IMC 2005 statistics — difficulty & discrimination

Studolymp / IMC / 2005

IMC 2005

contestants 227 · problems 12 (6+6) · scale 0–20 · per-problem yes

Per-problem difficulty

Day 1

Day 2

Difficulty vs discrimination

Each dot is one problem. X — how many solved it (scored ≥ 8 of 10); Y — discrimination, i.e. how well the problem told strong contestants from weak ones (score-vs-total correlation).

A good problem sits high and away from the edges. Bottom-left dots separated nobody — almost everyone failed them the same way.

Problem statistics

Same data as the Day 1 / Day 2 charts above. Add diploma cohorts to compare winners against the field.

	#	difficulty	all			disc	topics
	#	difficulty	avg	solved	near-0	disc	topics
Day 1
	P1	easy	9.1	91%	2%	0.35	linear algebra
	P2	easy	7.0	67%	23%	0.57	combinatorics
	P3	hard	2.6	20%	63%	0.51	integration inequalities
	P4	hard	2.7	21%	63%	0.53	polynomials
	P5	very hard	1.5	10%	81%	0.38	real analysis
	P6	killer	0.2	0%	94%	0.26	group theory
Day 2
	P7	easy	9.0	84%	1%	0.46	inequalities polynomials
	P8	easy	6.2	53%	29%	0.52	polynomials real analysis
	P9	hard	3.9	22%	37%	0.61	linear algebra
	P10	hard	4.3	25%	44%	0.49	real analysis
	P11	killer	0.6	2%	92%	0.30	real analysis
	P12	killer	1.5	4%	72%	0.33	number theory linear algebra

A diploma-cohort cell needs at least 5 scores, else it shows “—”. How these statistics are computed →