Multivariate statistics | Mathematical optimization | Geometric algorithms | Nonparametric statistics | Means | Descriptive statistics
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the L1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation. The special case of the problem for three points in the plane (that is, m = 3 and n = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricelli. Its solution is now known as the Fermat point of the triangle formed by the three sample points. The geometric median may in turn be generalized to the problem of minimizing the sum of weighted distances, known as the Weber problem after Alfred Weber's discussion of the problem in his 1909 book on facility location. Some sources instead call Weber's problem the Fermat–Weber problem, but others use this name for the unweighted geometric median problem. provides a survey of the geometric median problem. See for generalizations of the problem to non-discrete point sets. (Wikipedia).
Median of a Triangle Formula, Example Problems, Properties, Definition, Geometry, Midpoint & Centroi
This geometry video tutorial provides a basic introduction into the median of a triangle. It provides the formula and equations necessary to calculate segment lengths within the median such as the distance between the vertex and centroid or between the midpoint and centroid. The median i
From playlist Geometry Video Playlist
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Concurrence of Medians (2 of 2: Proof via coordinate geometry)
More resources available at www.misterwootube.com
From playlist Further Linear Relationships
How to determine the geometric mean between two numbers
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Determining the sum of a geometric sum when there is no sum
👉 Learn how to find the geometric sum of a series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given by Sn = a[(r^n - 1)/(r - 1)], where a is the first term
From playlist Series
Learn how to find the geometric mean between two numbers
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Ayelet Heimowitz - Center of Mass Alignment for Noisy Tomographic Projections - IPAM at UCLA
Recorded 17 November 2022. Ayelet Heimowitz of Ariel University presents "Center of Mass Alignment for Noisy Tomographic Projections" at IPAM's Cryo-Electron Microscopy and Beyond Workshop. Abstract: Under the weak-phase object approximation, the center of mass of a 3-D macromolecule is pr
From playlist 2022 Cryo-Electron Microscopy and Beyond
Arithmetic (mean) versus geometric (median) stock return
The expected return of a stock is ambiguous because, if we assume returns are normal, then price levels are lognormal. In which case, the mean does not equal the median future stock price.
From playlist Intro to Quant Finance
Measures of Location, Mean, Median, Mode and Central Tendency in Business Statistics (Week 5A)
Three measures of central tendency (i.e. location) tell us mean, median, and mode of data. We choose our measure of location based on the level of the data, such as the mode for nominal, median for ordinal, and mean for scale variables. We may change our measure of location based on the ch
From playlist Basic Business Statistics (QBA 237 - Missouri State University)
Subspace and Network Averaging for Computer Vision and Bioinformatics -- Math Major Seminar
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From playlist MathMajor Seminar
How to Find the Median of a Data Set | Statistics
Do you want to know how to find the median of a data set? That is the subject of today's stats math lesson! The median of a data set is the value separating the lower half of data from the upper half of data. To find the median of a data set, we list the data points from least to greatest
From playlist Set Theory
Level 1 Chartered Financial Analyst (CFA ®): Statistical concepts and Quantiles
Session 2, Reading 8 (Part 1): Statistics is broadly either descriptive (aka, exploratory data analysis, EDA) or inferential (e.g., making predictions or forecasts). There is generally only one defined population and descriptive measures of the population are called parameters (and denoted
From playlist Level 1 Chartered Financial Analyst (CFA ®) Volume 1
Joe Neeman: Gaussian isoperimetry and related topics I
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Mean angle is not a usual average. Means on circle - Intro to directional statistics (3B1B SoME1)
How to indicate the mean direction (or average direction) of the wind? How to calculate the mean position (or average position) on the circle? [Timestamps below] This video shows that such a simple thing like mean or average changes its meaning for the points belonging to the circle or wh
From playlist Summer of Math Exposition Youtube Videos
How to determine the altitude by using the geometric mean
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
Cornelia Drutu - Connections between hyperbolic geometry and median geometry
The interest of median geometry comes from its connections with property (T) and a-T-menability and, in its discrete version, with the solution to the virtual Haken conjecture. In this talk I shall explain how groups endowed with various forms of hyperbolic geometry, from lattices in rank
From playlist Geometry in non-positive curvature and Kähler groups
Using the geometric mean to determine the missing parts of a triangle
Learn about the geometric mean of numbers. The geometric mean of n numbers is the nth root of the product of the numbers. To find the geometric mean of n numbers, we first multiply the numbers and then take the nth root of the product.
From playlist Geometry - GEOMETRIC MEAN
From playlist k-Nearest Neighbor Algorithm
StatQuest: DESeq2, part 1, Library Normalization
DESeq2 is a complicated program used to identified differentially expressed genes. Here I clearly explain the first thing it does, normalize the libraries. There is an error at 9:28: I have log(reads for gene X) - log(average for gene X), but it should be: log(reads for gene X) - average(
From playlist StatQuest
Mean v Median and the implications
Differences between the mean and median suggest the presence of outliers and/or the possible shape of a distribution
From playlist Unit 1: Descriptive Statistics