252:
depend on the number of samples, this seven-number summary does not, and is somewhat more stable, since its whisker-ends are protected from the usual wild swings in the extreme values of the sample by replacing them with the more steady 2nd and 98th percentiles.
605:
Note that the middle five of the seven numbers can all be obtained by successive partitioning of the ordered data into subsets of equal size. Extending the seven-number summary by continued partitioning produces the
245:, so the plotted values provide a convenient visual check for validity of later tests, simply by scanning to see if the marks for those seven percentiles appear to be equal distances apart on the graph.
260:. The 2nd and 98th percentiles are represented by the ends of the whiskers, and hatch-marks across the whiskers mark the 9th and 91st percentiles.
237:
The two unusual percentiles at either end are used because the locations of all seven values will be approximately equally spaced if the data is
647:
The seven equally spaced percentiles with three digits of precision are 2.15%, 8.87%, 25.0%, 50.0%, 75.0%, 91.13%, and 97.85%.
434:, which for a normal distribution can be scaled to give a reasonably efficient estimate of standard deviation, and the 10%
427:
Note that the middle five of the seven numbers are very nearly the same as for the seven number summary, above.
731:
272:
711:
623:
17:
681:
705:
8:
249:
242:
238:
227:
62:
52:
29:
25:
675:
431:
686:
the seven positions are the maximum and minimum, median, quartiles, and two deciles
594:
498:
416:
320:
725:
671:
268:
39:, adding hatch-marks on the "whiskers" for two of the additional numbers.
581:
513:
454:
701:
481:
450:
435:
303:
83:
76:
48:
35:
As with the five-number summary, it can be represented by a modified
563:
549:
526:
458:
439:
385:
371:
348:
280:
257:
231:
223:
215:
172:
154:
130:
36:
628:
543:
403:
365:
335:
276:
219:
150:
275:, called a "seven-figure summary", including the extremes,
438:, which when compared to the median gives an idea of the
453:
used a seven-number summary consisting of the extremes,
430:
The addition of the deciles allow one to compute the
723:
263:
445:
256:The values can be represented using a modified
248:Notice that whereas the extreme values of the
666:
664:
230:and are the standard values for the box in a
696:
694:
661:
226:– are the usual statistics from the
51:are (approximately) evenly spaced under a
691:
32:. There are three similar, common forms.
597:(nominal: lowest hundredth percentile)
419:(nominal: lowest hundredth percentile)
42:
724:
670:
501:(nominal: highest zero-th percentile)
323:(nominal: highest zero-th percentile)
700:
214:The middle three values – the
13:
14:
743:
677:Elementary Manual of Statistics
241:Some statistical tests require
641:
293:Bowley’s seven summary figures
192:upper whisker crosshatch mark
116:lower whisker crosshatch mark
1:
654:
471:Tukey’s seven summary figures
264:Bowley’s seven-figure summary
28:, and is an extension of the
634:
446:Tukey’s seven-number summary
7:
617:
10:
748:
283:, along with the median.
81: More precise
707:Exploratory Data Analysis
273:non-parametric statistics
243:normally distributed data
102:lower whisker bottom end
74: Approximate
24:is a collection of seven
680:(3rd ed.). p.
464:The seven numbers are:
624:Three-point estimation
286:Thus the numbers are:
206:upper whisker top end
18:descriptive statistics
612:eleven-number summary
65:seven summary numbers
239:normally distributed
53:normally distributed
43:Seven-number summary
22:seven-number summary
608:nine-number summary
546:, middle value, or
473:
368:, middle value, or
295:
250:five-number summary
228:five-number summary
153:, middle value, or
67:
63:Normal distribution
30:five-number summary
732:Summary statistics
487:Alternate name(s)
469:
461:, and the median.
309:Alternate name(s)
291:
88:Alternate name(s)
60:
26:summary statistics
601:
600:
432:interdecile range
423:
422:
210:
209:
739:
716:
715:
698:
689:
688:
668:
648:
645:
474:
472:
468:
296:
294:
290:
68:
66:
59:
747:
746:
742:
741:
740:
738:
737:
736:
722:
721:
720:
719:
699:
692:
669:
662:
657:
652:
651:
646:
642:
637:
620:
470:
448:
292:
266:
156:second quartile
82:
75:
61:
45:
12:
11:
5:
745:
735:
734:
718:
717:
690:
659:
658:
656:
653:
650:
649:
639:
638:
636:
633:
632:
631:
626:
619:
616:
603:
602:
599:
598:
595:sample maximum
592:
589:
585:
584:
578:
575:
571:
570:
568:third quartile
564:upper quartile
561:
558:
554:
553:
541:
538:
534:
533:
531:first quartile
527:lower quartile
524:
521:
517:
516:
510:
507:
503:
502:
499:sample minimum
496:
493:
489:
488:
485:
478:
447:
444:
442:in the tails.
425:
424:
421:
420:
417:sample maximum
414:
411:
407:
406:
400:
397:
393:
392:
390:third quartile
386:upper quartile
383:
380:
376:
375:
363:
360:
356:
355:
353:first quartile
349:lower quartile
346:
343:
339:
338:
332:
329:
325:
324:
321:sample minimum
318:
315:
311:
310:
307:
300:
271:used a set of
265:
262:
224:upper quartile
216:lower quartile
212:
211:
208:
207:
204:
201:
198:
194:
193:
190:
187:
184:
180:
179:
177:third quartile
173:upper quartile
170:
167:
164:
160:
159:
148:
145:
142:
138:
137:
135:first quartile
131:lower quartile
128:
125:
122:
118:
117:
114:
111:
108:
104:
103:
100:
97:
94:
90:
89:
86:
79:
72:
47:The following
44:
41:
9:
6:
4:
3:
2:
744:
733:
730:
729:
727:
713:
709:
708:
703:
697:
695:
687:
683:
679:
678:
673:
667:
665:
660:
644:
640:
630:
627:
625:
622:
621:
615:
614:, and so on.
613:
609:
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586:
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579:
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569:
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428:
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367:
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308:
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278:
274:
270:
269:Arthur Bowley
261:
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120:
119:
115:
112:
109:
106:
105:
101:
98:
95:
92:
91:
87:
85:
80:
78:
73:
70:
69:
64:
58:
57:
56:
54:
50:
40:
38:
33:
31:
27:
23:
19:
706:
685:
676:
643:
611:
607:
604:
567:
547:
530:
463:
449:
429:
426:
389:
369:
352:
285:
267:
255:
247:
236:
213:
176:
155:
134:
46:
34:
21:
15:
113: 8.87%
99: 2.15%
49:percentiles
710:. p.
672:Bowley, A.
655:References
482:Percentile
451:John Tukey
436:midsummary
304:Percentile
84:percentile
77:percentile
55:variable:
702:Tukey, J.
635:Footnotes
459:quartiles
281:quartiles
110: 9th
96: 2nd
726:Category
704:(1977).
674:(1920).
618:See also
550:quartile
440:skewness
372:quartile
258:box plot
232:box plot
37:box plot
629:Stanine
548:second
484:
480:
455:octiles
370:second
306:
302:
277:deciles
610:, the
582:octile
544:median
514:octile
512:first
404:decile
366:median
336:decile
334:first
279:, and
222:, and
220:median
203:97.85%
189:91.13%
169:75.00%
151:median
147:50.00%
127:25.00%
20:, the
580:last
577:87.5%
560:75.0%
540:50.0%
523:25.0%
509:12.5%
402:last
591:100%
413:100%
200:98th
186:91st
166:75th
144:50th
124:25th
566:or
529:or
477:Nr.
399:90%
388:or
382:75%
362:50%
351:or
345:25%
331:10%
299:Nr.
175:or
133:or
71:Nr.
16:In
728::
712:53
693:^
684:.
682:62
663:^
588:#7
574:#6
557:#5
537:#4
520:#3
506:#2
495:0%
492:#1
457:,
410:#7
396:#6
379:#5
359:#4
342:#3
328:#2
317:0%
314:#1
234:.
218:,
197:#7
183:#6
163:#5
141:#4
121:#3
107:#2
93:#1
714:.
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