variance - 2025 ACF Fall

Tossup

This quantity is minimized for an unbiased estimator (-5[1])that is a function of a complete and sufficient (10[1])statistic by the Lehmann–Scheffé (“LAY-man shef-FAY”) theorem. (-5[1])Ronald Fisher developed a test that generalizes the t-test to more than two groups named (-5[1])for the “analysis of” (10[1]-5[1])this quantity. (10[19]-5[4])For (-5[1])two (10[1])random (10[2])variables (10[1]-5[1])X and Y, (10[1]-5[2])the expected (-5[1])value of (10[1])X times Y minus the (10[1])product (10[2])of (10[1])the expected (10[3])values (10[1])of X (10[1])and Y (10[1]-5[1])gives this quantity’s (10[3]-5[1])“co-” (10[2]-5[1])form. (10[16]-5[1])This (10[2]-5[2])quantity (10[5])is (10[1])the (10[2]-5[1])second (10[3])central (10[3])moment (10[3])of a distribution, (10[2]-5[1])and is equal to the mean for a Poisson (“pwa-SAWN”) distribution. (10[3]-5[1])For a random variable X, this quantity is the (-5[1])[read slowly] expected (-5[1])value of X squared, minus the square of the expected value of X. (10[2])For 10 points, the square of the standard deviation (10[1]-5[1])is equal to what (10[5])measure (10[3])of (10[1])spread? (10[5])■END■ (10[20]0[8])

ANSWER: variance [accept uniformly minimum-variance unbiased estimator; accept minimum-variance unbiased estimator; accept analysis of variance; accept covariance]

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Buzzes

Player	Team	Opponent	Position	Value
Justin Sato	Stanford A	UCSC	7	-5
Zach Majorowicz	St. Thomas	Macalester	16	10
Ada Bendel	Bristol	Imperial C	21	-5
Yoyo Liu	British Columbia C	Washington State	36	-5
March Delfin	UCSD A	UCSD B	40	-5
Matthew Westley	Purdue A	Chicago B	40	10
Vijay Hans	Berkeley Boss Bandit	Stanford B	42	10
Hansen Jin	Berkeley Skeleton King	Berkeley Little Prince	42	10
Charlotte Bauer	McGill C	McGill A	42	10
Devito Stevanus	McGill B	Ottawa D	42	10
Deepanshi Matai	Toronto C	Toronto B	42	10
Matthew Lam	Ohio State A	Louisville B	42	10
Thomas Jenkins	Michigan B	Michigan A	42	10
Nate Brown	CWRU C	Michigan D	42	10
Jason Thieu	Michigan State A	Louisville A	42	-5
Walter Carson	NCSU B	Liberty B	42	10
Zachary Bornstein	Virginia Tech A	UNC A	42	10
Charlie Weaver	Virginia Tech B	Virginia A	42	10
Eric Morshed	Johns Hopkins	George Mason B	42	-5
Johnathan Ahdout	Princeton	Columbia A	42	10
Aidan Drain	NYU C	Rutgers C	42	-5
Anthony Xu	Amherst A	Tufts A	42	-5
Cy Stavros	Vermont A	Tufts B	42	10
Indigo Khanna	Vermont B	Williams A	42	10
George Matsumura	Washington Chum	Alberta B	42	10
Daniel Lu	Washington Pink	Washington Masu	42	10
Antara Bhattacharya	Cambridge A	Southampton	42	10
Advaith Jagannath	Cambridge C	Cambridge E	42	10
Danny Cutbill	RIT A	ESF	42	10
Simarya Ahuja	Washington Sockeye	Arizona State A	43	-5
Claire Wilson	Lehigh B	NYU B	44	10
Tianyi Zheng	UCSD B	UCSD A	45	10
Juliette Flatau	Imperial A	Cambridge D	45	10
Brian Qian	Illinois Canada	Purdue B	46	-5
Will Huang	Wisconsin A	Iowa State	46	10
Jesse Mindel	NCSU A	William & Mary A	49	10
Claire Harvey	Vassar B	Rowan	49	-5
James Headon	Edinburgh A	Sheffield A	49	-5
Daniel Chen	Emory A	Georgia A	51	-5
Roy Yang	WashU Grolars	Indiana A	53	10
Sidarth Erat	MIT A	Brown B	58	10
Adrian O'Leary	Waterloo A	Toronto A	59	10
Nikhil Nair	Boston University B	Amherst B	59	10
Bharath Ram	Georgia Tech A	Georgia Tech C	60	10
Pace Klein	CWRU B	CWRU A	62	10
Daniel Huang	Michigan C	CWRU D	62	10
Jeremy Scurlock	Chipola College	Clemson A	62	10
Scott Sibley	UC Irvine	Claremont C	63	10
Anirudh Terdal	LSE	Warwick	65	10
James Zhao	Vanderbilt C	Auburn C	67	-5
Tal Bowen	Durham A	Edinburgh C	67	10
Taman Truong	USC B	UCLA A	70	10
Imtiaz Kidwai	Toronto F	McMaster C	70	10
Zaid Asif	NYU A	Maryland C	70	10
Asheton Wilbanks	Clemson B	Montevallo	70	-5
Rishi Mathur	Claremont B	UCLA B	71	10
Maya Hunt	Michigan State C	Ohio State D	71	-5
Rob Morris	Durham D	Edinburgh D	71	10
Aaryan Sumesh	Berkeley Archer Queen	Berkeley Mighty Miner	72	10
Winston Zuo	UC Santa Barbara	UCLA C	72	10
Annika Larson	Claremont A	UCLA D	72	10
Diana Obiozo	USC A	UCLA E	72	-5
Ryan Gomes	Florida Tech A	Florida B	72	10
Andrew McKenzie	Ohio State B	Michigan State B	72	10
Vedh Ramesh	Penn	Rutgers D	72	10
Samson Vickrey	Purdue D	Rose-Hulman A	72	10
Ethan Ma	Illinois Blue	William Woods University A	72	10
Vivian Lu	Wisconsin C	Michigan Tech	72	10
Jonathan Schnipper	Brandeis Mozart	Boston College A	72	10
Judah Friedman	UConn A	Boston University A	72	10
Akif Ismail	Williams C	Dartmouth C	72	10
Yuxuan Lu	Vanderbilt A	Alabama A	72	10
Alina Moore	Tennessee A	South Carolina A	72	10
Charlotte Nicholas	Durham B	Edinburgh B	72	10
Judah Garlic	Cornell C	Binghamton B	72	10
Lily Katz	Stony Brook	Vassar A	73	10
Sam Alahi	Illinois Orange	Indiana B	73	-5
Elliott Gomes	Dartmouth A	Brown A	73	-5
Shivam Saxena	Georgia Tech F	Georgia Tech E	73	10
Daniel Abrams	Rutgers B	Lehigh A	74	10
Jason Lee	Rutgers A	Maryland A	74	10
Anne Fjeld	Alberta A	Washington Atlantic	74	10
Arhith Dharaendra	Georgia Tech B	Auburn B	74	10
Jerry Lin	Vanderbilt B	Mississippi State A	74	10
Alden Thompson	Carleton A	McGill E	75	10
Seth Allen	McMaster A	Toronto D	76	10
Noah Fine	UNC D	Virginia Tech C	76	10
James Stadler	Imperial B	Birmingham	76	-5
Platon Gorokhov	Toronto E	Guelph A	77	10
Nathan Woolery	Louisville C	Michigan State D	77	10
Stephen Donoghue	Sheffield B	Durham C	77	10
Sam Kung	UNC C	UNC B	78	10
David Thomas	Purdue C	Iowa A	78	10
Eric Zhu	Cornell D	Cornell A	78	10
Zack Wiffen	Waterloo B	Toronto G	79	10
Pratham Bhanushali	WVU B	WVU A	79	10
Joyann Hua	British Columbia B	Texas	79	10
Michael Xu	McMaster B	Waterloo C	82	-5
Eric Parrilla	Chicago A	WashU Grizzlers	82	10
Alan Fan	Washington Steelhead	Washington Chinook	82	10
Sicheng Jiang	Toronto H	Toronto I	92	-5
Aryan Malhotra	Rutgers C	NYU C	92	10
Andrew Park	Harvard	Brandeis Beethoven	92	10
Ollie Glin-Conway	Imperial D	Oxford	92	10
Corey Pope	Florida State A	ERAU Daytona A	101	-5
Cooper Morris	Columbia B	George Mason C	102	-5
Yashaswi Jaishy	Iowa B	Illinois Champaign	115	10
Will Barton	Imperial C	Bristol	115	10
AnnaMaria Donnelly	UCF A	Florida A	124	-5
Sophia Jagels	William & Mary B	JMU A	124	10
Miles Spieler	Ohio State C	Louisville D	128	10
Beckett Pursey	Purdue B	Illinois Canada	128	10
Brendan Liaw	British Columbia A	Washington Coho	128	10
Eli O'Sick Johnson	Binghamton C	Rochester	128	10
Eli O'Sick Johnson	Binghamton C	Rochester	128	10
Alex Randall	Kentucky	Pittsburgh	129	10
Akhil Upadrasta	Ohio State D	Michigan State C	129	10
Nikki Chaco	Georgia Tech D	Tennessee B	129	10
Jackson Price	Dartmouth B	Williams B	130	10
Valerie Brown	Carleton B	Ottawa C	131	10
Elena Thai	Waterloo C	McMaster B	131	10
Gabriel Dodds	Liberty C	Tusculum A	131	10
Noah Lang	Wisconsin B	Minnesota	131	10
Madeline Strauss	Tufts A	Amherst A	131	10
Lorie Au-Yeung	UCSC	Stanford A	132	10
Joseph Wang	UCLA E	USC A	132	10
Rebecca Li	Ottawa A	Ottawa B	132	0
Abhay Ariyapappillil	Ottawa B	Ottawa A	132	10
Ellie Wang	Brock A	Queen's A	132	0
Simon Choist	Queen's A	Brock A	132	10
Saju Ramraj	Toronto I	Toronto H	132	0
Heidi Moyer	ERAU Daytona A	Florida State A	132	0
Joshua Ziegler	South Florida A	Florida Tech B	132	10
June Miller	Florida A	UCF A	132	0
Snehan Saroch	Louisville A	Michigan State A	132	10
Nathan Redford	Liberty A	William & Mary C	132	0
Charles Miller	William & Mary C	Liberty A	132	10
Abbi Tesreau	George Mason C	Columbia B	132	10
Margaret Withers	George Mason B	Johns Hopkins	132	10
John Shelly	Rowan	Vassar B	132	10
Emily Justak	Indiana B	Illinois Orange	132	0
Eames Weeks	Brown A	Dartmouth A	132	10
Rae Meyers	Arizona State A	Washington Sockeye	132	10
Ryan Zhang	Washington State	British Columbia C	132	10
Doug Frederick	Auburn A	Tennessee Tech	132	0
Jonas Cross	Tennessee Tech	Auburn A	132	10
Andrew Wilson	Montevallo	Clemson B	132	10
Aman Sreshta	Clemson C	Sewanne	132	10
Britt Bernstein	Georgia A	Emory A	132	10
Jaie Somaia	Sheffield A	Edinburgh A	132	10
James Mogg	Birmingham	Imperial B	132	10
Owen Linder	Binghamton A	RIT B	132	10

Summary

Tournament	Edition	TUH	Conv. %	Neg %	Average Buzz
UK (North)	UK	5	100%	20%	83.80
UK (South)	UK	7	100%	29%	76.14
Northern California	US	4	100%	25%	72.00
Southern California	US	7	100%	29%	75.00
Eastern Canada (1)	US	5	100%	0%	84.40
Eastern Canada (2)	US	9	89%	22%	83.25
Florida	US	4	50%	50%	102.00
Great Lakes	US	12	100%	17%	83.00
Lower Mid-Atlantic	US	9	100%	0%	79.56
Upper Mid-Atlantic	US	10	100%	40%	86.30
Upper Mid-Atlantic	US	1	100%	0%	74.00
Midwest	US	9	89%	22%	80.00
North	US	4	100%	0%	66.25
Northeast	US	11	100%	18%	82.00
Pacific	US	8	100%	25%	88.88
Southeast	US	13	92%	23%	95.33
Upstate NY	US	6	100%	0%	96.67