IMO 1965 — Statistics
Score Distribution
| P1 | P2 | P3 | P4 | P5 | P6 |
| Num( P# = 0 ) | 6 | 17 | 23 | 2 | 15 | 21 |
| Num( P# = 1 ) | 13 | 18 | 10 | 5 | 12 | 13 |
| Num( P# = 2 ) | 14 | 10 | 6 | 19 | 8 | 10 |
| Num( P# = 3 ) | 10 | 6 | 0 | 4 | 4 | 13 |
| Num( P# = 4 ) | 37 | 4 | 3 | 7 | 3 | 11 |
| Num( P# = 5 ) | 0 | 6 | 3 | 6 | 3 | 0 |
| Num( P# = 6 ) | 0 | 19 | 2 | 37 | 9 | 0 |
| Num( P# = 7 ) | 0 | 0 | 3 | 0 | 26 | 2 |
| Num( P# = 8 ) | 0 | 0 | 30 | 0 | 0 | 0 |
| Num( P# = 9 ) | 0 | 0 | 0 | 0 | 0 | 10 |
Summary Statistics
| P1 | P2 | P3 | P4 | P5 | P6 |
| Mean( P# ) | 2.738 | 2.700 | 4.025 | 4.188 | 3.788 | 2.750 |
| Max( P# ) | 4 | 6 | 8 | 6 | 7 | 9 |
| σ( P# ) | 1.376 | 2.310 | 3.535 | 1.963 | 2.858 | 2.848 |
Correlations
| P1 | P2 | P3 | P4 | P5 | P6 |
| Corr( P#, Sum ) | 0.651 | 0.767 | 0.798 | 0.630 | 0.727 | 0.739 |
| Corr( P#, P1 ) | | 0.463 | 0.364 | 0.379 | 0.533 | 0.388 |
| Corr( P#, P2 ) | 0.463 | | 0.503 | 0.456 | 0.464 | 0.498 |
| Corr( P#, P3 ) | 0.364 | 0.503 | | 0.417 | 0.452 | 0.490 |
| Corr( P#, P4 ) | 0.379 | 0.456 | 0.417 | | 0.297 | 0.355 |
| Corr( P#, P5 ) | 0.533 | 0.464 | 0.452 | 0.297 | | 0.384 |
| Corr( P#, P6 ) | 0.388 | 0.498 | 0.490 | 0.355 | 0.384 | |
