# 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.

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### How does Excel calculate quartiles?

I have the data set [3,7,9,10]. Excel and Desmos both return the value 8 for the median, which agrees with my understanding of ...
14 views

### Median for continuous function explanation

So, I was wondering what the continous version of the median is (not a homework problem, just curious)? Can someone provide me with an explenation of the continous median, and maybe show how to derive ...
15 views

### Decision to use median or average in a skewed or uniform distribution [closed]

Goal: To determine whether to use the median or average (or a weighted combination of the ...
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### Clarify answer for asymtotic of median smoothing

Calculating algorithmic complexity for median smoothing in Time Series I came up with the question same as this. Quote it here: A time series with T observations is given. Median smoothing with width ...
1 vote
18 views

### Skewed data: choosing the average or median

Goal: The data below shows (in order) the date, median, average, ...
69 views

### Why are mean, median, and mode called central tendency?

Is there any difference between the two terms "Central tendency" and "representative values"? Why are mean, median, and mode called central tendency or representative values?
67 views

### Probability that the median roll of 21 rolls is 6

Let's say I roll a fair 6-sided dice 21 times. Assume 𝑀 tracks the median of the 21 numbers rolled. What is 𝑃(𝑀 = 6)? So far, I believe that this implies at least 11 of the rolls have to be 6, and ...
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### A better definition of "median"?

Referring to the definition in Wikipedia, paraphrased: Formally, a median of a population is any value such that at most half of the population is less than the proposed median and at most half is ...
1 vote
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1 vote
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### minimizing the distance between values

Find all values of $a$ that minimize the expression $|a- x_1| + |a-x_2|+\cdots + |a-x_n|$, where $x_1\leq x_2\leq \cdots \leq x_n$. I know the minimum is achieved when $a=x_{\lfloor n/2\rfloor + 1}$ ...
1 vote
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### Is it true that the sum of squares of perpendicular medians in a triangle is equal to the square of the third median?

I am aware of the fact that two medians are perpendicular in a triangle if and only if the Sum of the squares of the lengths of the sides to which these medians are drawn is $5$ times greater than ...
158 views

### Solve a triangle given one angle of the median, and a side and an angle of its external triangle

This is a modified version of this question, and as such I'm using similar wording and visuals. Given: $α_2$, one of the two angles which the vertex $A$ is split by the median $m$; $\overline{AD}$, ...
18 views

### Median of function Z (Random Variable of Present Value of Benefit) of Multiple Decrement Model

I have a problem in determining median in life insurance context. Here we have $Z$ as random variable of present value of benefit of insurance like this: It will give benefits of $1000$ (at the moment ...
1 vote
53 views

### Minimizing $E(|Y-f(X)|)$.

Assume that $X$ and $Y$ are random varaibles. The theory of conditional expectation says that the function f that minimizes $E[(Y-f(X))^2]$ is $f(x)=E[Y|X=x]$. My book says that the function that ...
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### using linear programming to find median

I'm trying to figure out how to transform a median solving problem for a list of number x to linear programming and with standard form of $$\text{min }c^Tx \text{ s.t: } Ax\le b \text{ and }x \geq 0$$ ...
62 views

### How to calculate median, variance and correlation on two-dimensional random variable. [closed]

Two random variables, X and Y, have the joint density function: $$f(x, y) = \begin{cases} 2 & 0 < x \le y < 1 \\ 0 & ioc\end{cases}$$ Calculate the correlation coefficient between X and ...
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### How close is the median of a uniformly chosen subsample to the median of the full set?

Take $N$ a set of n numbers, sample s numbers from $N$ uniformly and with replacement giving us the set $S$. What is the relationship between the median of $N$ and the median of $S$ ? I want a result ...
1 vote
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### Why would you use a different calculation for finding median from a histogram rather than from a regular set of data?

I've always learned that you should use $\frac{n+1}{2}$ to find the median of a regular set of data. For example, the median of $$1, 2, 3, 4, 5, 6, 7$$ would be $4$ because of $\frac{n+1}{2}$. But ...
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### Median for grouped/ungrouped data

If I am given a series of, let's say, 50 observations, of a continuous data, for example, the height of some group of people: 165.23 cm, 134.28 cm, and so on, and I want to find the box plot, I need ...
54 views

### Name and interpretation of the median of $xf(x).$

Is there a name for $\operatorname{median}(xf(x))$ where $f(x)$ is a probability density function on real numbers (or positive real numbers)? If yes, what are the properties of this number? This ...
31 views

### Mode and median of a discrete random variable - Exercise

I've the random variable $X=(0,25,25,50,100)$. Is it correct to say that: $$mode = 25$$ and $$median = 25$$ because $P(X \leq 25) = 2/5 = 0.4$ ?
1 vote
67 views

### Why is finding the median and quartiles different on a cumulative frequency graph? (Or is it?)

When finding the median we look for the (n+1)/2 value in the ordered data set. For the lower quartile it's the (n+1)/4 value and the upper quartile is 3/4(n+1). However, I've been helping my ...
33 views

### How to find the median of a p.d.f with unknown integral limits

I have been given the p.d.f: $$f(x) = \frac{1}{b}\exp \left(\frac{-(x-a)}{b}\right)\exp\left(-\exp\left(\frac{-(x-a)}{b}\right)\right)$$ where $-∞ < a < ∞$ and $b > 0$. And I need to show ...
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### Why do we get the median of an arithmetic series by getting the average?

I'm wondering why we get the median of an arithmetic series by getting the average. Example: $2 , 4 , 6 , 8$ The median is $5$⇒ $\frac{4+6}2$. Meanwhile, the average is also $5$⇒ $\frac{2+4+6+8}4$ A ...
84 views

### What's the median of $f(x) = 4xe^{-2x}$?

I'm trying to find the median of $f(x) = 4xe^{-2x}$. So far, I've tried solving for $q_{50}$ by plugging it into an integral and setting it equal to 0.5 like so: $\int_{0}^{q_{50}} 4xe^{-2x} dx = 0.5$....
1 vote
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### Is it possible to make a formula for median that works with both even or odd amounts of values?

Everyone here probably knows the median formula. It's the middle number of the set if the number of values in the set is odd, or the average of the two middle numbers in the set if the number of ...
1 vote
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### Absolute geometry and concurence of medians

I'm trying with a friend to find ....the simplest proof that in absolute(neutral) geometry the medians concur. In Bachmann's book (in German-Aufbau der Geoemtrie aus Spiegelungsbegriff) there is a ...
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### How do I find the mode when my data points have decimals?

My data has numbers such as 70.35, 70.39, 70.1. None of the numbers are exactly the same. How do I find the mode?