International Young Naturalists’ Tournament

Slides:



Advertisements
Similar presentations
Grammar 1. The Future (Buduća vremena)
Advertisements

Sampling Distribution of a Sample Proportion Lecture 26 Sections 8.1 – 8.2 Wed, Mar 8, 2006.
Ch.18 Normal approximation using probability histograms Review measures center and spread –List of numbers (histogram of data) –Box model For a “large”
Central Limit Theorem and Normal Distribution EE3060 Probability Yi-Wen Liu November 2010.
DISTRIBUTION OF THE SAMPLE MEAN
Section 5.7 Suppose X 1, X 2, …, X n is a random sample from a Bernoulli distribution with success probability p. Then Y = X 1 + X 2 + … + X n has a distribution.
J.G. Benito, G. Meglio, I.Ippolito, M. Re and A.M. Vidales Lab. de Ciencia de Superficies y Medios Porosos, UN San Luis, Grupo de Medios Porosos, Fac.
BCOR 1020 Business Statistics Lecture 18 – March 20, 2008.
Chapter 8 Counting Techniques PASCAL’S TRIANGLE AND THE BINOMIAL THEOREM.
9. Distances in open space Serbian team Regional Center For Talented Youth Belgrade II.
International Young Naturalists’ Tournament 2. Invent yourself-Biology Serbian team Regional Center For Talented Youth II.
Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.
Statistics 300: Elementary Statistics Section 6-5.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.. Chap 7-1 Developing a Sampling Distribution Assume there is a population … Population size N=4.
: An alternative representation of level of significance. - normal distribution applies. - α level of significance (e.g. 5% in two tails) determines the.
Prof: doc.dr. Samir Lemeš student: Samir Hrnjić. System restore je komponenta Microsoftovih operativnih sistema Windows Serveri ne podržavaju opciju System.
Lecture 5 Introduction to Sampling Distributions.
6.Disappearing Ink Serbian team Regional Center for Talented Youth Belgrade 2.
Strange jobs Jelena Maksimovic VIII-3 Jovana Maksimovic VIII-3 Ljubica Radenkovic VIII-3 Milena Jovanovic VIII-3.
Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:
m/sampling_dist/index.html.
A marbles game Changqing Li. A marble falls into the container. When the marble crashes the barrier in the first row, then the marble falls into the.
The normal approximation for probability histograms.
Sampling Distributions Chapter 9 Central Limit Theorem.
The Galton board The Galton board (or Quincunx) was devised by Sir Francis Galton to physically demonstrate the relationship between the binomial and normal.
On the spectrum of Hamiltonians in finite dimensions Roberto Oliveira Paraty, August 14 th Joint with David DiVincenzo and Barbara IBM Watson.
Ch5.4 Central Limit Theorem
TENSES: PAST SIMPLE and PAST CONTINUOUS Prošla vremena: forma i upotreba Past simple ili obično prošlo vreme gradi se tako što se na infinitiv glagola.
Chapter 7 Sampling and Sampling Distributions

KAKO IZRADITI IGRU: Izrežite tabele, sličice, kartice, žetone. Ostavite 1mm bijelog ruba oko okvira. Nalijepite ih na karton u boji (hamer), jako lijepo.
Uvod u programiranje - matematika – VI predavanje
CASE naredba višestrukog grananja
Simple Past protiv Present Perfect-a
Naredbe ciklusa.
Microsoft Office 2007 MS Office je programski paket koji sadrži više programa: MS Word – program za obradu teksta MS Excel – program za izradu tabela sa.
Statistical Inference for the Mean Confidence Interval
What’s the time? (Koliko je sati?)
Uvod u programiranje - matematika – X predavanje
Seminar: “Usavršavanje nastavnih procesa – Case study metod” Tema:Case study u očima protagonista By Jasmin Hošo.
Naredba Case Višestruko grananje.
Regional Center for Talented Youth Belgrade II
M-datoteke.
Using the Tables for the standard normal distribution
The Binomial Distribution
Kyle Burgess Josh Edmiston Evan Gangaware William Sullivan
Articles.
Do While ... Loop struktura
Sampling Distributions
International Young Naturalists’ Tournament
Up, Up & Away (The Great Balloon Launcher)
BLOOMOVA TAKSONOMIJA I
Programiranje - Naredbe za kontrolu toka programa – 3. dio
MODUL 5: PRIJENOS ZNANJA
International Young Naturalists’ Tournament
Regional Center for Talented Youth Belgrade II
Summary of Tests Confidence Limits
CHAPTER 7 Sampling Distributions
Project by: Amber Thomas Andrea Williams Lindsey Sharp Shayna Chapman
CHAPTER 7 Sampling Distributions
Chance Errors in Sampling (Dr. Monticino)
11.1 Find Measures of Central Tendency & Dispersion
Hananto Normal Distribution Hananto
CHAPTER 7 Sampling Distributions
Sampling Distributions
Regional Center for Talented Youth Belgrade II
CHAPTER 7 Sampling Distributions
Hour of Code Coding Jetpack Jumper Mateja Hržica, MSP.
Algebra 2 Ch.6 Notes Page 23 P Pascal's Triangle and The Binomial Theorem.
Presentation transcript:

International Young Naturalists’ Tournament 14. Galton box Serbian team 2 Regional Center For Talented Youth Belgrade II

14. Galton box In the Galton box, a regular 2D lattice of obstacles disperses a thin flow of falling particles. When falling on the bottom of the box, the particles show a normal distribution. Use various types or particles and different arrangements of the obstacles to find the conditions when the distribution is no longer normal. U objasnjenju problema je pisalo kako tokom galtonovog ekperimenta uz pomoc galtonove kutije dobijamo normalnu distribuciju i nas zadatak je glasio da koristimo razlicite tipove i oblike prepreka kako ta distribucija vise ne bi bila normalna

Galton box 50%-50% chance – Bernoulli principle Galton box is a machine which was made by Frensis Galton Prvo trebamo da znamo nesto uopsteno o galtonovoj kutiji. Galtonova kutija je uredjaj koji je napravio Frensis Galton kako bi mogao uraditi galtonov eksperiment i dokazati da slucajno bacena zrna pasulja mogu ciniti normalnu distribuciju. A sad da objasnimo nacin rada galtonove kutije. Prvo kroz levak na vrhu uredjaja bacamo loptice i svaka loptica svoj put pocinje od centra. Kako loptica stigne do prepreke ona moze da skrene levo ili desno i verovatnoca za to je 50-50%. Kada je verovatnoca da se nesto desi 50-50% onda se to naziva bernulijev eksperiment. Takvo kretanje klikera u galtonovoj kutiji se naziva paskalovo kretanje. Posle odredjenog vremena svaki od klikera ce pasti na dno uredjaja u jedan od pretinaca. Kada padne dovoljan broj klikera pojavice se normalna distribucija. The rolling of marbles through Galton box is called Pascal movement

Working principle of Galton box Ovde smo prikazali princip rada galtonove kutije o kome smo pricali na prethondnom slajdu.

Pascal triangle Galton box uses the principle of work of Pascal triangle Galtonova kutija koristi princip rada paskalovog trougla.

If the number of rows of pins is large enough, this would approximate a normal distribution due to the central limit theorem. Normal distribution x=the bin position e.g. x=0 could be treated as the left-most bin, and x=N could be treated as the right-most bin P=the probabilaty of x p=the probability of bouncing right (if x=0 represents the left-most bin). In an unbiased machine: p=0.5 N=the number of rows of pins i.e. The number of times a ball bounces

ANIMATION http://teacherlink.org/content/math/interactive/flash/quincunx/quincunx.html

SOLUTION number 1 We drop all the particles at the same time If we dropped all the particles at the same time they would hit each other and bounce back which would also cause them to form a different distribution. they hit each other and bounce back

SOLUTION number 2 If we turn obstacles upside-down.

SOLUTION number 3 There isn’t enough number of the columns at the bottom of the galton box.

Our visit...

Our visit...

CONCLUSION The ways the normal distribution can be changed is by not having the funnel, turning that part with obstacles upside-down and by changing the number of the columns.

THANK YOU FOR YOUR ATTENTION!!!

Reference http://www.statisticalconsultants.co.nz/blog/the-galton-box.html http://teacherlink.org/content/math/interactive/flash/quincunx/quincunx.html http://www.mathsisfun.com/data/quincunx.html http://www.mathsisfun.com/data/standard-normal-distribution.html