International Mathematical Olympiad 2010 (Astana, Kazakhstan) Scores

At the 2010 IMO held in Astana, Kazakhstan, 516 contestants from 95 countries competed. 47 gold medals were awarded to those scoring at least 27; 103 silver medals were awarded to those scoring from 21 to 26; and 115 bronze medals were awarded to those scoring from 15 to 20.

Further statistics are shown below. Detailed tables of results by country or contestant are available:

Total scores of each country, in descending order of total score (the IMO is an individual competition, so country orderings are unofficial only).
Total scores of each country, in alphabetical order.
Individual scores, in descending order of score.
Individual scores, in order of contestant code.

The maximum individual score possible was 42 (which only one contestant attained). The mean individual score was 15.138, with a standard deviation of 7.944. The following table shows how many contestants attained each possible score.

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	1
36	3
35	2
34	2
33	0
32	2
31	3
30	2
29	9
28	15
27	6
26	5
25	7
24	4
23	12
22	30
21	45
20	16
19	7
18	13
17	12
16	27
15	40
14	47
13	24
12	14
11	15
10	20
9	15
8	17
7	27
6	16
5	12
4	4
3	7
2	9
1	8
0	16

The following table shows the maximum attainable score, mean score and standard deviation of scores for each individual question.

Question number	1	2	3	4	5	6
Maximum score	7	7	7	7	7	7
Mean score	5.450	2.578	0.465	5.345	0.932	0.368
Standard deviation	2.293	3.088	1.414	2.718	1.982	1.403

The following table shows the correlation coefficients between the scores on each pair of questions. To make sense of these figures you will probably wish to look at the problems themselves (from Mathlinks) to see which are on similar or different topics.

	1	2	3	4	5	6
1		0.337	0.194	0.373	0.135	0.098
2	0.337		0.372	0.415	0.132	0.228
3	0.194	0.372		0.195	0.206	0.246
4	0.373	0.415	0.195		0.067	0.149
5	0.135	0.132	0.206	0.067		0.211
6	0.098	0.228	0.246	0.149	0.211

The following table shows the distribution of scores on each individual question with the total number of each score on any question.

	Score 0	Score 1	Score 2	Score 3	Score 4	Score 5	Score 6	Score 7
Question 1	39	17	27	16	34	35	54	294
Question 2	223	93	23	8	2	4	2	161
Question 3	428	48	10	4	4	4	2	16
Question 4	84	2	10	47	2	4	2	365
Question 5	352	85	26	3	0	2	11	37
Question 6	470	14	4	3	0	6	4	15
Total	1596	259	100	81	42	55	75	888

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Contact: Joseph Myers (jsm@polyomino.org.uk)
Last updated: 9 October 2016

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	1
36	3
35	2
34	2
33	0
32	2
31	3
30	2
29	9
28	15
27	6
26	5
25	7
24	4
23	12
22	30
21	45
20	16
19	7
18	13
17	12
16	27
15	40
14	47
13	24
12	14
11	15
10	20
9	15
8	17
7	27
6	16
5	12
4	4
3	7
2	9
1	8
0	16

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	1
36	3
35	2
34	2
33	0
32	2
31	3
30	2
29	9
28	15
27	6
26	5
25	7
24	4
23	12
22	30
21	45
20	16
19	7
18	13
17	12
16	27
15	40
14	47
13	24
12	14
11	15
10	20
9	15
8	17
7	27
6	16
5	12
4	4
3	7
2	9
1	8
0	16

Score	Number of contestants
42	1
41	0
40	0
39	1
38	0
37	1
36	3
35	2
34	2
33	0
32	2
31	3
30	2
29	9
28	15
27	6
26	5
25	7
24	4
23	12
22	30
21	45
20	16
19	7
18	13
17	12
16	27
15	40
14	47
13	24
12	14
11	15
10	20
9	15
8	17
7	27
6	16
5	12
4	4
3	7
2	9
1	8
0	16