question? Suppose $P(X = x) = \displaystyle\tfrac{x}{21}$ for $x = 1, 2, ...
9
votes
4answers
544 views

A continuous function defined on an interval can have a mean value. What about a median?

A function can have an average value $$\frac{1}{b-a}\int_{a}^{b} f(x)dx$$ Can a continuous function have a median? How would that be computed?
2
votes
2answers
56 views

Proof of $\sigma^2\geq (\mu-m)^2$ without resorting to Jensen's or Chebychev's inequality.

I asked a group of undergrad students (engineering) to prove that $\sigma^2\geq (\mu-m)^2$, where $\sigma^2$, $\mu$ and $m$ are the variance, mean and median of a continuous random variable. For the ...
0
votes
2answers
297 views

Why mean=median=mode of a bell curve?

I was reading this link - source - http://www.mathsisfun.com/data/standard-normal-distribution.html Here they say that for the bell curve - the mean = mode = median are identical. How mean i.e. ...
0
votes
0answers
33 views

Distribution estimate from a sample or just a probability theory task

Here is the task: I have a sample of replies to my e-mail from my mail box. A sample is taken over a period of 90 days, 1000 e-mails and replies if any. (We only consider a pair of {my original ...
0
votes
1answer
116 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
vote
2answers
642 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
votes
1answer
44 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 ...