Coordinate set, specific point

In summary, the conversation discusses the calculation of the barycenter and other interesting points in 2D space. The barycenter is found by summing all values with respect to the x-axis and y-axis separately, then dividing by the number of coordinates. Other points such as median value, mean variations, and multiple occurrences of coordinates are also considered. The question also mentions incorporating different measures, such as minimizing the sum of squared distances and geometric median, to find specific points in 2D space. The overall goal is to find specific points with certain characteristics in 2D space.
  • #1
onako
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Given a set of 2D coordinates (real numbers, involves positives and negatives), I could calculate the (weighted) barycenter by simply using the logic with plain numbers. For the barycenter calculations, I sum all the values with respect to x-axis and y-axis separately, and then divide with the number of coordinates (in weighted case, the weight coordinate product is incorporated).
However, I wonder what other interesting points I might analyse. For median value calculation, I would have to select the middle one. But, in 2D world, do I select the median coordinate (if such a thing exists) based on median x-axis value and median y-axis value (usually not the same coordinate)?

Also, there are other specific points I might use based on "mean variations", but I wonder which of those could be translated to 2D world. For example, harmonic and geometric mean are related to the set of positive numbers. What would be the way to incorporate the ideas into the 2D world?

The question in the Probability and Statistics subforum, meaning that calculating other specific points, based on different measures, is an option I might want to consider. Any suggestions on which measure to consider is welcome. These might incorporate the value (coordinate) spread, multiple occurrences of (nearly) same coordinates, emphasizing coordinates "on the border"...
Thanks.
 
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  • #2
To simplify; the barycenter of the coordinates is the point that minimizes the sum of squared distances; also, geometric median is the point that minimizes the sum of distances.
I'm interested about other specific points in 2D space with certain characteristic (in above examples, these would be "minimizing the sum of distances").
 

1. What is a coordinate set?

A coordinate set is a collection of two or more coordinates that represent a specific location or point in space. It is typically written as (x, y) or (x, y, z) and is used to determine the exact position of an object or point in a coordinate system.

2. How do you plot a specific point on a coordinate system?

To plot a specific point on a coordinate system, you need to have the coordinates of the point. Then, you can locate the corresponding point on the grid by counting the number of units along the x and y axes. For example, if the coordinates are (3, 5) you would count 3 units along the x-axis and 5 units along the y-axis to locate the point.

3. What is the difference between a specific point and a general point?

A specific point has definite coordinates that can be plotted on a coordinate system, while a general point does not have specific coordinates and can represent any point in a given space. Specific points are often used in mathematics and geometry, while general points are more commonly used in physics and other sciences.

4. How can you find the distance between two specific points on a coordinate system?

To find the distance between two specific points on a coordinate system, you can use the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2). This formula uses the coordinates of the two points to calculate the distance between them. Alternatively, you can also count the units along the x and y axes to find the distance.

5. Can you have a negative coordinate in a coordinate set?

Yes, you can have a negative coordinate in a coordinate set. In a two-dimensional coordinate system, the origin (0,0) is the point where the x and y axes intersect. Coordinates to the left or below the origin will have negative values, while coordinates to the right or above the origin will have positive values. In a three-dimensional coordinate system, the origin (0,0,0) is the point where the x, y, and z axes intersect, and the same principle applies.

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