Quantiltabelle
# Quantiltabelle

Eine Quantiltabelle ist eine Tabelle in der Stochastik, welche numerisch berechnete Quantile bestimmter Wahrscheinlichkeitsverteilungen enthält.

Quantilstabellen werden an zahlreichen Stellen in der mathematischen Statistik verwendet. So werden sie beispielsweise für die Bestimmung von Konfidenzintervallen herangezogen. Des Weiteren lassen sich bei normalverteilten Zufallsvariablen mit gegebener Varianz und gegebenem Erwartungswert über die Z-Transformation in Kombination mit der entsprechenden Quantiltabelle direkt Wahrscheinlichkeiten bestimmen.

## Rahmenbedingungen

Als p-Quantil einer Wahrscheinlichkeitsverteilung $P$ auf den reellen Zahlen wird eine reelle Zahl $x_{p}$ bezeichnet, so dass

    $P((-\infty ,x_{p}])\geq p$ und $P([x_{p},+\infty ))\geq 1-p$

ist. Hierbei ist $p\in (0,1)$. Besitzt die Wahrscheinlichkeitsverteilung eine stetige Verteilungsfunktion $F$, so ist die äquivalent zu

    $F(x_{p})=p$.

Ist die Verteilungsfunktion streng monoton wachsend. so ist $x_{p}$ eindeutig bestimmt. Das p-Quantil trennt dann die reellen Zahlen in zwei Teile: der Teil kleiner als $x_{p}$, welcher die Wahrscheinlichkeit $p$ erhält, und der Teil größer als $x_{p}$, welcher die Wahrscheinlichkeit $1-p$ erhält.

In vielen Anwendungen der Statistik benötigt man häufig die Quantile gewisser Wahrscheinlichkeitsverteilungen. Zu diesen Verteilungen gehören:

* Normalverteilung
* Chi-Quadrat-Verteilung
* Student-Verteilung
* Fisher-Verteilung

Alle Quantile dieser Verteilungen sind eindeutig. Jedoch existiert für manche Verteilungen keine geschlossene Darstellung der Verteilungsfunktion (Normalverteilung) oder diese geschlossene Darstellung ist sehr komplex beziehungsweise das Lösen der Gleichung

    $F(x_{p})=p$

ist nicht praktikabel. Daher werden die wichtigen Quantile diese Verteilungen mit der notwendigen Genauigkeit numerisch bestimmt und in Tabellen zusammengefasst. So können sie nachgeschlagen werden, ohne jedes Mal erneut numerisch bestimmt zu werden.

Welche Werte die Tabelle genau enthält und wie viele Nachkommastellen sie enthält, hängt von der jeweiligen Verteilung ab und dem Kontext, in dem diese benötigt wird. So wird für die leicht zu normierende Normalverteilung beispielsweise nur die Standardnormalverteilung tabelliert, hierbei dann jedoch mit $x_{p}$ auf zwei Nachkommastellen genau und das entsprechende $p$ auf vier Nachkommastellen. Für die Student-Verteilung werden dagegen nur die Quantile $p=0{,}9;0{,}95;0{,}99;0{,}995$ etc. angegeben, dafür aber mit variabler Anzahl an Freiheitsgraden. Details hierzu und zur Verwendung der einzelnen Tabellen finden sich in den entsprechenden Abschnitten.

## Wichtige Quantiltabellen

Nachfolgend sind einige wichtige Quantiltabellen aufgeführt. Die Auswahl der tabellierten Werte folgt dabei

### Normalverteilung

Die Quantiltabelle der Normalverteilung, genauer der Standardnormalverteilung, befindet sich im Artikel Standardnormalverteilungstabelle. Dort ist auch der Umgang mit der Tabelle erklärt sowie einige Beispiele aufgeführt.

### Chi-Quadrat-Verteilung

p-Quantile der Chi-Quadrat-Verteilung mit n Freiheitsgraden :

| | p=0,005 | 0,010 | 0,020 | 0,025 | 0,050 | 0,100 | 0,250 | 0,500 | 0,750 | 0,900 | 0,950 | 0,975 | 0,980 | 0,990 | 0,995 |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| n=1 | 3,927e-5 | 1,571e-4 | 6,285e-4 | 9,820e-4 | 3,932e-3 | 1,579e-2 | 1,015e-1 | 4,549e-1 | 1,323 | 2,706 | 3,841 | 5,024 | 5,412 | 6,635 | 7,879 |
| 2 | 1,003e-2 | 2,010e-2 | 4,041e-2 | 5,064e-2 | 1,026e-1 | 2,107e-1 | 5,754e-1 | 1,386 | 2,773 | 4,605 | 5,991 | 7,378 | 7,824 | 9,210 | 10,60 |
| 3 | 7,172e-2 | 1,1480e-1 | 1,848e-1 | 2,158e-1 | 3,518e-1 | 5,844e-1 | 1,213 | 2,366 | 4,108 | 6,251 | 7,815 | 9,348 | 9,837 | 11,34 | 12,84 |
| 4 | 2,070e-1 | 2,971e-1 | 4,294e-1 | 4,844e-1 | 7,107e-1 | 1,064 | 1,923 | 3,357 | 5,385 | 7,779 | 9,488 | 11,14 | 11,67 | 13,28 | 14,86 |
| 5 | 4,117e-1 | 5,543e-1 | 7,519e-1 | 8,312e-1 | 1,145 | 1,6100 | 2,675 | 4,351 | 6,626 | 9,236 | 11,07 | 12,83 | 13,39 | 15,09 | 16,75 |
| 6 | 6,757e-1 | 8,721e-1 | 1,134 | 1,237 | 1,635 | 2,204 | 3,455 | 5,348 | 7,841 | 10,64 | 12,59 | 14,45 | 15,03 | 16,81 | 18,55 |
| 7 | 0,9893 | 1,239 | 1,564 | 1,6900 | 2,167 | 2,833 | 4,255 | 6,346 | 9,037 | 12,02 | 14,07 | 16,01 | 16,62 | 18,48 | 20,28 |
| 8 | 1,344 | 1,646 | 2,032 | 2,180 | 2,733 | 3,490 | 5,071 | 7,344 | 10,22 | 13,36 | 15,51 | 17,53 | 18,17 | 20,09 | 21,95 |
| 9 | 1,735 | 2,088 | 2,532 | 2,700 | 3,325 | 4,168 | 5,899 | 8,343 | 11,39 | 14,68 | 16,92 | 19,02 | 19,68 | 21,67 | 23,59 |
| 10 | 2,156 | 2,558 | 3,059 | 3,247 | 3,940 | 4,865 | 6,737 | 9,342 | 12,55 | 15,99 | 18,31 | 20,48 | 21,16 | 23,21 | 25,19 |
| 11 | 2,603 | 3,053 | 3,609 | 3,816 | 4,575 | 5,578 | 7,584 | 10,34 | 13,70 | 17,28 | 19,68 | 21,92 | 22,62 | 24,72 | 26,76 |
| 12 | 3,074 | 3,571 | 4,178 | 4,404 | 5,226 | 6,304 | 8,438 | 11,34 | 14,85 | 18,55 | 21,03 | 23,34 | 24,05 | 26,22 | 28,30 |
| 13 | 3,565 | 4,107 | 4,765 | 5,009 | 5,892 | 7,042 | 9,299 | 12,34 | 15,98 | 19,81 | 22,36 | 24,74 | 25,47 | 27,69 | 29,82 |
| 14 | 4,075 | 4,660 | 5,368 | 5,629 | 6,571 | 7,790 | 10,17 | 13,34 | 17,12 | 21,06 | 23,68 | 26,12 | 26,87 | 29,14 | 31,32 |
| 15 | 4,601 | 5,229 | 5,985 | 6,262 | 7,261 | 8,547 | 11,04 | 14,34 | 18,25 | 22,31 | 25,00 | 27,49 | 28,26 | 30,58 | 32,80 |
| 16 | 5,142 | 5,812 | 6,614 | 6,908 | 7,962 | 9,312 | 11,91 | 15,34 | 19,37 | 23,54 | 26,30 | 28,85 | 29,63 | 32,00 | 34,27 |
| 17 | 5,697 | 6,408 | 7,255 | 7,564 | 8,672 | 10,09 | 12,79 | 16,34 | 20,49 | 24,77 | 27,59 | 30,19 | 31,00 | 33,41 | 35,72 |
| 18 | 6,265 | 7,015 | 7,906 | 8,231 | 9,390 | 10,86 | 13,68 | 17,34 | 21,60 | 25,99 | 28,87 | 31,53 | 32,35 | 34,81 | 37,16 |
| 19 | 6,844 | 7,633 | 8,567 | 8,907 | 10,12 | 11,65 | 14,56 | 18,34 | 22,72 | 27,20 | 30,14 | 32,85 | 33,69 | 36,19 | 38,58 |
| 20 | 7,434 | 8,260 | 9,237 | 9,591 | 10,85 | 12,44 | 15,45 | 19,34 | 23,83 | 28,41 | 31,41 | 34,17 | 35,02 | 37,57 | 40,00 |
| 21 | 8,034 | 8,897 | 9,915 | 10,28 | 11,59 | 13,24 | 16,34 | 20,34 | 24,93 | 29,62 | 32,67 | 35,48 | 36,34 | 38,93 | 41,40 |
| 22 | 8,643 | 9,542 | 10,60 | 10,98 | 12,34 | 14,04 | 17,24 | 21,34 | 26,04 | 30,81 | 33,92 | 36,78 | 37,66 | 40,29 | 42,80 |
| 23 | 9,260 | 10,20 | 11,29 | 11,69 | 13,09 | 14,85 | 18,14 | 22,34 | 27,14 | 32,01 | 35,17 | 38,08 | 38,97 | 41,64 | 44,18 |
| 24 | 9,886 | 10,86 | 11,99 | 12,40 | 13,85 | 15,66 | 19,04 | 23,34 | 28,24 | 33,20 | 36,42 | 39,36 | 40,27 | 42,98 | 45,56 |
| 25 | 10,52 | 11,52 | 12,70 | 13,12 | 14,61 | 16,47 | 19,94 | 24,34 | 29,34 | 34,38 | 37,65 | 40,65 | 41,57 | 44,31 | 46,93 |
| 26 | 11,16 | 12,20 | 13,41 | 13,84 | 15,38 | 17,29 | 20,84 | 25,34 | 30,43 | 35,56 | 38,89 | 41,92 | 42,86 | 45,64 | 48,29 |
| 27 | 11,81 | 12,88 | 14,13 | 14,57 | 16,15 | 18,11 | 21,75 | 26,34 | 31,53 | 36,74 | 40,11 | 43,19 | 44,14 | 46,96 | 49,64 |
| 28 | 12,46 | 13,56 | 14,85 | 15,31 | 16,93 | 18,94 | 22,66 | 27,34 | 32,62 | 37,92 | 41,34 | 44,46 | 45,42 | 48,28 | 50,99 |
| 29 | 13,12 | 14,26 | 15,57 | 16,05 | 17,71 | 19,77 | 23,57 | 28,34 | 33,71 | 39,09 | 42,56 | 45,72 | 46,69 | 49,59 | 52,34 |
| 30 | 13,79 | 14,95 | 16,31 | 16,79 | 18,49 | 20,60 | 24,48 | 29,34 | 34,80 | 40,26 | 43,77 | 46,98 | 47,96 | 50,89 | 53,67 |
| 35 | 17,19 | 18,51 | 20,03 | 20,57 | 22,47 | 24,80 | 29,05 | 34,34 | 40,22 | 46,06 | 49,80 | 53,20 | 54,24 | 57,34 | 60,27 |
| 40 | 20,71 | 22,16 | 23,84 | 24,43 | 26,51 | 29,05 | 33,66 | 39,34 | 45,62 | 51,81 | 55,76 | 59,34 | 60,44 | 63,69 | 66,77 |
| 45 | 24,31 | 25,90 | 27,72 | 28,37 | 30,61 | 33,35 | 38,29 | 44,34 | 50,98 | 57,51 | 61,66 | 65,41 | 66,56 | 69,96 | 73,17 |
| 50 | 27,99 | 29,71 | 31,66 | 32,36 | 34,76 | 37,69 | 42,94 | 49,33 | 56,33 | 63,17 | 67,50 | 71,42 | 72,61 | 76,15 | 79,49 |
| 55 | 31,73 | 33,57 | 35,66 | 36,40 | 38,96 | 42,06 | 47,61 | 54,33 | 61,66 | 68,80 | 73,31 | 77,38 | 78,62 | 82,29 | 85,75 |
| 60 | 35,53 | 37,48 | 39,70 | 40,48 | 43,19 | 46,46 | 52,29 | 59,33 | 66,98 | 74,40 | 79,08 | 83,30 | 84,58 | 88,38 | 91,95 |
| 70 | 43,28 | 45,44 | 47,89 | 48,76 | 51,74 | 55,33 | 61,70 | 69,33 | 77,58 | 85,53 | 90,53 | 95,02 | 96,39 | 100,4 | 104,2 |
| 80 | 51,17 | 53,54 | 56,21 | 57,15 | 60,39 | 64,28 | 71,14 | 79,33 | 88,13 | 96,58 | 101,9 | 106,6 | 108,1 | 112,3 | 116,3 |
| 90 | 59,20 | 61,75 | 64,63 | 65,65 | 69,13 | 73,29 | 80,62 | 89,33 | 98,65 | 107,6 | 113,1 | 118,1 | 119,6 | 124,1 | 128,3 |
| 100 | 67,33 | 70,06 | 73,14 | 74,22 | 77,93 | 82,36 | 90,13 | 99,33 | 109,1 | 118,5 | 124,3 | 129,6 | 131,1 | 135,8 | 140,2 |
| 150 | 109,1 | 112,7 | 116,6 | 118,0 | 122,7 | 128,3 | 138,0 | 149,3 | 161,3 | 172,6 | 179,6 | 185,8 | 187,7 | 193,2 | 198,4 |
| 200 | 152,2 | 156,4 | 161,1 | 162,7 | 168,3 | 174,8 | 186,2 | 199,3 | 213,1 | 226,0 | 234,0 | 241,1 | 243,2 | 249,4 | 255,3 |
| 250 | 196,2 | 200,9 | 206,2 | 208,1 | 214,4 | 221,8 | 234,6 | 249,3 | 264,7 | 279,1 | 287,9 | 295,7 | 298,0 | 304,9 | 311,3 |
| 300 | 240,7 | 246,0 | 251,9 | 253,9 | 260,9 | 269,1 | 283,1 | 299,3 | 316,1 | 331,8 | 341,4 | 349,9 | 352,4 | 359,9 | 366,8 |
| 400 | 330,9 | 337,2 | 344,1 | 346,5 | 354,6 | 364,2 | 380,6 | 399,3 | 418,7 | 436,6 | 447,6 | 457,3 | 460,2 | 468,7 | 476,6 |
| 600 | 514,5 | 522,4 | 531,0 | 534,0 | 544,2 | 556,1 | 576,3 | 599,3 | 623,0 | 644,8 | 658,1 | 669,8 | 673,3 | 683,5 | 693,0 |
| 800 | 700,7 | 709,9 | 720,0 | 723,5 | 735,4 | 749,2 | 772,7 | 799,3 | 826,6 | 851,7 | 866,9 | 880,3 | 884,3 | 896,0 | 906,8 |
| 1000 | 888,6 | 898,9 | 910,3 | 914,3 | 927,6 | 943,1 | 969,5 | 999,3 | 1029 | 1057 | 1074 | 1089 | 1094, | 1107, | 1118 |

### Studentsche t-Verteilung

p-Quantile der Studentschen t-Verteilung mit n Freiheitsgraden :

| | p=0,9 | 0,95 | 0,96 | 0,975 | 0,98 | 0,99 | 0,995 | 0,999 | 0,9995 |
| - | - | - | - | - | - | - | - | - | - |
| n=1 | 3,078 | 6,314 | 7,916 | 12,71 | 15,89 | 31,82 | 63,66 | 318,3 | 636,6 |
| 2 | 1,886 | 2,920 | 3,320 | 4,303 | 4,849 | 6,965 | 9,925 | 22,33 | 31,60 |
| 3 | 1,638 | 2,353 | 2,605 | 3,182 | 3,482 | 4,541 | 5,841 | 10,21 | 12,92 |
| 4 | 1,533 | 2,132 | 2,333 | 2,776 | 2,999 | 3,747 | 4,604 | 7,173 | 8,610 |
| 5 | 1,476 | 2,015 | 2,191 | 2,571 | 2,757 | 3,365 | 4,032 | 5,893 | 6,869 |
| 6 | 1,440 | 1,943 | 2,104 | 2,447 | 2,612 | 3,143 | 3,707 | 5,208 | 5,959 |
| 7 | 1,415 | 1,895 | 2,046 | 2,365 | 2,517 | 2,998 | 3,499 | 4,785 | 5,408 |
| 8 | 1,397 | 1,860 | 2,004 | 2,306 | 2,449 | 2,896 | 3,355 | 4,501 | 5,041 |
| 9 | 1,383 | 1,833 | 1,973 | 2,262 | 2,398 | 2,821 | 3,250 | 4,297 | 4,781 |
| 10 | 1,372 | 1,812 | 1,948 | 2,228 | 2,359 | 2,764 | 3,169 | 4,144 | 4,587 |
| 11 | 1,363 | 1,796 | 1,928 | 2,201 | 2,328 | 2,718 | 3,106 | 4,025 | 4,437 |
| 12 | 1,356 | 1,782 | 1,912 | 2,179 | 2,303 | 2,681 | 3,055 | 3,930 | 4,318 |
| 13 | 1,350 | 1,771 | 1,899 | 2,160 | 2,282 | 2,650 | 3,012 | 3,852 | 4,221 |
| 14 | 1,345 | 1,761 | 1,887 | 2,145 | 2,264 | 2,624 | 2,977 | 3,787 | 4,140 |
| 15 | 1,341 | 1,753 | 1,878 | 2,131 | 2,249 | 2,602 | 2,947 | 3,733 | 4,073 |
| 16 | 1,337 | 1,746 | 1,869 | 2,120 | 2,235 | 2,583 | 2,921 | 3,686 | 4,015 |
| 17 | 1,333 | 1,740 | 1,862 | 2,110 | 2,224 | 2,567 | 2,898 | 3,646 | 3,965 |
| 18 | 1,330 | 1,734 | 1,855 | 2,101 | 2,214 | 2,552 | 2,878 | 3,610 | 3,922 |
| 19 | 1,328 | 1,729 | 1,850 | 2,093 | 2,205 | 2,539 | 2,861 | 3,579 | 3,883 |
| 20 | 1,325 | 1,725 | 1,844 | 2,086 | 2,197 | 2,528 | 2,845 | 3,552 | 3,850 |
| 21 | 1,323 | 1,721 | 1,840 | 2,080 | 2,189 | 2,518 | 2,831 | 3,527 | 3,819 |
| 22 | 1,321 | 1,717 | 1,835 | 2,074 | 2,183 | 2,508 | 2,819 | 3,505 | 3,792 |
| 23 | 1,319 | 1,714 | 1,832 | 2,069 | 2,177 | 2,500 | 2,807 | 3,485 | 3,768 |
| 24 | 1,318 | 1,711 | 1,828 | 2,064 | 2,172 | 2,492 | 2,797 | 3,467 | 3,745 |
| 25 | 1,316 | 1,708 | 1,825 | 2,060 | 2,167 | 2,485 | 2,787 | 3,450 | 3,725 |
| 26 | 1,315 | 1,706 | 1,822 | 2,056 | 2,162 | 2,479 | 2,779 | 3,435 | 3,707 |
| 27 | 1,314 | 1,703 | 1,819 | 2,052 | 2,158 | 2,473 | 2,771 | 3,421 | 3,690 |
| 28 | 1,313 | 1,701 | 1,817 | 2,048 | 2,154 | 2,467 | 2,763 | 3,408 | 3,674 |
| 29 | 1,311 | 1,699 | 1,814 | 2,045 | 2,150 | 2,462 | 2,756 | 3,396 | 3,659 |
| 30 | 1,310 | 1,697 | 1,812 | 2,042 | 2,147 | 2,457 | 2,750 | 3,385 | 3,646 |
| 35 | 1,306 | 1,690 | 1,803 | 2,030 | 2,133 | 2,438 | 2,724 | 3,340 | 3,591 |
| 40 | 1,303 | 1,684 | 1,796 | 2,021 | 2,123 | 2,423 | 2,704 | 3,307 | 3,551 |
| 45 | 1,301 | 1,679 | 1,791 | 2,014 | 2,115 | 2,412 | 2,690 | 3,281 | 3,520 |
| 50 | 1,299 | 1,676 | 1,787 | 2,009 | 2,109 | 2,403 | 2,678 | 3,261 | 3,496 |
| 60 | 1,296 | 1,671 | 1,781 | 2,000 | 2,099 | 2,390 | 2,660 | 3,232 | 3,460 |
| 70 | 1,294 | 1,667 | 1,776 | 1,994 | 2,093 | 2,381 | 2,648 | 3,211 | 3,435 |
| 80 | 1,292 | 1,664 | 1,773 | 1,990 | 2,088 | 2,374 | 2,639 | 3,195 | 3,416 |
| 90 | 1,291 | 1,662 | 1,771 | 1,987 | 2,084 | 2,368 | 2,632 | 3,183 | 3,402 |
| 100 | 1,290 | 1,660 | 1,769 | 1,984 | 2,081 | 2,364 | 2,626 | 3,174 | 3,390 |
| 150 | 1,287 | 1,655 | 1,763 | 1,976 | 2,072 | 2,351 | 2,609 | 3,145 | 3,357 |
| 200 | 1,286 | 1,653 | 1,760 | 1,972 | 2,067 | 2,345 | 2,601 | 3,131 | 3,340 |
| 250 | 1,285 | 1,651 | 1,758 | 1,969 | 2,065 | 2,341 | 2,596 | 3,123 | 3,330 |
| 300 | 1,284 | 1,650 | 1,757 | 1,968 | 2,063 | 2,339 | 2,592 | 3,118 | 3,323 |
| 400 | 1,284 | 1,649 | 1,755 | 1,966 | 2,060 | 2,336 | 2,588 | 3,111 | 3,315 |
| 500 | 1,283 | 1,648 | 1,754 | 1,965 | 2,059 | 2,334 | 2,586 | 3,107 | 3,310 |
| 600 | 1,283 | 1,647 | 1,754 | 1,964 | 2,058 | 2,333 | 2,584 | 3,104 | 3,307 |
| 800 | 1,283 | 1,647 | 1,753 | 1,963 | 2,057 | 2,331 | 2,582 | 3,100 | 3,303 |
| 1000 | 1,282 | 1,646 | 1,752 | 1,962 | 2,056 | 2,330 | 2,581 | 3,098 | 3,300 |
| 100000 | 1,282 | 1,645 | 1,751 | 1,960 | 2,054 | 2,326 | 2,576 | 3,090 | 3,291 |

### Fisher-Verteilung

0.95-Quantile der Fisher-Verteilung mit n Freiheitsgraden im Nenner und m Freiheitsgraden im Zähler :

| | m=1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 30 | 40 | 50 | 60 | 100 | 100000 |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| n=1 | 161,4 | 199,5 | 215,7 | 224,6 | 230,2 | 234,0 | 236,8 | 238,9 | 240,5 | 241,9 | 243,0 | 243,9 | 244,7 | 245,4 | 245,9 | 246,5 | 246,9 | 247,3 | 247,7 | 248,0 | 248,3 | 248,6 | 248,8 | 249,1 |
| 2 | 18,51 | 19,00 | 19,16 | 19,25 | 19,30 | 19,33 | 19,35 | 19,37 | 19,38 | 19,40 | 19,40 | 19,41 | 19,42 | 19,42 | 19,43 | 19,43 | 19,44 | 19,44 | 19,44 | 19,45 | 19,45 | 19,45 | 19,45 | 19,45 |
| 3 | 10,13 | 9,552 | 9,277 | 9,117 | 9,013 | 8,941 | 8,887 | 8,845 | 8,812 | 8,786 | 8,763 | 8,745 | 8,729 | 8,715 | 8,703 | 8,692 | 8,683 | 8,675 | 8,667 | 8,660 | 8,654 | 8,648 | 8,643 | 8,639 |
| 4 | 7,709 | 6,944 | 6,591 | 6,388 | 6,256 | 6,163 | 6,094 | 6,041 | 5,999 | 5,964 | 5,936 | 5,912 | 5,891 | 5,873 | 5,858 | 5,844 | 5,832 | 5,821 | 5,811 | 5,803 | 5,795 | 5,787 | 5,781 | 5,774 |
| 5 | 6,608 | 5,786 | 5,409 | 5,192 | 5,050 | 4,950 | 4,876 | 4,818 | 4,772 | 4,735 | 4,704 | 4,678 | 4,655 | 4,636 | 4,619 | 4,604 | 4,590 | 4,579 | 4,568 | 4,558 | 4,549 | 4,541 | 4,534 | 4,527 |
| 6 | 5,987 | 5,143 | 4,757 | 4,534 | 4,387 | 4,284 | 4,207 | 4,147 | 4,099 | 4,060 | 4,027 | 4,000 | 3,976 | 3,956 | 3,938 | 3,922 | 3,908 | 3,896 | 3,884 | 3,874 | 3,865 | 3,856 | 3,849 | 3,841 |
| 7 | 5,591 | 4,737 | 4,347 | 4,120 | 3,972 | 3,866 | 3,787 | 3,726 | 3,677 | 3,637 | 3,603 | 3,575 | 3,550 | 3,529 | 3,511 | 3,494 | 3,480 | 3,467 | 3,455 | 3,445 | 3,435 | 3,426 | 3,418 | 3,410 |
| 8 | 5,318 | 4,459 | 4,066 | 3,838 | 3,687 | 3,581 | 3,500 | 3,438 | 3,388 | 3,347 | 3,313 | 3,284 | 3,259 | 3,237 | 3,218 | 3,202 | 3,187 | 3,173 | 3,161 | 3,150 | 3,140 | 3,131 | 3,123 | 3,115 |
| 9 | 5,117 | 4,256 | 3,863 | 3,633 | 3,482 | 3,374 | 3,293 | 3,230 | 3,179 | 3,137 | 3,102 | 3,073 | 3,048 | 3,025 | 3,006 | 2,989 | 2,974 | 2,960 | 2,948 | 2,936 | 2,926 | 2,917 | 2,908 | 2,900 |
| 10 | 4,965 | 4,103 | 3,708 | 3,478 | 3,326 | 3,217 | 3,135 | 3,072 | 3,020 | 2,978 | 2,943 | 2,913 | 2,887 | 2,865 | 2,845 | 2,828 | 2,812 | 2,798 | 2,785 | 2,774 | 2,764 | 2,754 | 2,745 | 2,737 |
| 11 | 4,844 | 3,982 | 3,587 | 3,357 | 3,204 | 3,095 | 3,012 | 2,948 | 2,896 | 2,854 | 2,818 | 2,788 | 2,761 | 2,739 | 2,719 | 2,701 | 2,685 | 2,671 | 2,658 | 2,646 | 2,636 | 2,626 | 2,617 | 2,609 |
| 12 | 4,747 | 3,885 | 3,490 | 3,259 | 3,106 | 2,996 | 2,913 | 2,849 | 2,796 | 2,753 | 2,717 | 2,687 | 2,660 | 2,637 | 2,617 | 2,599 | 2,583 | 2,568 | 2,555 | 2,544 | 2,533 | 2,523 | 2,514 | 2,505 |
| 13 | 4,667 | 3,806 | 3,411 | 3,179 | 3,025 | 2,915 | 2,832 | 2,767 | 2,714 | 2,671 | 2,635 | 2,604 | 2,577 | 2,554 | 2,533 | 2,515 | 2,499 | 2,484 | 2,471 | 2,459 | 2,448 | 2,438 | 2,429 | 2,420 |
| 14 | 4,600 | 3,739 | 3,344 | 3,112 | 2,958 | 2,848 | 2,764 | 2,699 | 2,646 | 2,602 | 2,565 | 2,534 | 2,507 | 2,484 | 2,463 | 2,445 | 2,428 | 2,413 | 2,400 | 2,388 | 2,377 | 2,367 | 2,357 | 2,349 |
| 15 | 4,543 | 3,682 | 3,287 | 3,056 | 2,901 | 2,790 | 2,707 | 2,641 | 2,588 | 2,544 | 2,507 | 2,475 | 2,448 | 2,424 | 2,403 | 2,385 | 2,368 | 2,353 | 2,340 | 2,328 | 2,316 | 2,306 | 2,297 | 2,288 |
| 16 | 4,494 | 3,634 | 3,239 | 3,007 | 2,852 | 2,741 | 2,657 | 2,591 | 2,538 | 2,494 | 2,456 | 2,425 | 2,397 | 2,373 | 2,352 | 2,333 | 2,317 | 2,302 | 2,288 | 2,276 | 2,264 | 2,254 | 2,244 | 2,235 |
| 17 | 4,451 | 3,592 | 3,197 | 2,965 | 2,810 | 2,699 | 2,614 | 2,548 | 2,494 | 2,450 | 2,413 | 2,381 | 2,353 | 2,329 | 2,308 | 2,289 | 2,272 | 2,257 | 2,243 | 2,230 | 2,219 | 2,208 | 2,199 | 2,190 |
| 18 | 4,414 | 3,555 | 3,160 | 2,928 | 2,773 | 2,661 | 2,577 | 2,510 | 2,456 | 2,412 | 2,374 | 2,342 | 2,314 | 2,290 | 2,269 | 2,250 | 2,233 | 2,217 | 2,203 | 2,191 | 2,179 | 2,168 | 2,159 | 2,150 |
| 19 | 4,381 | 3,522 | 3,127 | 2,895 | 2,740 | 2,628 | 2,544 | 2,477 | 2,423 | 2,378 | 2,340 | 2,308 | 2,280 | 2,256 | 2,234 | 2,215 | 2,198 | 2,182 | 2,168 | 2,155 | 2,144 | 2,133 | 2,123 | 2,114 |
| 20 | 4,351 | 3,493 | 3,098 | 2,866 | 2,711 | 2,599 | 2,514 | 2,447 | 2,393 | 2,348 | 2,310 | 2,278 | 2,250 | 2,225 | 2,203 | 2,184 | 2,167 | 2,151 | 2,137 | 2,124 | 2,112 | 2,102 | 2,092 | 2,082 |
| 21 | 4,325 | 3,467 | 3,072 | 2,840 | 2,685 | 2,573 | 2,488 | 2,420 | 2,366 | 2,321 | 2,283 | 2,250 | 2,222 | 2,197 | 2,176 | 2,156 | 2,139 | 2,123 | 2,109 | 2,096 | 2,084 | 2,073 | 2,063 | 2,054 |
| 22 | 4,301 | 3,443 | 3,049 | 2,817 | 2,661 | 2,549 | 2,464 | 2,397 | 2,342 | 2,297 | 2,259 | 2,226 | 2,198 | 2,173 | 2,151 | 2,131 | 2,114 | 2,098 | 2,084 | 2,071 | 2,059 | 2,048 | 2,038 | 2,028 |
| 23 | 4,279 | 3,422 | 3,028 | 2,796 | 2,640 | 2,528 | 2,442 | 2,375 | 2,320 | 2,275 | 2,236 | 2,204 | 2,175 | 2,150 | 2,128 | 2,109 | 2,091 | 2,075 | 2,061 | 2,048 | 2,036 | 2,025 | 2,014 | 2,005 |
| 24 | 4,260 | 3,403 | 3,009 | 2,776 | 2,621 | 2,508 | 2,423 | 2,355 | 2,300 | 2,255 | 2,216 | 2,183 | 2,155 | 2,130 | 2,108 | 2,088 | 2,070 | 2,054 | 2,040 | 2,027 | 2,015 | 2,003 | 1,993 | 1,984 |
| 25 | 4,242 | 3,385 | 2,991 | 2,759 | 2,603 | 2,490 | 2,405 | 2,337 | 2,282 | 2,236 | 2,198 | 2,165 | 2,136 | 2,111 | 2,089 | 2,069 | 2,051 | 2,035 | 2,021 | 2,007 | 1,995 | 1,984 | 1,974 | 1,964 |
| 26 | 4,225 | 3,369 | 2,975 | 2,743 | 2,587 | 2,474 | 2,388 | 2,321 | 2,265 | 2,220 | 2,181 | 2,148 | 2,119 | 2,094 | 2,072 | 2,052 | 2,034 | 2,018 | 2,003 | 1,990 | 1,978 | 1,966 | 1,956 | 1,946 |
| 27 | 4,210 | 3,354 | 2,960 | 2,728 | 2,572 | 2,459 | 2,373 | 2,305 | 2,250 | 2,204 | 2,166 | 2,132 | 2,103 | 2,078 | 2,056 | 2,036 | 2,018 | 2,002 | 1,987 | 1,974 | 1,961 | 1,950 | 1,940 | 1,930 |
| 28 | 4,196 | 3,340 | 2,947 | 2,714 | 2,558 | 2,445 | 2,359 | 2,291 | 2,236 | 2,190 | 2,151 | 2,118 | 2,089 | 2,064 | 2,041 | 2,021 | 2,003 | 1,987 | 1,972 | 1,959 | 1,946 | 1,935 | 1,924 | 1,915 |
| 29 | 4,183 | 3,328 | 2,934 | 2,701 | 2,545 | 2,432 | 2,346 | 2,278 | 2,223 | 2,177 | 2,138 | 2,104 | 2,075 | 2,050 | 2,027 | 2,007 | 1,989 | 1,973 | 1,958 | 1,945 | 1,932 | 1,921 | 1,910 | 1,901 |
| 30 | 4,171 | 3,316 | 2,922 | 2,690 | 2,534 | 2,421 | 2,334 | 2,266 | 2,211 | 2,165 | 2,126 | 2,092 | 2,063 | 2,037 | 2,015 | 1,995 | 1,976 | 1,960 | 1,945 | 1,932 | 1,919 | 1,908 | 1,897 | 1,887 |
| 31 | 4,160 | 3,305 | 2,911 | 2,679 | 2,523 | 2,409 | 2,323 | 2,255 | 2,199 | 2,153 | 2,114 | 2,080 | 2,051 | 2,026 | 2,003 | 1,983 | 1,965 | 1,948 | 1,933 | 1,920 | 1,907 | 1,896 | 1,885 | 1,875 |
| 32 | 4,149 | 3,295 | 2,901 | 2,668 | 2,512 | 2,399 | 2,313 | 2,244 | 2,189 | 2,142 | 2,103 | 2,070 | 2,040 | 2,015 | 1,992 | 1,972 | 1,953 | 1,937 | 1,922 | 1,908 | 1,896 | 1,884 | 1,873 | 1,864 |
| 33 | 4,139 | 3,285 | 2,892 | 2,659 | 2,503 | 2,389 | 2,303 | 2,235 | 2,179 | 2,133 | 2,093 | 2,060 | 2,030 | 2,004 | 1,982 | 1,961 | 1,943 | 1,926 | 1,911 | 1,898 | 1,885 | 1,873 | 1,863 | 1,853 |
| 34 | 4,130 | 3,276 | 2,883 | 2,650 | 2,494 | 2,380 | 2,294 | 2,225 | 2,170 | 2,123 | 2,084 | 2,050 | 2,021 | 1,995 | 1,972 | 1,952 | 1,933 | 1,917 | 1,902 | 1,888 | 1,875 | 1,863 | 1,853 | 1,843 |
| 35 | 4,121 | 3,267 | 2,874 | 2,641 | 2,485 | 2,372 | 2,285 | 2,217 | 2,161 | 2,114 | 2,075 | 2,041 | 2,012 | 1,986 | 1,963 | 1,942 | 1,924 | 1,907 | 1,892 | 1,878 | 1,866 | 1,854 | 1,843 | 1,833 |
| 40 | 4,113 | 3,259 | 2,866 | 2,634 | 2,477 | 2,364 | 2,277 | 2,209 | 2,153 | 2,106 | 2,067 | 2,033 | 2,003 | 1,977 | 1,954 | 1,934 | 1,915 | 1,899 | 1,883 | 1,870 | 1,857 | 1,845 | 1,834 | 1,824 |
| 45 | 4,105 | 3,252 | 2,859 | 2,626 | 2,470 | 2,356 | 2,270 | 2,201 | 2,145 | 2,098 | 2,059 | 2,025 | 1,995 | 1,969 | 1,946 | 1,926 | 1,907 | 1,890 | 1,875 | 1,861 | 1,848 | 1,837 | 1,826 | 1,816 |
| 50 | 4,098 | 3,245 | 2,852 | 2,619 | 2,463 | 2,349 | 2,262 | 2,194 | 2,138 | 2,091 | 2,051 | 2,017 | 1,988 | 1,962 | 1,939 | 1,918 | 1,899 | 1,883 | 1,867 | 1,853 | 1,841 | 1,829 | 1,818 | 1,808 |
| 55 | 4,091 | 3,238 | 2,845 | 2,612 | 2,456 | 2,342 | 2,255 | 2,187 | 2,131 | 2,084 | 2,044 | 2,010 | 1,981 | 1,954 | 1,931 | 1,911 | 1,892 | 1,875 | 1,860 | 1,846 | 1,833 | 1,821 | 1,810 | 1,800 |
| 60 | 4,085 | 3,232 | 2,839 | 2,606 | 2,449 | 2,336 | 2,249 | 2,180 | 2,124 | 2,077 | 2,038 | 2,003 | 1,974 | 1,948 | 1,924 | 1,904 | 1,885 | 1,868 | 1,853 | 1,839 | 1,826 | 1,814 | 1,803 | 1,793 |
| 70 | 4,079 | 3,226 | 2,833 | 2,600 | 2,443 | 2,330 | 2,243 | 2,174 | 2,118 | 2,071 | 2,031 | 1,997 | 1,967 | 1,941 | 1,918 | 1,897 | 1,879 | 1,862 | 1,846 | 1,832 | 1,819 | 1,807 | 1,796 | 1,786 |
| 80 | 4,073 | 3,220 | 2,827 | 2,594 | 2,438 | 2,324 | 2,237 | 2,168 | 2,112 | 2,065 | 2,025 | 1,991 | 1,961 | 1,935 | 1,912 | 1,891 | 1,872 | 1,855 | 1,840 | 1,826 | 1,813 | 1,801 | 1,790 | 1,780 |
| 90 | 4,067 | 3,214 | 2,822 | 2,589 | 2,432 | 2,318 | 2,232 | 2,163 | 2,106 | 2,059 | 2,020 | 1,985 | 1,955 | 1,929 | 1,906 | 1,885 | 1,866 | 1,849 | 1,834 | 1,820 | 1,807 | 1,795 | 1,784 | 1,773 |
| 100 | 4,062 | 3,209 | 2,816 | 2,584 | 2,427 | 2,313 | 2,226 | 2,157 | 2,101 | 2,054 | 2,014 | 1,980 | 1,950 | 1,924 | 1,900 | 1,879 | 1,861 | 1,844 | 1,828 | 1,814 | 1,801 | 1,789 | 1,778 | 1,767 |
| 120 | 4,057 | 3,204 | 2,812 | 2,579 | 2,422 | 2,308 | 2,221 | 2,152 | 2,096 | 2,049 | 2,009 | 1,974 | 1,945 | 1,918 | 1,895 | 1,874 | 1,855 | 1,838 | 1,823 | 1,808 | 1,795 | 1,783 | 1,772 | 1,762 |
| 150 | 4,052 | 3,200 | 2,807 | 2,574 | 2,417 | 2,304 | 2,216 | 2,147 | 2,091 | 2,044 | 2,004 | 1,969 | 1,940 | 1,913 | 1,890 | 1,869 | 1,850 | 1,833 | 1,817 | 1,803 | 1,790 | 1,778 | 1,767 | 1,756 |
| 200 | 4,047 | 3,195 | 2,802 | 2,570 | 2,413 | 2,299 | 2,212 | 2,143 | 2,086 | 2,039 | 1,999 | 1,965 | 1,935 | 1,908 | 1,885 | 1,864 | 1,845 | 1,828 | 1,812 | 1,798 | 1,785 | 1,773 | 1,762 | 1,751 |
| 300 | 4,043 | 3,191 | 2,798 | 2,565 | 2,409 | 2,295 | 2,207 | 2,138 | 2,082 | 2,035 | 1,995 | 1,960 | 1,930 | 1,904 | 1,880 | 1,859 | 1,840 | 1,823 | 1,807 | 1,793 | 1,780 | 1,768 | 1,757 | 1,746 |
| 400 | 4,038 | 3,187 | 2,794 | 2,561 | 2,404 | 2,290 | 2,203 | 2,134 | 2,077 | 2,030 | 1,990 | 1,956 | 1,926 | 1,899 | 1,876 | 1,855 | 1,836 | 1,819 | 1,803 | 1,789 | 1,775 | 1,763 | 1,752 | 1,742 |
| 500 | 4,034 | 3,183 | 2,790 | 2,557 | 2,400 | 2,286 | 2,199 | 2,130 | 2,073 | 2,026 | 1,986 | 1,952 | 1,921 | 1,895 | 1,871 | 1,850 | 1,831 | 1,814 | 1,798 | 1,784 | 1,771 | 1,759 | 1,748 | 1,737 |
| 100000 | 4,030 | 3,179 | 2,786 | 2,553 | 2,397 | 2,283 | 2,195 | 2,126 | 2,069 | 2,022 | 1,982 | 1,947 | 1,917 | 1,891 | 1,867 | 1,846 | 1,827 | 1,810 | 1,794 | 1,780 | 1,767 | 1,754 | 1,743 | 1,733 |

0.99-Quantile der Fisher-Verteilung mit n Freiheitsgraden im Nenner und m Freiheitsgraden im Zähler :

| | m=1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 30 | 40 | 50 | 60 | 100 | 100000 |
| - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| n=1 | 4052, | 4999 | 5403 | 5624 | 5763 | 5859 | 5928 | 5981 | 6022 | 6055 | 6083 | 6106 | 6125 | 6142 | 6157 | 6170 | 6181 | 6191 | 6200 | 6208 | 6216 | 6222 | 6229 | 6234 |
| 2 | 98,50 | 99,00 | 99,17 | 99,25 | 99,30 | 99,33 | 99,36 | 99,37 | 99,39 | 99,40 | 99,41 | 99,42 | 99,42 | 99,43 | 99,43 | 99,44 | 99,44 | 99,44 | 99,45 | 99,45 | 99,45 | 99,45 | 99,46 | 99,46 |
| 3 | 34,12 | 30,82 | 29,46 | 28,71 | 28,24 | 27,91 | 27,67 | 27,49 | 27,35 | 27,23 | 27,13 | 27,05 | 26,98 | 26,92 | 26,87 | 26,83 | 26,79 | 26,75 | 26,72 | 26,69 | 26,66 | 26,64 | 26,62 | 26,60 |
| 4 | 21,20 | 18,00 | 16,69 | 15,98 | 15,52 | 15,21 | 14,98 | 14,80 | 14,66 | 14,55 | 14,45 | 14,37 | 14,31 | 14,25 | 14,20 | 14,15 | 14,11 | 14,08 | 14,05 | 14,02 | 13,99 | 13,97 | 13,95 | 13,93 |
| 5 | 16,26 | 13,27 | 12,06 | 11,39 | 10,97 | 10,67 | 10,46 | 10,29 | 10,16 | 10,05 | 9,963 | 9,888 | 9,825 | 9,770 | 9,722 | 9,680 | 9,643 | 9,610 | 9,580 | 9,553 | 9,528 | 9,506 | 9,485 | 9,466 |
| 6 | 13,75 | 10,92 | 9,780 | 9,148 | 8,746 | 8,466 | 8,260 | 8,102 | 7,976 | 7,874 | 7,790 | 7,718 | 7,657 | 7,605 | 7,559 | 7,519 | 7,483 | 7,451 | 7,422 | 7,396 | 7,372 | 7,351 | 7,331 | 7,313 |
| 7 | 12,25 | 9,547 | 8,451 | 7,847 | 7,460 | 7,191 | 6,993 | 6,840 | 6,719 | 6,620 | 6,538 | 6,469 | 6,410 | 6,359 | 6,314 | 6,275 | 6,240 | 6,209 | 6,181 | 6,155 | 6,132 | 6,111 | 6,092 | 6,074 |
| 8 | 11,26 | 8,649 | 7,591 | 7,006 | 6,632 | 6,371 | 6,178 | 6,029 | 5,911 | 5,814 | 5,734 | 5,667 | 5,609 | 5,559 | 5,515 | 5,477 | 5,442 | 5,412 | 5,384 | 5,359 | 5,336 | 5,316 | 5,297 | 5,279 |
| 9 | 10,56 | 8,022 | 6,992 | 6,422 | 6,057 | 5,802 | 5,613 | 5,467 | 5,351 | 5,257 | 5,178 | 5,111 | 5,055 | 5,005 | 4,962 | 4,924 | 4,890 | 4,860 | 4,833 | 4,808 | 4,786 | 4,765 | 4,746 | 4,729 |
| 10 | 10,04 | 7,559 | 6,552 | 5,994 | 5,636 | 5,386 | 5,200 | 5,057 | 4,942 | 4,849 | 4,772 | 4,706 | 4,650 | 4,601 | 4,558 | 4,520 | 4,487 | 4,457 | 4,430 | 4,405 | 4,383 | 4,363 | 4,344 | 4,327 |
| 11 | 9,646 | 7,206 | 6,217 | 5,668 | 5,316 | 5,069 | 4,886 | 4,744 | 4,632 | 4,539 | 4,462 | 4,397 | 4,342 | 4,293 | 4,251 | 4,213 | 4,180 | 4,150 | 4,123 | 4,099 | 4,077 | 4,057 | 4,038 | 4,021 |
| 12 | 9,330 | 6,927 | 5,953 | 5,412 | 5,064 | 4,821 | 4,640 | 4,499 | 4,388 | 4,296 | 4,220 | 4,155 | 4,100 | 4,052 | 4,010 | 3,972 | 3,939 | 3,909 | 3,883 | 3,858 | 3,836 | 3,816 | 3,798 | 3,780 |
| 13 | 9,074 | 6,701 | 5,739 | 5,205 | 4,862 | 4,620 | 4,441 | 4,302 | 4,191 | 4,100 | 4,025 | 3,960 | 3,905 | 3,857 | 3,815 | 3,778 | 3,745 | 3,716 | 3,689 | 3,665 | 3,643 | 3,622 | 3,604 | 3,587 |
| 14 | 8,862 | 6,515 | 5,564 | 5,035 | 4,695 | 4,456 | 4,278 | 4,140 | 4,030 | 3,939 | 3,864 | 3,800 | 3,745 | 3,698 | 3,656 | 3,619 | 3,586 | 3,556 | 3,529 | 3,505 | 3,483 | 3,463 | 3,444 | 3,427 |
| 15 | 8,683 | 6,359 | 5,417 | 4,893 | 4,556 | 4,318 | 4,142 | 4,004 | 3,895 | 3,805 | 3,730 | 3,666 | 3,612 | 3,564 | 3,522 | 3,485 | 3,452 | 3,423 | 3,396 | 3,372 | 3,350 | 3,330 | 3,311 | 3,294 |
| 16 | 8,531 | 6,226 | 5,292 | 4,773 | 4,437 | 4,202 | 4,026 | 3,890 | 3,780 | 3,691 | 3,616 | 3,553 | 3,498 | 3,451 | 3,409 | 3,372 | 3,339 | 3,310 | 3,283 | 3,259 | 3,237 | 3,216 | 3,198 | 3,181 |
| 17 | 8,400 | 6,112 | 5,185 | 4,669 | 4,336 | 4,102 | 3,927 | 3,791 | 3,682 | 3,593 | 3,519 | 3,455 | 3,401 | 3,353 | 3,312 | 3,275 | 3,242 | 3,212 | 3,186 | 3,162 | 3,139 | 3,119 | 3,101 | 3,084 |
| 18 | 8,285 | 6,013 | 5,092 | 4,579 | 4,248 | 4,015 | 3,841 | 3,705 | 3,597 | 3,508 | 3,434 | 3,371 | 3,316 | 3,269 | 3,227 | 3,190 | 3,158 | 3,128 | 3,101 | 3,077 | 3,055 | 3,035 | 3,016 | 2,999 |
| 19 | 8,185 | 5,926 | 5,010 | 4,500 | 4,171 | 3,939 | 3,765 | 3,631 | 3,523 | 3,434 | 3,360 | 3,297 | 3,242 | 3,195 | 3,153 | 3,116 | 3,084 | 3,054 | 3,027 | 3,003 | 2,981 | 2,961 | 2,942 | 2,925 |
| 20 | 8,096 | 5,849 | 4,938 | 4,431 | 4,103 | 3,871 | 3,699 | 3,564 | 3,457 | 3,368 | 3,294 | 3,231 | 3,177 | 3,130 | 3,088 | 3,051 | 3,018 | 2,989 | 2,962 | 2,938 | 2,916 | 2,895 | 2,877 | 2,859 |
| 21 | 8,017 | 5,780 | 4,874 | 4,369 | 4,042 | 3,812 | 3,640 | 3,506 | 3,398 | 3,310 | 3,236 | 3,173 | 3,119 | 3,072 | 3,030 | 2,993 | 2,960 | 2,931 | 2,904 | 2,880 | 2,857 | 2,837 | 2,818 | 2,801 |
| 22 | 7,945 | 5,719 | 4,817 | 4,313 | 3,988 | 3,758 | 3,587 | 3,453 | 3,346 | 3,258 | 3,184 | 3,121 | 3,067 | 3,019 | 2,978 | 2,941 | 2,908 | 2,879 | 2,852 | 2,827 | 2,805 | 2,785 | 2,766 | 2,749 |
| 23 | 7,881 | 5,664 | 4,765 | 4,264 | 3,939 | 3,710 | 3,539 | 3,406 | 3,299 | 3,211 | 3,137 | 3,074 | 3,020 | 2,973 | 2,931 | 2,894 | 2,861 | 2,832 | 2,805 | 2,781 | 2,758 | 2,738 | 2,719 | 2,702 |
| 24 | 7,823 | 5,614 | 4,718 | 4,218 | 3,895 | 3,667 | 3,496 | 3,363 | 3,256 | 3,168 | 3,094 | 3,032 | 2,977 | 2,930 | 2,889 | 2,852 | 2,819 | 2,789 | 2,762 | 2,738 | 2,716 | 2,695 | 2,676 | 2,659 |
| 25 | 7,770 | 5,568 | 4,675 | 4,177 | 3,855 | 3,627 | 3,457 | 3,324 | 3,217 | 3,129 | 3,056 | 2,993 | 2,939 | 2,892 | 2,850 | 2,813 | 2,780 | 2,751 | 2,724 | 2,699 | 2,677 | 2,657 | 2,638 | 2,620 |
| 26 | 7,721 | 5,526 | 4,637 | 4,140 | 3,818 | 3,591 | 3,421 | 3,288 | 3,182 | 3,094 | 3,021 | 2,958 | 2,904 | 2,857 | 2,815 | 2,778 | 2,745 | 2,715 | 2,688 | 2,664 | 2,642 | 2,621 | 2,602 | 2,585 |
| 27 | 7,677 | 5,488 | 4,601 | 4,106 | 3,785 | 3,558 | 3,388 | 3,256 | 3,149 | 3,062 | 2,988 | 2,926 | 2,871 | 2,824 | 2,783 | 2,746 | 2,713 | 2,683 | 2,656 | 2,632 | 2,609 | 2,589 | 2,570 | 2,552 |
| 28 | 7,636 | 5,453 | 4,568 | 4,074 | 3,754 | 3,528 | 3,358 | 3,226 | 3,120 | 3,032 | 2,959 | 2,896 | 2,842 | 2,795 | 2,753 | 2,716 | 2,683 | 2,653 | 2,626 | 2,602 | 2,579 | 2,559 | 2,540 | 2,522 |
| 29 | 7,598 | 5,420 | 4,538 | 4,045 | 3,725 | 3,499 | 3,330 | 3,198 | 3,092 | 3,005 | 2,931 | 2,868 | 2,814 | 2,767 | 2,726 | 2,689 | 2,656 | 2,626 | 2,599 | 2,574 | 2,552 | 2,531 | 2,512 | 2,495 |
| 30 | 7,562 | 5,390 | 4,510 | 4,018 | 3,699 | 3,473 | 3,304 | 3,173 | 3,067 | 2,979 | 2,906 | 2,843 | 2,789 | 2,742 | 2,700 | 2,663 | 2,630 | 2,600 | 2,573 | 2,549 | 2,526 | 2,506 | 2,487 | 2,469 |
| 31 | 7,530 | 5,362 | 4,484 | 3,993 | 3,675 | 3,449 | 3,281 | 3,149 | 3,043 | 2,955 | 2,882 | 2,820 | 2,765 | 2,718 | 2,677 | 2,640 | 2,606 | 2,577 | 2,550 | 2,525 | 2,502 | 2,482 | 2,463 | 2,445 |
| 32 | 7,499 | 5,336 | 4,459 | 3,969 | 3,652 | 3,427 | 3,258 | 3,127 | 3,021 | 2,934 | 2,860 | 2,798 | 2,744 | 2,696 | 2,655 | 2,618 | 2,584 | 2,555 | 2,527 | 2,503 | 2,480 | 2,460 | 2,441 | 2,423 |
| 33 | 7,471 | 5,312 | 4,437 | 3,948 | 3,630 | 3,406 | 3,238 | 3,106 | 3,000 | 2,913 | 2,840 | 2,777 | 2,723 | 2,676 | 2,634 | 2,597 | 2,564 | 2,534 | 2,507 | 2,482 | 2,460 | 2,439 | 2,420 | 2,402 |
| 34 | 7,444 | 5,289 | 4,416 | 3,927 | 3,611 | 3,386 | 3,218 | 3,087 | 2,981 | 2,894 | 2,821 | 2,758 | 2,704 | 2,657 | 2,615 | 2,578 | 2,545 | 2,515 | 2,488 | 2,463 | 2,440 | 2,420 | 2,400 | 2,383 |
| 35 | 7,419 | 5,268 | 4,396 | 3,908 | 3,592 | 3,368 | 3,200 | 3,069 | 2,963 | 2,876 | 2,803 | 2,740 | 2,686 | 2,639 | 2,597 | 2,560 | 2,527 | 2,497 | 2,470 | 2,445 | 2,422 | 2,401 | 2,382 | 2,364 |
| 40 | 7,396 | 5,248 | 4,377 | 3,890 | 3,574 | 3,351 | 3,183 | 3,052 | 2,946 | 2,859 | 2,786 | 2,723 | 2,669 | 2,622 | 2,580 | 2,543 | 2,510 | 2,480 | 2,453 | 2,428 | 2,405 | 2,384 | 2,365 | 2,347 |
| 45 | 7,373 | 5,229 | 4,360 | 3,873 | 3,558 | 3,334 | 3,167 | 3,036 | 2,930 | 2,843 | 2,770 | 2,707 | 2,653 | 2,606 | 2,564 | 2,527 | 2,494 | 2,464 | 2,437 | 2,412 | 2,389 | 2,368 | 2,349 | 2,331 |
| 50 | 7,353 | 5,211 | 4,343 | 3,858 | 3,542 | 3,319 | 3,152 | 3,021 | 2,915 | 2,828 | 2,755 | 2,692 | 2,638 | 2,591 | 2,549 | 2,512 | 2,479 | 2,449 | 2,421 | 2,397 | 2,374 | 2,353 | 2,334 | 2,316 |
| 55 | 7,333 | 5,194 | 4,327 | 3,843 | 3,528 | 3,305 | 3,137 | 3,006 | 2,901 | 2,814 | 2,741 | 2,678 | 2,624 | 2,577 | 2,535 | 2,498 | 2,465 | 2,434 | 2,407 | 2,382 | 2,360 | 2,339 | 2,319 | 2,302 |
| 60 | 7,314 | 5,179 | 4,313 | 3,828 | 3,514 | 3,291 | 3,124 | 2,993 | 2,888 | 2,801 | 2,727 | 2,665 | 2,611 | 2,563 | 2,522 | 2,484 | 2,451 | 2,421 | 2,394 | 2,369 | 2,346 | 2,325 | 2,306 | 2,288 |
| 70 | 7,296 | 5,163 | 4,299 | 3,815 | 3,501 | 3,278 | 3,111 | 2,980 | 2,875 | 2,788 | 2,715 | 2,652 | 2,598 | 2,551 | 2,509 | 2,472 | 2,438 | 2,408 | 2,381 | 2,356 | 2,333 | 2,312 | 2,293 | 2,275 |
| 80 | 7,280 | 5,149 | 4,285 | 3,802 | 3,488 | 3,266 | 3,099 | 2,968 | 2,863 | 2,776 | 2,703 | 2,640 | 2,586 | 2,539 | 2,497 | 2,460 | 2,426 | 2,396 | 2,369 | 2,344 | 2,321 | 2,300 | 2,281 | 2,263 |
| 90 | 7,264 | 5,136 | 4,273 | 3,790 | 3,476 | 3,254 | 3,087 | 2,957 | 2,851 | 2,764 | 2,691 | 2,629 | 2,575 | 2,527 | 2,485 | 2,448 | 2,415 | 2,385 | 2,357 | 2,332 | 2,310 | 2,289 | 2,269 | 2,251 |
| 100 | 7,248 | 5,123 | 4,261 | 3,778 | 3,465 | 3,243 | 3,076 | 2,946 | 2,840 | 2,754 | 2,680 | 2,618 | 2,564 | 2,516 | 2,475 | 2,437 | 2,404 | 2,374 | 2,346 | 2,321 | 2,299 | 2,278 | 2,258 | 2,240 |
| 120 | 7,234 | 5,110 | 4,249 | 3,767 | 3,454 | 3,232 | 3,066 | 2,935 | 2,830 | 2,743 | 2,670 | 2,608 | 2,553 | 2,506 | 2,464 | 2,427 | 2,393 | 2,363 | 2,336 | 2,311 | 2,288 | 2,267 | 2,248 | 2,230 |
| 150 | 7,220 | 5,099 | 4,238 | 3,757 | 3,444 | 3,222 | 3,056 | 2,925 | 2,820 | 2,733 | 2,660 | 2,598 | 2,544 | 2,496 | 2,454 | 2,417 | 2,384 | 2,353 | 2,326 | 2,301 | 2,278 | 2,257 | 2,238 | 2,220 |
| 200 | 7,207 | 5,087 | 4,228 | 3,747 | 3,434 | 3,213 | 3,046 | 2,916 | 2,811 | 2,724 | 2,651 | 2,588 | 2,534 | 2,487 | 2,445 | 2,408 | 2,374 | 2,344 | 2,316 | 2,291 | 2,268 | 2,247 | 2,228 | 2,210 |
| 300 | 7,194 | 5,077 | 4,218 | 3,737 | 3,425 | 3,204 | 3,037 | 2,907 | 2,802 | 2,715 | 2,642 | 2,579 | 2,525 | 2,478 | 2,436 | 2,399 | 2,365 | 2,335 | 2,307 | 2,282 | 2,259 | 2,238 | 2,219 | 2,201 |
| 400 | 7,182 | 5,066 | 4,208 | 3,728 | 3,416 | 3,195 | 3,028 | 2,898 | 2,793 | 2,706 | 2,633 | 2,571 | 2,517 | 2,469 | 2,427 | 2,390 | 2,356 | 2,326 | 2,299 | 2,274 | 2,251 | 2,229 | 2,210 | 2,192 |
| 500 | 7,171 | 5,057 | 4,199 | 3,720 | 3,408 | 3,186 | 3,020 | 2,890 | 2,785 | 2,698 | 2,625 | 2,562 | 2,508 | 2,461 | 2,419 | 2,382 | 2,348 | 2,318 | 2,290 | 2,265 | 2,242 | 2,221 | 2,202 | 2,183 |
| 100000 | 7,159 | 5,047 | 4,191 | 3,711 | 3,400 | 3,178 | 3,012 | 2,882 | 2,777 | 2,690 | 2,617 | 2,555 | 2,500 | 2,453 | 2,411 | 2,374 | 2,340 | 2,310 | 2,282 | 2,257 | 2,234 | 2,213 | 2,194 | 2,175 |
