Introduction to Statistics
Common Mistakes and Tables
This article includes the following tables:
Table : Binomial Probabilities, P(x) for n ≤ 20
Table : Standard Normal Probabilities
Table : t Distribution Critical Values
Table : χ2 Critical Values
| n = 2 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 | 0.9025 0.0950 0.0025 | 0.8100 0.1800 0.0100 | 0.7225 0.2550 0.0225 | 0.6400 0.3200 0.0400 | 0.5625 0.3750 0.0625 | 0.4900 0.4200 0.0900 | 0.4225 0.4550 0.1225 | 0.3600 0.4800 0.1600 | 0.3025 0.4950 0.2025 | 0.2500 0.5000 0.2500 | 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 3 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 | 0.8574 0.1354 0.0071 0.0001 | 0.7290 0.2430 0.0270 0.0010 | 0.6141 0.3251 0.0574 0.0034 | 0.5120 0.3840 0.0960 0.0080 | 0.4219 0.4219 0.1406 0.0156 | 0.3430 0.4410 0.1890 0.0270 | 0.2746 0.4436 0.2389 0.0429 | 0.2160 0.4320 0.2880 0.0640 | 0.1664 0.4084 0.3341 0.0911 | 0.1250 0.3750 0.3750 0.1250 | 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 4 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 | 0.8145 0.1715 0.0135 0.0005 0.0000 | 0.6561 0.2916 0.0486 0.0036 0.0001 | 0.5220 0.3685 0.0975 0.0115 0.0005 | 0.4096 0.4096 0.1536 0.0256 0.0016 | 0.3164 0.4219 0.2109 0.0469 0.0039 | 0.2401 0.4116 0.2646 0.0756 0.0081 | 0.1785 0.3845 0.3105 0.1115 0.0150 | 0.1296 0.3456 0.3456 0.1536 0.0256 | 0.0915 0.2995 0.3675 0.2005 0.0410 | 0.0625 0.2500 0.3750 0.2500 0.0625 | 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 5 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 | 0.7738 0.2036 0.0214 0.0011 0.0000 0.0000 | 0.5905 0.3281 0.0729 0.0081 0.0005 0.0000 | 0.4437 0.3915 0.1382 0.0244 0.0022 0.0001 | 0.3277 0.4096 0.2048 0.0512 0.0064 0.0003 | 0.2373 0.3955 0.2637 0.0879 0.0146 0.0010 | 0.1681 0.3602 0.3087 0.1323 0.0284 0.0024 | 0.1160 0.3124 0.3364 0.1811 0.0488 0.0053 | 0.0778 0.2592 0.3456 0.2304 0.0768 0.0102 | 0.0503 0.2059 0.3369 0.2757 0.1128 0.0185 | 0.0313 0.1563 0.3125 0.3125 0.1563 0.0313 | 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 6 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 | 0.7351 0.2321 0.0305 0.0021 0.0001 0.0000 0.0000 | 0.5314 0.3543 0.0984 0.0146 0.0012 0.0001 0.0000 | 0.3771 0.3993 0.1762 0.0415 0.0055 0.0004 0.0000 | 0.2621 0.3932 0.2458 0.0819 0.0154 0.0015 0.0001 | 0.1780 0.3560 0.2966 0.1318 0.0330 0.0044 0.0002 | 0.1176 0.3025 0.3241 0.1852 0.0595 0.0102 0.0007 | 0.0754 0.2437 0.3280 0.2355 0.0951 0.0205 0.0018 | 0.0467 0.1866 0.3110 0.2765 0.1382 0.0369 0.0041 | 0.0277 0.1359 0.2780 0.3032 0.1861 0.0609 0.0083 | 0.0156 0.0938 0.2344 0.3125 0.2344 0.0938 0.0156 | 6 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 7 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 | 0.6983 0.2573 0.0406 0.0036 0.0002 0.0000 0.0000 0.0000 | 0.4783 0.3720 0.1240 0.0230 0.0026 0.0002 0.0000 0.0000 | 0.3206 0.3960 0.2097 0.0617 0.0109 0.0012 0.0001 0.0000 | 0.2097 0.3670 0.2753 0.1147 0.0287 0.0043 0.0004 0.0000 | 0.1335 0.3115 0.3115 0.1730 0.0577 0.0115 0.0013 0.0001 | 0.0824 0.2471 0.3177 0.2269 0.0972 0.0250 0.0036 0.0002 | 0.0490 0.1848 0.2985 0.2679 0.1442 0.0466 0.0084 0.0006 | 0.0280 0.1306 0.2613 0.2903 0.1935 0.0774 0.0172 0.0016 | 0.0152 0.0872 0.2140 0.2918 0.2388 0.1172 0.0320 0.0037 | 0.0078 0.0547 0.1641 0.2734 0.2734 0.1641 0.0547 0.0078 | 7 6 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 8 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 | 0.6634 0.2793 0.0515 0.0054 0.0004 0.0000 0.0000 0.0000 0.0000 | 0.4305 0.3826 0.1488 0.0331 0.0046 0.0004 0.0000 0.0000 0.0000 | 0.2725 0.3847 0.2376 0.0839 0.0185 0.0026 0.0002 0.0000 0.0000 | 0.1678 0.3355 0.2936 0.1468 0.0459 0.0092 0.0011 0.0001 0.0000 | 0.1001 0.2670 0.3115 0.2076 0.0865 0.0231 0.0038 0.0004 0.0000 | 0.0576 0.1977 0.2965 0.2541 0.1361 0.0467 0.0100 0.0012 0.0001 | 0.0319 0.1373 0.2587 0.2786 0.1875 0.0808 0.0217 0.0033 0.0002 | 0.0168 0.0896 0.2090 0.2787 0.2322 0.1239 0.0413 0.0079 0.0007 | 0.0084 0.0548 0.1569 0.2568 0.2627 0.1719 0.0703 0.0164 0.0017 | 0.0039 0.0313 0.1094 0.2188 0.2734 0.2188 0.1094 0.0313 0.0039 | 8 7 6 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 9 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 9 | 0.6302 0.2985 0.0629 0.0077 0.0006 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.3874 0.3874 0.1722 0.0446 0.0074 0.0008 0.0001 0.0000 0.0000 0.0000 | 0.2316 0.3679 0.2597 0.1069 0.0283 0.0050 0.0006 0.0000 0.0000 0.0000 | 0.1342 0.3020 0.3020 0.1762 0.0661 0.0165 0.0028 0.0003 0.0000 0.0000 | 0.0751 0.2253 0.3003 0.2336 0.1168 0.0389 0.0087 0.0012 0.0001 0.0000 | 0.0404 0.1556 0.2668 0.2668 0.1715 0.0735 0.0210 0.0039 0.0004 0.0000 | 0.0207 0.1004 0.2162 0.2716 0.2194 0.1181 0.0424 0.0098 0.0013 0.0001 | 0.0101 0.0605 0.1612 0.2508 0.2508 0.1672 0.0743 0.0212 0.0035 0.0003 | 0.0046 0.0339 0.1110 0.2119 0.2600 0.2128 0.1160 0.0407 0.0083 0.0008 | 0.0020 0.0176 0.0703 0.1641 0.2461 0.2461 0.1641 0.0703 0.0176 0.0020 | 9 8 7 6 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 10 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 9 10 | 0.5987 0.3151 0.0746 0.0105 0.0010 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.3487 0.3874 0.1937 0.0574 0.0112 0.0015 0.0001 0.0000 0.0000 0.0000 0.0000 | 0.1969 0.3474 0.2759 0.1298 0.0401 0.0085 0.0012 0.0001 0.0000 0.0000 0.0000 | 0.1074 0.2684 0.3020 0.2013 0.0881 0.0264 0.0055 0.0008 0.0001 0.0000 0.0000 | 0.0563 0.1877 0.2816 0.2503 0.1460 0.0584 0.0162 0.0031 0.0004 0.0000 0.0000 | 0.0282 0.1211 0.2335 0.2668 0.2001 0.1029 0.0368 0.0090 0.0014 0.0001 0.0000 | 0.0135 0.0725 0.1757 0.2522 0.2377 0.1536 0.0689 0.0212 0.0043 0.0005 0.0000 | 0.0060 0.0403 0.1209 0.2150 0.2508 0.2007 0.1115 0.0425 0.0106 0.0016 0.0001 | 0.0025 0.0207 0.0763 0.1665 0.2384 0.2340 0.1596 0.0746 0.0229 0.0042 0.0003 | 0.0010 0.0098 0.0439 0.1172 0.2051 0.2461 0.2051 0.1172 0.0439 0.0098 0.0010 | 10 9 8 7 6 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 12 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 9 10 11 12 | 0.5404 0.3413 0.0988 0.0173 0.0021 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.2824 0.3766 0.2301 0.0852 0.0213 0.0038 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.1422 0.3012 0.2924 0.1720 0.0683 0.0193 0.0040 0.0006 0.0001 0.0000 0.0000 0.0000 0.0000 | 0.0687 0.2062 0.2835 0.2362 0.1329 0.0532 0.0155 0.0033 0.0005 0.0001 0.0000 0.0000 0.0000 | 0.0317 0.1267 0.2323 0.2581 0.1936 0.1032 0.0401 0.0115 0.0024 0.0004 0.0000 0.0000 0.0000 | 0.0138 0.0712 0.1678 0.2397 0.2311 0.1585 0.0792 0.0291 0.0078 0.0015 0.0002 0.0000 0.0000 | 0.0057 0.0368 0.1088 0.1954 0.2367 0.2039 0.1281 0.0591 0.0199 0.0048 0.0008 0.0001 0.0000 | 0.0022 0.0174 0.0639 0.1419 0.2128 0.2270 0.1766 0.1009 0.0420 0.0125 0.0025 0.0003 0.0000 | 0.0008 0.0075 0.0339 0.0923 0.1700 0.2225 0.2124 0.1489 0.0762 0.0277 0.0068 0.0010 0.0001 | 0.0002 0.0029 0.0161 0.0537 0.1208 0.1934 0.2256 0.1934 0.1208 0.0537 0.0161 0.0029 0.0002 | 12 11 10 9 8 7 6 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 14 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 | 0.4877 0.3593 0.1229 0.0259 0.0037 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.2288 0.3559 0.2570 0.1142 0.0349 0.0078 0.0013 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.1028 0.2539 0.2912 0.2056 0.0998 0.0352 0.0093 0.0019 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0440 0.1539 0.2501 0.2501 0.1720 0.0860 0.0322 0.0092 0.0020 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0178 0.0832 0.1802 0.2402 0.2202 0.1468 0.0734 0.0280 0.0082 0.0018 0.0003 0.0000 0.0000 0.0000 0.0000 | 0.0068 0.0407 0.1134 0.1943 0.2290 0.1963 0.1262 0.0618 0.0232 0.0066 0.0014 0.0002 0.0000 0.0000 0.0000 | 0.0024 0.0181 0.0634 0.1366 0.2022 0.2178 0.1759 0.1082 0.0510 0.0183 0.0049 0.0010 0.0001 0.0000 0.0000 | 0.0008 0.0073 0.0317 0.0845 0.1549 0.2066 0.2066 0.1574 0.0918 0.0408 0.0136 0.0033 0.0005 0.0001 0.0000 | 0.0002 0.0027 0.0141 0.0462 0.1040 0.1701 0.2088 0.1952 0.1398 0.0762 0.0312 0.0093 0.0019 0.0002 0.0000 | 0.0001 0.0009 0.0056 0.0222 0.0611 0.1222 0.1833 0.2095 0.1833 0.1222 0.0611 0.0222 0.0056 0.0009 0.0001 | 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 16 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | 0.4401 0.3706 0.1463 0.0359 0.0061 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.1853 0.3294 0.2745 0.1423 0.0514 0.0137 0.0028 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0743 0.2097 0.2775 0.2285 0.1311 0.0555 0.0180 0.0045 0.0009 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0281 0.1126 0.2111 0.2463 0.2001 0.1201 0.0550 0.0197 0.0055 0.0012 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0100 0.0535 0.1336 0.2079 0.2252 0.1802 0.1101 0.0524 0.0197 0.0058 0.0014 0.0002 0.0000 0.0000 0.0000 0.0000 | 0.0033 0.0228 0.0732 0.1465 0.2040 0.2099 0.1649 0.1010 0.0487 0.0185 0.0056 0.0013 0.0002 0.0000 0.0000 0.0000 | 0.0010 0.0087 0.0353 0.0888 0.1553 0.2008 0.1982 0.1524 0.0923 0.0442 0.0167 0.0049 0.0011 0.0002 0.0000 0.0000 | 0.0003 0.0030 0.0150 0.0468 0.1014 0.1623 0.1983 0.1889 0.1417 0.0840 0.0392 0.0142 0.0040 0.0008 0.0001 0.0000 | 0.0001 0.0009 0.0056 0.0215 0.0572 0.1123 0.1684 0.1969 0.1812 0.1318 0.0755 0.0337 0.0115 0.0029 0.0005 0.0001 | 0.0000 0.0002 0.0018 0.0085 0.0278 0.0667 0.1222 0.1746 0.1964 0.1746 0.1222 0.0667 0.0278 0.0085 0.0018 0.0002 | 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 18 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | 0.3972 0.3763 0.1683 0.0473 0.0093 0.0014 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.1501 0.3002 0.2835 0.1680 0.0700 0.0218 0.0052 0.0010 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0536 0.1704 0.2556 0.2406 0.1592 0.0787 0.0301 0.0091 0.0022 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0180 0.0811 0.1723 0.2297 0.2153 0.1507 0.0816 0.0350 0.0120 0.0033 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0056 0.0338 0.0958 0.1704 0.2130 0.1988 0.1436 0.0820 0.0376 0.0139 0.0042 0.0010 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0016 0.0126 0.0458 0.1046 0.1681 0.2017 0.1873 0.1376 0.0811 0.0386 0.0149 0.0046 0.0012 0.0002 0.0000 0.0000 0.0000 0.0000 | 0.0004 0.0042 0.0190 0.0547 0.1104 0.1664 0.1941 0.1792 0.1327 0.0794 0.0385 0.0151 0.0047 0.0012 0.0002 0.0000 0.0000 0.0000 | 0.0001 0.0012 0.0069 0.0246 0.0614 0.1146 0.1655 0.1892 0.1734 0.1284 0.0771 0.0374 0.0145 0.0045 0.0011 0.0002 0.0000 0.0000 | 0.0000 0.0003 0.0022 0.0095 0.0291 0.0666 0.1181 0.1657 0.1864 0.1694 0.1248 0.0742 0.0354 0.0134 0.0039 0.0009 0.0001 0.0000 | 0.0000 0.0001 0.0006 0.0031 0.0117 0.0327 0.0708 0.1214 0.1669 0.1855 0.1669 0.1214 0.0708 0.0327 0.0117 0.0031 0.0006 0.0001 | 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
| n = 20 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| x↓ | 0.05 | 0.10 | 0.15 | 0.20 | π 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | |
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | 0.3585 0.3774 0.1887 0.0596 0.0133 0.0022 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.1216 0.2702 0.2852 0.1901 0.0898 0.0319 0.0089 0.0020 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0388 0.1368 0.2293 0.2428 0.1821 0.1028 0.0454 0.0160 0.0046 0.0011 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0115 0.0576 0.1369 0.2054 0.2182 0.1746 0.1091 0.0545 0.0222 0.0074 0.0020 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0032 0.0211 0.0669 0.1339 0.1897 0.2023 0.1686 0.1124 0.0609 0.0271 0.0099 0.0030 0.0008 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 | 0.0008 0.0068 0.0278 0.0716 0.1304 0.1789 0.1916 0.1643 0.1144 0.0654 0.0308 0.0120 0.0039 0.0010 0.0002 0.0000 0.0000 0.0000 0.0000 | 0.0002 0.0020 0.0100 0.0323 0.0738 0.1272 0.1712 0.1844 0.1614 0.1158 0.0686 0.0336 0.0136 0.0045 0.0012 0.0003 0.0000 0.0000 0.0000 | 0.0000 0.0005 0.0031 0.0123 0.0350 0.0746 0.1244 0.1659 0.1797 0.1597 0.1171 0.0710 0.0355 0.0146 0.0049 0.0013 0.0003 0.0000 0.0000 | 0.0000 0.0001 0.0008 0.0040 0.0139 0.0365 0.0746 0.1221 0.1623 0.1771 0.1593 0.1185 0.0727 0.0366 0.0150 0.0049 0.0013 0.0002 0.0000 | 0.0000 0.0000 0.0002 0.0011 0.0046 0.0148 0.0370 0.0739 0.1201 0.1602 0.1762 0.1602 0.1201 0.0739 0.0370 0.0148 0.0046 0.0011 0.0002 | 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 |
| 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | x↑ | |
|
(Table entry is probability at or below z.)  |
| z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | z |
|---|---|---|---|---|---|---|---|---|---|---|---|
| –3.4 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0003 | 0.0002 | –3.4 |
| –3.3 | 0.0005 | 0.0005 | 0.0005 | 0.0004 | 0.0004 | 0.0004 | 0.0004 | 0.0004 | 0.0004 | 0.0003 | –3.3 |
| –3.2 | 0.0007 | 0.0007 | 0.0006 | 0.0006 | 0.0006 | 0.0006 | 0.0006 | 0.0005 | 0.0005 | 0.0005 | –3.2 |
| –3.1 | 0.0010 | 0.0009 | 0.0009 | 0.0009 | 0.0008 | 0.0008 | 0.0008 | 0.0008 | 0.0007 | 0.0007 | –3.1 |
| –3.0 | 0.0013 | 0.0013 | 0.0013 | 0.0012 | 0.0012 | 0.0011 | 0.0011 | 0.0011 | 0.0010 | 0.0010 | –3.0 |
| –2.9 | 0.0019 | 0.0018 | 0.0018 | 0.0017 | 0.0016 | 0.0016 | 0.0015 | 0.0015 | 0.0014 | 0.0014 | –2.9 |
| –2.8 | 0.0026 | 0.0025 | 0.0024 | 0.0023 | 0.0023 | 0.0022 | 0.0021 | 0.0021 | 0.0020 | 0.0019 | –2.8 |
| –2.7 | 0.0035 | 0.0034 | 0.0033 | 0.0032 | 0.0031 | 0.0030 | 0.0029 | 0.0028 | 0.0027 | 0.0026 | –2.7 |
| –2.6 | 0.0047 | 0.0045 | 0.0044 | 0.0043 | 0.0041 | 0.0040 | 0.0039 | 0.0038 | 0.0037 | 0.0036 | –2.6 |
| –2.5 | 0.0062 | 0.0060 | 0.0059 | 0.0057 | 0.0055 | 0.0054 | 0.0052 | 0.0051 | 0.0049 | 0.0048 | –2.5 |
| –2.4 | 0.0082 | 0.0080 | 0.0078 | 0.0075 | 0.0073 | 0.0071 | 0.0069 | 0.0068 | 0.0066 | 0.0064 | –2.4 |
| –2.3 | 0.0107 | 0.0104 | 0.0102 | 0.0099 | 0.0096 | 0.0094 | 0.0091 | 0.0089 | 0.0087 | 0.0084 | –2.3 |
| –2.2 | 0.0139 | 0.0136 | 0.0132 | 0.0129 | 0.0125 | 0.0122 | 0.0119 | 0.0116 | 0.0113 | 0.0110 | –2.2 |
| –2.1 | 0.0179 | 0.0174 | 0.0170 | 0.0166 | 0.0162 | 0.0158 | 0.0154 | 0.0150 | 0.0146 | 0.0143 | –2.1 |
| –2.0 | 0.0228 | 0.0222 | 0.0217 | 0.0212 | 0.0207 | 0.0202 | 0.0197 | 0.0192 | 0.0188 | 0.0183 | –2.0 |
| –1.9 | 0.0287 | 0.0281 | 0.0274 | 0.0268 | 0.0262 | 0.0256 | 0.0250 | 0.0244 | 0.0239 | 0.0233 | –1.9 |
| –1.8 | 0.0359 | 0.0351 | 0.0344 | 0.0336 | 0.0329 | 0.0322 | 0.0314 | 0.0307 | 0.0301 | 0.0294 | –1.8 |
| –1.7 | 0.0446 | 0.0436 | 0.0427 | 0.0418 | 0.0409 | 0.0401 | 0.0392 | 0.0384 | 0.0375 | 0.0367 | –1.7 |
| –1.6 | 0.0548 | 0.0537 | 0.0526 | 0.0516 | 0.0505 | 0.0495 | 0.0485 | 0.0475 | 0.0465 | 0.0455 | –1.6 |
| –1.5 | 0.0668 | 0.0655 | 0.0643 | 0.0630 | 0.0618 | 0.0606 | 0.0594 | 0.0582 | 0.0571 | 0.0559 | –1.5 |
| –1.4 | 0.0808 | 0.0793 | 0.0778 | 0.0764 | 0.0749 | 0.0735 | 0.0721 | 0.0708 | 0.0694 | 0.0681 | –1.4 |
| –1.3 | 0.0968 | 0.0951 | 0.0934 | 0.0918 | 0.0901 | 0.0885 | 0.0869 | 0.0853 | 0.0838 | 0.0823 | –1.3 |
| –1.2 | 0.1151 | 0.1131 | 0.1112 | 0.1093 | 0.1075 | 0.1056 | 0.1038 | 0.1020 | 0.1003 | 0.0985 | –1.2 |
| –1.1 | 0.1357 | 0.1335 | 0.1314 | 0.1292 | 0.1271 | 0.1251 | 0.1230 | 0.1210 | 0.1190 | 0.1170 | –1.1 |
| –1.0 | 0.1587 | 0.1562 | 0.1539 | 0.1515 | 0.1492 | 0.1469 | 0.1446 | 0.1423 | 0.1401 | 0.1379 | –1.0 |
| –0.9 | 0.1841 | 0.1814 | 0.1788 | 0.1762 | 0.1736 | 0.1711 | 0.1685 | 0.1660 | 0.1635 | 0.1611 | –0.9 |
| –0.8 | 0.2119 | 0.2090 | 0.2061 | 0.2033 | 0.2005 | 0.1977 | 0.1949 | 0.1922 | 0.1894 | 0.1867 | –0.8 |
| –0.7 | 0.2420 | 0.2389 | 0.2358 | 0.2327 | 0.2296 | 0.2266 | 0.2236 | 0.2206 | 0.2177 | 0.2148 | –0.7 |
| –0.6 | 0.2743 | 0.2709 | 0.2676 | 0.2643 | 0.2611 | 0.2578 | 0.2546 | 0.2514 | 0.2483 | 0.2451 | –0.6 |
| –0.5 | 0.3085 | 0.3050 | 0.3015 | 0.2981 | 0.2946 | 0.2912 | 0.2877 | 0.2843 | 0.2810 | 0.2776 | –0.5 |
| –0.4 | 0.3446 | 0.3409 | 0.3372 | 0.3336 | 0.3300 | 0.3264 | 0.3228 | 0.3192 | 0.3156 | 0.3121 | –0.4 |
| –0.3 | 0.3821 | 0.3783 | 0.3745 | 0.3707 | 0.3669 | 0.3632 | 0.3594 | 0.3557 | 0.3520 | 0.3483 | –0.3 |
| –0.2 | 0.4207 | 0.4168 | 0.4129 | 0.4090 | 0.4052 | 0.4013 | 0.3974 | 0.3936 | 0.3897 | 0.3859 | –0.2 |
| –0.1 | 0.4602 | 0.4562 | 0.4522 | 0.4483 | 0.4443 | 0.4404 | 0.4364 | 0.4325 | 0.4286 | 0.4247 | –0.1 |
| –0.0 | 0.5000 | 0.4960 | 0.4920 | 0.4880 | 0.4840 | 0.4801 | 0.4761 | 0.4721 | 0.4681 | 0.4641 | –0.0 |
 |
| z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | z |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.0 | 0.5000 | 0.5040 | 0.5080 | 0.5120 | 0.5160 | 0.5199 | 0.5239 | 0.5279 | 0.5319 | 0.5359 | 0.0 |
| 0.1 | 0.5398 | 0.5438 | 0.5478 | 0.5517 | 0.5557 | 0.5596 | 0.5636 | 0.5675 | 0.5714 | 0.5753 | 0.1 |
| 0.2 | 0.5793 | 0.5832 | 0.5871 | 0.5910 | 0.5948 | 0.5987 | 0.6026 | 0.6064 | 0.6103 | 0.6141 | 0.2 |
| 0.3 | 0.6179 | 0.6217 | 0.6255 | 0.6293 | 0.6331 | 0.6368 | 0.6406 | 0.6443 | 0.6480 | 0.6517 | 0.3 |
| 0.4 | 0.6554 | 0.6591 | 0.6628 | 0.6664 | 0.6700 | 0.6736 | 0.6772 | 0.6808 | 0.6844 | 0.6879 | 0.4 |
| 0.5 | 0.6915 | 0.6950 | 0.6985 | 0.7019 | 0.7054 | 0.7088 | 0.7123 | 0.7157 | 0.7190 | 0.7224 | 0.5 |
| 0.6 | 0.7257 | 0.7291 | 0.7324 | 0.7357 | 0.7389 | 0.7422 | 0.7454 | 0.7486 | 0.7517 | 0.7549 | 0.6 |
| 0.7 | 0.7580 | 0.7611 | 0.7642 | 0.7673 | 0.7704 | 0.7734 | 0.7764 | 0.7794 | 0.7823 | 0.7852 | 0.7 |
| 0.8 | 0.7881 | 0.7910 | 0.7939 | 0.7967 | 0.7995 | 0.8023 | 0.8051 | 0.8078 | 0.8106 | 0.8133 | 0.8 |
| 0.9 | 0.8159 | 0.8186 | 0.8212 | 0.8238 | 0.8264 | 0.8289 | 0.8315 | 0.8340 | 0.8365 | 0.8389 | 0.9 |
| 1.0 | 0.8413 | 0.8438 | 0.8461 | 0.8485 | 0.8508 | 0.8531 | 0.8554 | 0.8577 | 0.8599 | 0.8621 | 1.0 |
| 1.1 | 0.8643 | 0.8665 | 0.8686 | 0.8708 | 0.8729 | 0.8749 | 0.8770 | 0.8790 | 0.8810 | 0.8830 | 1.1 |
| 1.2 | 0.8849 | 0.8869 | 0.8888 | 0.8907 | 0.8925 | 0.8944 | 0.8962 | 0.8980 | 0.8997 | 0.9015 | 1.2 |
| 1.3 | 0.9032 | 0.9049 | 0.9066 | 0.9082 | 0.9099 | 0.9115 | 0.9131 | 0.9147 | 0.9162 | 0.9177 | 1.3 |
| 1.4 | 0.9192 | 0.9207 | 0.9222 | 0.9236 | 0.9251 | 0.9265 | 0.9279 | 0.9292 | 0.9306 | 0.9319 | 1.4 |
| 1.5 | 0.9332 | 0.9345 | 0.9357 | 0.9370 | 0.9382 | 0.9394 | 0.9406 | 0.9418 | 0.9429 | 0.9441 | 1.5 |
| 1.6 | 0.9452 | 0.9463 | 0.9474 | 0.9484 | 0.9495 | 0.9505 | 0.9515 | 0.9525 | 0.9535 | 0.9545 | 1.6 |
| 1.7 | 0.9554 | 0.9564 | 0.9573 | 0.9582 | 0.9591 | 0.9599 | 0.9608 | 0.9616 | 0.9625 | 0.9633 | 1.7 |
| 1.8 | 0.9641 | 0.9649 | 0.9656 | 0.9664 | 0.9671 | 0.9678 | 0.9686 | 0.9693 | 0.9699 | 0.9706 | 1.8 |
| 1.9 | 0.9713 | 0.9719 | 0.9726 | 0.9732 | 0.9738 | 0.9744 | 0.9750 | 0.9756 | 0.9761 | 0.9767 | 1.9 |
| 2.0 | 0.9772 | 0.9778 | 0.9783 | 0.9788 | 0.9793 | 0.9798 | 0.9803 | 0.9808 | 0.9812 | 0.9817 | 2.0 |
| 2.1 | 0.9821 | 0.9826 | 0.9830 | 0.9834 | 0.9838 | 0.9842 | 0.9846 | 0.9850 | 0.9854 | 0.9857 | 2.1 |
| 2.2 | 0.9861 | 0.9864 | 0.9868 | 0.9871 | 0.9875 | 0.9878 | 0.9881 | 0.9884 | 0.9887 | 0.9890 | 2.2 |
| 2.3 | 0.9893 | 0.9896 | 0.9898 | 0.9901 | 0.9904 | 0.9906 | 0.9909 | 0.9911 | 0.9913 | 0.9916 | 2.3 |
| 2.4 | 0.9918 | 0.9920 | 0.9922 | 0.9925 | 0.9927 | 0.9929 | 0.9931 | 0.9932 | 0.9934 | 0.9936 | 2.4 |
| 2.5 | 0.9938 | 0.9940 | 0.9941 | 0.9943 | 0.9945 | 0.9946 | 0.9948 | 0.9949 | 0.9951 | 0.9952 | 2.5 |
| 2.6 | 0.9953 | 0.9955 | 0.9956 | 0.9957 | 0.9959 | 0.9960 | 0.9961 | 0.9962 | 0.9963 | 0.9964 | 2.6 |
| 2.7 | 0.9965 | 0.9966 | 0.9967 | 0.9968 | 0.9969 | 0.9970 | 0.9971 | 0.9972 | 0.9973 | 0.9974 | 2.7 |
| 2.8 | 0.9974 | 0.9975 | 0.9976 | 0.9977 | 0.9977 | 0.9978 | 0.9979 | 0.9979 | 0.9980 | 0.9981 | 2.8 |
| 2.9 | 0.9981 | 0.9982 | 0.9982 | 0.9983 | 0.9984 | 0.9984 | 0.9985 | 0.9985 | 0.9986 | 0.9986 | 2.9 |
| 3.0 | 0.9987 | 0.9987 | 0.9987 | 0.9988 | 0.9988 | 0.9989 | 0.9989 | 0.9989 | 0.9990 | 0.9990 | 3.0 |
| 3.1 | 0.9990 | 0.9991 | 0.9991 | 0.9991 | 0.9992 | 0.9992 | 0.9992 | 0.9992 | 0.9993 | 0.9993 | 3.1 |
| 3.2 | 0.9993 | 0.9993 | 0.9994 | 0.9994 | 0.9994 | 0.9994 | 0.9994 | 0.9995 | 0.9995 | 0.9995 | 3.2 |
| 3.3 | 0.9995 | 0.9995 | 0.9995 | 0.9996 | 0.9996 | 0.9996 | 0.9996 | 0.9996 | 0.9996 | 0.9997 | 3.3 |
| 3.4 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9997 | 0.9998 | 3.4 |
|
(Table entry is the point t* with given probability p lying above it.)  |
| df | p | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.25 | 0.20 | 0.15 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 | |
| 1 | 1.000 | 1.376 | 1.963 | 3.078 | 6.314 | 12.71 | 15.89 | 31.82 | 63.66 | 127.3 | 318.3 | 636.6 |
| 2 | 0.816 | 1.061 | 1.386 | 1.886 | 2.920 | 4.303 | 4.849 | 6.965 | 9.925 | 14.09 | 22.33 | 31.60 |
| 3 | 0.765 | 0.978 | 1.250 | 1.638 | 2.353 | 3.182 | 3.482 | 4.541 | 5.841 | 7.453 | 10.21 | 12.92 |
| 4 | 0.741 | 0.941 | 1.190 | 1.533 | 2.132 | 2.776 | 2.999 | 3.747 | 4.604 | 5.598 | 7.173 | 8.610 |
| 5 | 0.727 | 0.920 | 1.156 | 1.476 | 2.015 | 2.571 | 2.757 | 3.365 | 4.032 | 4.773 | 5.893 | 6.869 |
| 6 | 0.718 | 0.906 | 1.134 | 1.440 | 1.943 | 2.447 | 2.612 | 3.143 | 3.707 | 4.317 | 5.208 | 5.959 |
| 7 | 0.711 | 0.896 | 1.119 | 1.415 | 1.895 | 2.365 | 2.517 | 2.998 | 3.499 | 4.029 | 4.785 | 5.408 |
| 8 | 0.706 | 0.889 | 1.108 | 1.397 | 1.860 | 2.306 | 2.449 | 2.896 | 3.355 | 3.833 | 4.501 | 5.041 |
| 9 | 0.703 | 0.883 | 1.100 | 1.383 | 1.833 | 2.262 | 2.398 | 2.821 | 3.250 | 3.690 | 4.297 | 4.781 |
| 10 | 0.700 | 0.879 | 1.093 | 1.372 | 1.812 | 2.228 | 2.359 | 2.764 | 3.169 | 3.581 | 4.144 | 4.587 |
| 11 | 0.697 | 0.876 | 1.088 | 1.363 | 1.796 | 2.201 | 2.328 | 2.718 | 3.106 | 3.497 | 4.025 | 4.437 |
| 12 | 0.695 | 0.873 | 1.083 | 1.356 | 1.782 | 2.179 | 2.303 | 2.681 | 3.055 | 3.428 | 3.930 | 4.318 |
| 13 | 0.694 | 0.870 | 1.079 | 1.350 | 1.771 | 2.160 | 2.282 | 2.650 | 3.012 | 3.372 | 3.852 | 4.221 |
| 14 | 0.692 | 0.868 | 1.076 | 1.345 | 1.761 | 2.145 | 2.264 | 2.624 | 2.977 | 3.326 | 3.787 | 4.140 |
| 15 | 0.691 | 0.866 | 1.074 | 1.341 | 1.753 | 2.131 | 2.249 | 2.602 | 2.947 | 3.286 | 3.733 | 4.073 |
| 16 | 0.690 | 0.865 | 1.071 | 1.337 | 1.746 | 2.120 | 2.235 | 2.583 | 2.921 | 3.252 | 3.686 | 4.015 |
| 17 | 0.689 | 0.863 | 1.069 | 1.333 | 1.740 | 2.110 | 2.224 | 2.567 | 2.898 | 3.222 | 3.646 | 3.965 |
| 18 | 0.688 | 0.862 | 1.067 | 1.330 | 1.734 | 2.101 | 2.214 | 2.552 | 2.878 | 3.197 | 3.610 | 3.922 |
| 19 | 0.688 | 0.861 | 1.066 | 1.328 | 1.729 | 2.093 | 2.205 | 2.539 | 2.861 | 3.174 | 3.579 | 3.883 |
| 20 | 0.687 | 0.860 | 1.064 | 1.325 | 1.725 | 2.086 | 2.197 | 2.528 | 2.845 | 3.153 | 3.552 | 3.850 |
| 21 | 0.686 | 0.859 | 1.063 | 1.323 | 1.721 | 2.080 | 2.189 | 2.518 | 2.831 | 3.135 | 3.527 | 3.819 |
| 22 | 0.686 | 0.858 | 1.061 | 1.321 | 1.717 | 2.074 | 2.183 | 2.508 | 2.819 | 3.119 | 3.505 | 3.792 |
| 23 | 0.685 | 0.858 | 1.060 | 1.319 | 1.714 | 2.069 | 2.177 | 2.500 | 2.807 | 3.104 | 3.485 | 3.768 |
| 24 | 0.685 | 0.857 | 1.059 | 1.318 | 1.711 | 2.064 | 2.172 | 2.492 | 2.797 | 3.091 | 3.467 | 3.745 |
| 25 | 0.684 | 0.856 | 1.058 | 1.316 | 1.708 | 2.060 | 2.167 | 2.485 | 2.787 | 3.078 | 3.450 | 3.725 |
| 26 | 0.684 | 0.856 | 1.058 | 1.315 | 1.706 | 2.056 | 2.162 | 2.479 | 2.779 | 3.067 | 3.435 | 3.707 |
| 27 | 0.684 | 0.855 | 1.057 | 1.314 | 1.703 | 2.052 | 2.158 | 2.473 | 2.771 | 3.057 | 3.421 | 3.690 |
| 28 | 0.683 | 0.855 | 1.056 | 1.313 | 1.701 | 2.048 | 2.154 | 2.467 | 2.763 | 3.047 | 3.408 | 3.674 |
| 29 | 0.683 | 0.854 | 1.055 | 1.311 | 1.699 | 2.045 | 2.150 | 2.462 | 2.756 | 3.038 | 3.396 | 3.659 |
| 30 | 0.683 | 0.854 | 1.055 | 1.310 | 1.697 | 2.042 | 2.147 | 2.457 | 2.750 | 3.030 | 3.385 | 3.646 |
| 40 | 0.681 | 0.851 | 1.050 | 1.303 | 1.684 | 2.021 | 2.123 | 2.423 | 2.704 | 2.971 | 3.307 | 3.551 |
| 50 | 0.679 | 0.849 | 1.047 | 1.299 | 1.676 | 2.009 | 2.109 | 2.403 | 2.678 | 2.937 | 3.261 | 3.496 |
| 60 | 0.679 | 0.848 | 1.045 | 1.296 | 1.671 | 2.000 | 2.099 | 2.390 | 2.660 | 2.915 | 3.232 | 3.460 |
| 80 | 0.678 | 0.846 | 1.043 | 1.292 | 1.664 | 1.990 | 2.088 | 2.374 | 2.639 | 2.887 | 3.195 | 3.416 |
| 100 | 0.677 | 0.845 | 1.042 | 1.290 | 1.660 | 1.984 | 2.081 | 2.364 | 2.626 | 2.871 | 3.174 | 3.390 |
| 1000 | 0.675 | 0.842 | 1.037 | 1.282 | 1.646 | 1.962 | 2.056 | 2.330 | 2.581 | 2.813 | 3.098 | 3.300 |
| ∞ | 0.674 | 0.841 | 1.036 | 1.282 | 1.645 | 1.960 | 2.054 | 2.326 | 2.576 | 2.807 | 3.091 | 3.291 |
|
(Table entry is the point χ2 with given probability p lying above it.)  |
| df | p | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.25 | 0.20 | 0.15 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 | |
| 1 | 1.32 | 1.64 | 2.07 | 2.71 | 3.84 | 5.02 | 5.41 | 6.63 | 7.88 | 9.14 | 10.83 | 12.12 |
| 2 | 2.77 | 3.22 | 3.79 | 4.61 | 5.99 | 7.38 | 7.82 | 9.21 | 10.60 | 11.98 | 13.82 | 15.20 |
| 3 | 4.11 | 4.64 | 5.32 | 6.25 | 7.81 | 9.35 | 9.84 | 11.34 | 12.84 | 14.32 | 16.27 | 17.73 |
| 4 | 5.39 | 5.99 | 6.74 | 7.78 | 9.49 | 11.14 | 11.67 | 13.28 | 14.86 | 16.42 | 18.47 | 20.00 |
| 5 | 6.63 | 7.29 | 8.12 | 9.24 | 11.07 | 12.83 | 13.39 | 15.09 | 16.75 | 18.39 | 20.52 | 22.11 |
| 6 | 7.84 | 8.56 | 9.45 | 10.64 | 12.59 | 14.45 | 15.03 | 16.81 | 18.55 | 20.25 | 22.46 | 24.10 |
| 7 | 9.04 | 9.80 | 10.75 | 12.02 | 14.07 | 16.01 | 16.62 | 18.48 | 20.28 | 22.04 | 24.32 | 26.02 |
| 8 | 10.22 | 11.03 | 12.03 | 13.36 | 15.51 | 17.53 | 18.17 | 20.09 | 21.95 | 23.77 | 26.12 | 27.87 |
| 9 | 11.39 | 12.24 | 13.29 | 14.68 | 16.92 | 19.02 | 19.68 | 21.67 | 23.59 | 25.46 | 27.88 | 29.67 |
| 10 | 12.55 | 13.44 | 14.53 | 15.99 | 18.31 | 20.48 | 21.16 | 23.21 | 25.19 | 27.11 | 29.59 | 31.42 |
| 11 | 13.70 | 14.63 | 15.77 | 17.28 | 19.68 | 21.92 | 22.62 | 24.72 | 26.76 | 28.73 | 31.26 | 33.14 |
| 12 | 14.85 | 15.81 | 16.99 | 18.55 | 21.03 | 23.34 | 24.05 | 26.22 | 28.30 | 30.32 | 32.91 | 34.82 |
| 13 | 15.98 | 16.98 | 18.20 | 19.81 | 22.36 | 24.74 | 25.47 | 27.69 | 29.82 | 31.88 | 34.53 | 36.48 |
| 14 | 17.12 | 18.15 | 19.41 | 21.06 | 23.68 | 26.12 | 26.87 | 29.14 | 31.32 | 33.43 | 36.12 | 38.11 |
| 15 | 18.25 | 19.31 | 20.60 | 22.31 | 25.00 | 27.49 | 28.26 | 30.58 | 32.80 | 34.95 | 37.70 | 39.72 |
| 16 | 19.37 | 20.47 | 21.79 | 23.54 | 26.30 | 28.85 | 29.63 | 32.00 | 34.27 | 36.46 | 39.25 | 41.31 |
| 17 | 20.49 | 21.61 | 22.98 | 24.77 | 27.59 | 30.19 | 31.00 | 33.41 | 35.72 | 37.95 | 40.79 | 42.88 |
| 18 | 21.60 | 22.76 | 24.16 | 25.99 | 28.87 | 31.53 | 32.35 | 34.81 | 37.16 | 39.42 | 42.31 | 44.43 |
| 19 | 22.72 | 23.90 | 25.33 | 27.20 | 30.14 | 32.85 | 33.69 | 36.19 | 38.58 | 40.88 | 43.82 | 45.97 |
| 20 | 23.83 | 25.04 | 26.50 | 28.41 | 31.41 | 34.17 | 35.02 | 37.57 | 40.00 | 42.34 | 45.31 | 47.50 |
| 21 | 24.93 | 26.17 | 27.66 | 29.62 | 32.67 | 35.48 | 36.34 | 38.93 | 41.40 | 43.78 | 46.80 | 49.01 |
| 22 | 26.04 | 27.30 | 28.82 | 30.81 | 33.92 | 36.78 | 37.66 | 40.29 | 42.80 | 45.20 | 48.27 | 50.51 |
| 23 | 27.14 | 28.43 | 29.98 | 32.01 | 35.17 | 38.08 | 38.97 | 41.64 | 44.18 | 46.62 | 49.73 | 52.00 |
| 24 | 28.24 | 29.55 | 31.13 | 33.20 | 36.42 | 39.36 | 40.27 | 42.98 | 45.56 | 48.03 | 51.18 | 53.48 |
| 25 | 29.34 | 30.68 | 32.28 | 34.38 | 37.65 | 40.65 | 41.57 | 44.31 | 46.93 | 49.44 | 52.62 | 54.95 |
| 26 | 30.43 | 31.79 | 33.43 | 35.56 | 38.89 | 41.92 | 42.86 | 45.64 | 48.29 | 50.83 | 54.05 | 56.41 |
| 27 | 31.53 | 32.91 | 34.57 | 36.74 | 40.11 | 43.19 | 44.14 | 46.96 | 49.64 | 52.22 | 55.48 | 57.86 |
| 28 | 32.62 | 34.03 | 35.71 | 37.92 | 41.34 | 44.46 | 45.42 | 48.28 | 50.99 | 53.59 | 56.89 | 59.30 |
| 29 | 33.71 | 35.14 | 36.85 | 39.09 | 42.56 | 45.72 | 46.69 | 49.59 | 52.34 | 54.97 | 58.30 | 60.73 |
| 30 | 34.80 | 36.25 | 37.99 | 40.26 | 43.77 | 46.98 | 47.96 | 50.89 | 53.67 | 56.33 | 59.70 | 62.16 |
| 40 | 45.62 | 47.27 | 49.24 | 51.81 | 55.76 | 59.34 | 60.44 | 63.69 | 66.77 | 69.70 | 73.40 | 76.09 |
| 50 | 56.33 | 58.16 | 60.35 | 63.17 | 67.50 | 71.42 | 72.61 | 76.15 | 79.49 | 82.66 | 86.66 | 89.56 |
| 60 | 66.98 | 68.97 | 71.34 | 74.40 | 79.08 | 83.30 | 84.58 | 88.38 | 91.95 | 95.34 | 99.61 | 102.7 |
| 80 | 88.13 | 90.41 | 93.11 | 96.58 | 101.9 | 106.6 | 108.1 | 112.3 | 116.3 | 120.1 | 124.8 | 128.3 |
| 100 | 109.1 | 111.7 | 114.7 | 118.5 | 124.3 | 129.6 | 131.1 | 135.8 | 140.2 | 144.3 | 149.4 | 153.2 |
