Discover the Lower Quartile Math Definition and Examples

Recent questions in Lower Quartile
High school statisticsAnswered question
Santino Bautista Santino Bautista 2022-06-19

Identifying the k points in 2D geographic space which are 'most distant' from each other
I have a set of DNA samples from Y plants in a given geographic area. I'm going to be doing DNA sequencing on individuals in this population (and a number of other, separate populations), however due to financial constraints I'm unable to perform sequencing on all Y individuals. I've decided that I can afford to sequence k (out of Y) in each separate area.
I'd like to select the k samples which are farthest apart/most geographically distributed within the Y samples I collected. Samples that are taken from plants in close proximity to each other are more likely to be closely related, and I'd like to sequence what are ultimately the most genetically diverse samples for my later analysis.
So, the question is: given a set of Y points/samples in 2d geographic space (lat/long coordinates), how do I select the k points that are most geographically distributed/distant from each other?
As I've explored this a bit, I think the problem I'm really having is how to define 'distance' or 'most distributed'. Some of the metrics I've though of (e.g. maximum average distance between the k points) result in really unintuitive point selection in certain cases (for example, if two points are right next to each other but far away from another cluster of all the other points, the two points will be included even if they're almost on top of each other).
I have a feeling that this is not an uncommon problem, and there must be good answers out there. I'll add that I have access to a large cluster and I can brute force the problem to some extent.
I'd appreciate any and all advice or discussion; this is an interesting theoretical topic to me.

High school statisticsAnswered question
Dwllane4 Dwllane4 2022-06-17

Hypergeometric Distribution
I hate to be that guy who comes here and asks one question, however I've been stuck on this problem for quite some time, and I'm going to assume that I shouldn't even be using the binomial theorem at this point
I was given this question:
"A teacher was asked by her principal to select 7 students at random from her class to take a standardized math test, which will be used to determine how well students at that school are doing with respect to math (and correspondingly, how well the teacher is doing at teaching math). The teacher previously had rank ordered her students on the basis of their performance in her class on math tests, and divided the class into quartiles, such that there were 5 students in the upper quartile and 15 students in the lower three quartiles. When the teacher handed the principal the names of the students she had randomly selected from the class, the number of students from the upper quartile was 5, and the number of students from the lower three quartiles was 2. Is there any statistical evidence that the teacher is biased toward selecting students from the upper quartile?"
The first question given was:
"Compute the probability that, of the students selected, 0 are upper quartile students. Round off to 4 decimal places."
I was able to answer that question with the answer 0.0830, this i was able to answer by doing (15/20)(14/19)(13/18)(12/17)(11/16)(10/15)(9/14), however when it asks a question such as computing the probability that of the students selected, 2 are upper quartile students, I get stuck, I tried using the binomial theorem, but to no avail, perhaps I'm doing something wrong, I can't find a fast enough way to determine all of the sequences that will produce two upper quartile students of the 7 draws.

When you start with the calculations and offer lower quartile word problems based on statistical data for your social sciences course or a school project under the supervision of your teacher, the lower quartile will help you to find the value that is under 25% when you are working with the information that is arranged in increasing order. You’ll be able to find the range of your spread and the leaning of the data towards one side. You can take a look at the lower quartile math definition and examples that can be found among the questions that we offer.