Grouping Definition and 31 Threads

In shooting sports, a shot grouping, or simply group, is the collective pattern of projectile impacts on a target from multiple consecutive shots taken in one shooting session. The tightness of the grouping (the proximity of all the shots to each other) is a measure of the precision of a weapon, and a measure of the shooter's consistency and skill. On the other hand, the grouping displacement (the distance between the calculated group center and the intended point of aim) is a measure of accuracy.
Tightness of shot groupings are calculated by measuring the maximum distance between any two bullet holes on the target (center-to-center) in length measurements such as millimeters or inches. Often that measurement is converted into angular measurements such as milliradians ("mils" or "mrads") or minutes of angle (MOAs), which expresses the size of shot scatter regardless of the target distance. Thus, by using angular measurements, one can reliably compare the relative tightness of shot groupings fired at different distances.

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  1. M

    MHB Find the best function grouping with an iterative method

    Hello to everyone! I'm having a problem, banal in form, but perhaps complex in practical application. Let's suppose we have 300 functions y = f (x) of random trend and we want to group these functions into 10 subgroups (each group consisting of 30 functions). However, this grouping must not be...
  2. W

    A Grouping Non-Continuous Variables

    Hi All, Is there a technique other than PCA (Principal Component Analysis) to decide whether it is somehow reasonable to group together , aka " collapse" several non-continuous ( Categorical, Likert, Ordinal, etc. ) into a single one. The idea is, of course, to lose only a negligible amount of...
  3. nearc

    I Tight grouping of exoplanets 295RA 45dec

    does anyone have any information on why the vast majority of exoplanets are located in one spot? any papers on the topic? the following link does not graph RA vs DEC but instead does something about planet size, if you wish to use it please select RA for the x-axis and DEC for the y-axis, both...
  4. M

    MHB How can the factor by grouping method simplify polynomials with multiple terms?

    Factor 8a^3 + 27b^3 + 2a + 3b. 8a^3 + 2a + 27b^3 + 3b 2a(4a^2 + 1) = Group A 3b(9b^2 + 1) = Group B (4a^2 + 1)(9b^2 + 1)(2a + 3b) Correct?
  5. M

    MHB Is there more factoring to come?

    Precalculus by David Cohen, 3rd Edition Chapter 1, Section 1.3. Question 48. Factor the expression by grouping. a^2t^2 + b^2t^2 - cb^2 - ca^2 Group A = a^2t^2 + b^2t^2 Group A = t^2(a^2 + b^2) Group B = -cb^2 - ca^2 Group B = -c(b^2 + a^2) Group B = -c(a^2 + b^2) Group A - Group B...
  6. H

    MHB Need help factoring and understanding Grouping

    I need to factor 6t^2+17t+7 when I break down the equation I get 6t^2+3t+14t+7 now I am not sure what to do after that to get my answer can someone please explain the steps for me thank you!
  7. S

    Finding the sum of a series by grouping

    Homework Statement Homework Equations Summation The Attempt at a Solution I know I could have simplified (3n-2)^3 +(3n-1)^3 -(3n)^3 and put the formulas in but I wonder is there any other method (I was thinking about grouping the terms, but to no avail) to work this out.
  8. S

    Grouping constrained optimization

    Hi all, I am looking for an efficient solution to solve the following problem. Can anybody help? Assume a set S of elements ki and a set V of possible groupings Gj. A grouping Gj is a subset of S. Associate a weight wij to each mapping ki to Gj. The weights are infinite if ki ⊄ Gj, and finite...
  9. N

    Nice grouping of primes under 105

    The simple algorithm shown in the uploaded file generates a nice grouping of primes under 105.
  10. C

    MHB Taking cubic with log in the grouping symbols

    Use Logarithms to compute the following, correct to four- accuracy. (In find N from Log N, don't interpolate).26. $$(\log\left({0.007211}\right))^3$$ Let N=$$(\log\left({0.007211}\right))^3$$ Then $\log\left({(\log\left({0.007211}\right))^3}\right)$=$$\log\left({N}\right) $\therefore$...
  11. P

    What Is a Grouping Factor in Graphical Modelling?

    I am staring a course in graphical modelling, and I have no idea what this is. For example, if I is a fixed grouping factor, and Y is a response, then it is natural to examine the densities fY/I (y/i) for each level i of I. Thanks!
  12. B

    MHB Grouping terms to start factoring.

    how would i go about properly grouping terms to start my factoring? 1. $12x^2y^3-24y^3z-6x^6+30y^4-15x^4y+4x^2y+12x^4z+10y^2-8yz$ thanks!
  13. W

    Grouping all of the units at the end? I.E. F=ma = 2.3*424.3 [kg*m/s]

    In some papers I've read, I've seen the authors write down all of the units at the end. For example ##F=ma = 2.3*424.3 [kg*m/s^2]## In high school, I've never seen the teachers or textbooks write like this. How common is this is method? Assuming one keeps track of their units properly, I...
  14. N

    MHB Geometric Progression sequence with an Arithmetic Progression grouping problem

    Good Day, My friends and I are stuck on solving the last part of the attached problem. The solution is 2^[(n^2 + n)/2] - 1. Can anyone help us with solving this? Thanks & Regards, Nicodemus
  15. P

    2d bin packing + selective grouping

    Hi everyone! Let me introduce myself, my name is Francisco and I'm an architecture student. I've recently become interested in algorithmic design, which is basically utilizing math to help design (an example would be structure or space optimization). To contextualize, I am a noob with...
  16. C

    Grouping Stores based on past retail sales.

    I have a set of retail data explaining how many sales per store occurred during each week of the past 52 weeks. I want to group these stores by which follow each other the best over the course of the year. Let's say they'll be 10-20 stores in each group, although this number will be refined...
  17. C

    What determines a bullet's grouping?

    What, other than recoil, the user's unsteady hands and gravity, causes bullets to impact different places on the target?
  18. S

    What is the difference between /\.[^.]*$/ and /(\.[^.]*)$/?

    I was just playing around with sed regular expressions and found something I wouldn't have expected. What is the difference between /\.[^.]*$/ and /(\.[^.]*)$/? Does the latter group it incorrectly somehow. Note that the former does what I want it to, to match an extension of a file...
  19. D

    Factoring polynomial through grouping

    Homework Statement 2n - 6m + 5n^2 - 15mn Homework Equations No particular equation since this is factoring The Attempt at a Solution Keep in mind that I struggle when it comes to grouping as I'm not sure where I'm supposed to start but... 2n - 6m + 5n^2 - 15mn Group first 2...
  20. L

    Question about kmaps and grouping

    Homework Statement I got a question about grouping of 1 in kmap, ex in 16 cell 1100 1100 1110 1010 so i box the top left 4 then i box the two on the bottom right. now this part i don't get, they box 4 other ones overlapping the top box. why don't they just box the two by them self, also can...
  21. K

    Is 'Grouping' Intelligence Possible?

    I recently read a book on the theory of intelligence by Jeff Hawkins aptly titled 'On Intelligence' which I highly recommend. In it, Hawkins posits that the basis of human intelligence lies in the hierarchical structure of the neocortex. Reading this book started me thinking about whether...
  22. T

    Counting and Grouping Feynman Diagrams

    I'm working through Srednicki's QFT text, and I'm continuously vexed by the various numerical factors in diagrams and vertices, as well as the grouping of diagrams. For example, in Chapter 10 (pg 75) Srednicki treats basic \phi\phi\rightarrow\phi\phi scattering processes in \phi^3. He claims...
  23. E

    Moment of Inertia of a grouping of pennies

    Hi, An old GRE problem asks what the moment of inertia of seven pennies, arranged in a hexagon with one in the center, all touching each others' edges is, about the axis that passes through the center of the central penny and is normal to the plane of the pennies. Each penny is a uniform...
  24. Jonnyb42

    Exploring Nucleus Grouping: Proton, Neutron, or Quark Clump?

    Nucleas Grouping?? Why do we say a nucleus is composed of protons and neutrons when those protons and neutrons are themselves composed of quarks? Is there really grouping to these protons and neutrons or do we just say it is composed of protons and neutrons for convenience (and that it is...
  25. K

    Grouping Elements: Making m Groups of n Elements w/ t Uses

    How many groups size m can you make from n elements (m<n) such that each element is used the same number of times t (t>0)? For instance, if you have 8 teams and group them in triplets, how many triplets do you need so that each team plays the same number of times?
  26. T

    Medical 8 letter word for a efficient grouping of cardiac muscle cells

    Doing a homework crossword and this is the last problem. I can't seem to find it anywhere. An efficient grouping of cardiac muscle cells, eight letters long ending in M. Any help would be much appreciated.
  27. R

    Math Grouping Help: 20 Students, 4 Groups of 5, Different Schools

    Homework Statement Divide 20 students in 4 groups of 5 each. Find the number of ways of doing this? Also find how can these gropus be sent to 4 different schools? The Attempt at a Solution I get both the answers as: 20C5*15C5*10C5*5C5 But my book gives two different answers for...
  28. R

    Reverse Partition grouping problem

    In an Excel group someone connected with the Texas caucus gave this math problem> how to subdivide the following set of precincts into subsets so that there are a maximum number of subsets from this set with each subset of precincts totaling at least 180 votes. Since the caucus is this month it...
  29. C

    Slight problem with grouping a set of numbers

    For some reason, the code I has compiles, but it just doesn't seem to do what it should. The code I have atm, involves opening a file of numbers, reading the numbers, and sorting them into groups. int nmax; // This is the number of lines in the file int i...
  30. A

    How many ways can 12 people be divided into 3 equal groups?

    The number of ways in which 12 people may be divided into 3 equal groups is_ My ans is 12C4*8C4*4C4=34650. But my test book contains the answer 5775. So iam confused. Is my answer correct or am i missing something?
  31. E

    Grouping & Multiplying 4x4 Matrices: A Quick Guide

    Some big matrix, like 4x4 ones, can be written as groups of 2x2 matrices. For example, H = \left(\begin{array}{cccc}1 & 0 & 1 & 0\\0 & 1 & 0 & 1\\1 & 0 & 1 & 0\\0 & 1 & 0 & 1\end{array}\right) = \left(\begin{array}{cc}1 & 1\\1 & 1\end{array}\right) where the 1 in the last matrix represents...
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