A sample of $N N(0, 1)$ observations is ranked from largest (rank 1) to smallest (rank $N$). The expected values of the order statistics (the ranked values) are given. Only the expected values for the upper half of the order statistics are given since the expected values are symmetric about zero. The column headings give the size of the sample and the row headings the rank of the order statistic.
Table 1: Expected values of normal order statistics.
  Sample size
Rank 2 3 4 5 6 7 8 9 10 11 12 13 14
1 .56419 .34628 1.02938 1.16296 1.26721 1.35218 1.42360 1.48501 1.53875 1.58644 1.62923 1.66799 1.70338
2   .00000 .29701 .49502 .64176 .75737 .85222 .93230 1.00136 1.06192 1.11573 1.16408 1.20790
3       .00000 .20155 .35271 .47282 .57197 .65606 .72884 .79284 .84983 .90113
4           .00000 .15251 .27453 .37576 .46198 .53684 .60285 .66176
5               .00000 .12267 .22489 .31225 .38833 .45557
6                   .00000 .10259 .19052 .26730
7                       .00000 .08816
  Sample size
Rank 15 16 17 18 19 20 21 22 23 24 25 26 27
1 1.73591 1.76599 1.79394 1.82003 1.84448 1.86748 1.88917 1.90969 1.92916 1.94767 1.96531 1.98216 1.99827
2 1.24794 1.28474 1.31878 1.35041 1.37994 1.40760 1.43362 1.45816 1.48137 1.50338 1.52430 1.54423 1.56326
3 .94769 .99027 1.02946 1.06573 1.09945 1.13095 1.16047 1.18824 1.21445 1.23924 1.26275 1.28511 1.30641
4 .71488 .76317 .80738 .84812 .88586 .92098 .95380 .98459 1.01356 1.04091 1.06679 1.09135 1.11471
5 .51570 .57001 .61946 .66479 .70661 .74538 .78150 .81527 .84697 .87682 .90501 .93171 .95705
6 .33530 .39622 .45133 .50158 .54771 .59030 .62982 .66667 .70115 .73354 .76405 .79289 .82021
7 .16530 .23375 .29519 .35084 .40164 .44833 .49148 .53157 .56896 .60299 .63690 .66794 .69727
8 .00000 .07729 .14599 .20774 .26374 .31493 .36203 .40559 .44609 .48391 .51935 .55267 .58411
9     .00000 .06880 .13072 .18696 .23841 .28579 .32965 .37047 .40860 .44436 .47801
10         .00000 .06200 .11836 .16997 .21755 .26163 .30268 .34105 .37706
11             .00000 .05642 .10813 .15583 .20006 .24128 .27983
12                 .00000 .05176 .09953 .14387 .18520
13                     .00000 .04781 .09220
14                         .00000
  Sample size
Rank 28 29 30 31 32 33 34 35 36 37 38 39  
1 2.01371 2.02852 2.04276 2.05646 2.06967 2.08241 2.09471 2.10661 2.11812 2.12928 2.14009 2.15059  
2 1.58145 1.59888 1.61560 1.63166 1.64712 1.66200 1.67636 1.69023 1.70362 1.71659 1.72914 1.74131  
3 1.32674 1.34619 1.36481 1.38268 1.39985 1.41637 1.43228 1.44762 1.46244 1.47676 1.49061 1.50402  
4 1.13697 1.15822 1.17855 1.19803 1.21672 1.23468 1.25196 1.26860 1.28466 1.30016 1.31514 1.32964  
5 .98115 1.00414 1.02609 1.04709 1.06721 1.08652 1.10509 1.12295 1.14016 1.15677 1.17280 1.18830  
6 .84615 .87084 .89439 .91688 .93841 .95905 .97886 .99790 1.01624 1.03390 1.05095 1.06741  
7 .72508 .75150 .77666 .80066 .82359 .84555 .86660 .88681 .90625 .92496 .94300 .96041  
8 .61385 .64205 .66885 .69438 .71875 .74204 .76435 .78574 .80629 .82605 .84508 .86343  
9 .50977 .53982 .56834 .59545 .62129 .64596 .66954 .69214 .71382 .73465 .75468 .77398  
10 .41096 .44298 .47329 .50206 .52943 .55552 .58043 .60427 .62710 .64902 .67009 .69035  
11 .31603 .35013 .38235 .41287 .44185 .46942 .49572 .52084 .54488 .56793 .59005 .61131  
12 .22389 .26023 .29449 .32686 .35755 .38669 .41444 .44091 .46620 .49042 .51363 .53592  
13 .13361 .17240 .20885 .24322 .27573 .30654 .33582 .36371 .39032 .41576 .44012 .46348  
14 .04442 .08588 .12473 .16126 .19572 .22832 .25924 .28863 .31663 .34336 .36892 .39340  
15   .00000 .04148 .08037 .11695 .15147 .18415 .21515 .24463 .27272 .29954 .32520  
16       .00000 .03890 .07552 .11009 .14282 .17388 .20342 .23159 .25849  
17           .00000 .03663 .07123 .10399 .13509 .16469 .19292  
18               .00000 .03461 .06739 .09853 .12817  
19                   .00000 .03280 .06395  
20                       .00000