245:
550:
53:
417:
409:
308:
350:
325:
in the late 1970s, and "midhinge" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the
240:{\displaystyle \operatorname {MH} (X)={\overline {Q_{1,3}(X)}}={\frac {Q_{1}(X)+Q_{3}(X)}{2}}={\frac {P_{25}(X)+P_{75}(X)}{2}}=M_{25}(X)}
633:
594:
545:{\displaystyle \operatorname {MH} (X)=2\operatorname {TM} (X)-\operatorname {med} (X)=2{\frac {Q_{1}+2Q_{2}+Q_{3}}{4}}-Q_{2}}
314:. The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles.
322:
359:
311:
261:
251:
561:
29:
590:
33:
332:
628:
622:
566:
44:
318:
40:
17:
609:
613:
36:
317:
The use of the term "hinge" for the lower or upper quartiles derives from
255:
25:
326:
352:), which originated in the same context and equals the average of the
353:
420:
362:
335:
264:
56:
544:
403:
344:
302:
239:
254:(IQR), the difference of the third and first
8:
536:
517:
504:
488:
481:
419:
404:{\displaystyle {\tilde {X}}=Q_{2}=P_{50}}
395:
382:
364:
363:
361:
334:
294:
281:
263:
222:
194:
172:
165:
141:
119:
112:
82:
75:
55:
578:
24:is the average of the first and third
7:
14:
303:{\displaystyle IQR=Q_{3}-Q_{1}}
250:The midhinge is related to the
472:
466:
454:
448:
433:
427:
369:
234:
228:
206:
200:
184:
178:
153:
147:
131:
125:
100:
94:
69:
63:
32:. Equivalently, it is the 25%
1:
104:
650:
634:Exploratory data analysis
587:Exploratory Data Analysis
323:exploratory data analysis
310:), which is a measure of
28:and is thus a measure of
546:
405:
346:
312:statistical dispersion
304:
241:
547:
406:
347:
305:
242:
585:Tukey, J. W. (1977)
418:
411:) and the midhinge.
360:
333:
262:
54:
252:interquartile range
589:, Addison-Wesley.
562:Interquartile mean
542:
401:
345:{\displaystyle TM}
342:
300:
237:
527:
372:
213:
160:
107:
641:
597:
583:
551:
549:
548:
543:
541:
540:
528:
523:
522:
521:
509:
508:
493:
492:
482:
410:
408:
407:
402:
400:
399:
387:
386:
374:
373:
365:
351:
349:
348:
343:
309:
307:
306:
301:
299:
298:
286:
285:
246:
244:
243:
238:
227:
226:
214:
209:
199:
198:
177:
176:
166:
161:
156:
146:
145:
124:
123:
113:
108:
103:
93:
92:
76:
649:
648:
644:
643:
642:
640:
639:
638:
619:
618:
606:
601:
600:
584:
580:
575:
558:
532:
513:
500:
484:
483:
416:
415:
391:
378:
358:
357:
331:
330:
290:
277:
260:
259:
218:
190:
168:
167:
137:
115:
114:
78:
77:
52:
51:
12:
11:
5:
647:
645:
637:
636:
631:
621:
620:
617:
616:
605:
604:External links
602:
599:
598:
577:
576:
574:
571:
570:
569:
564:
557:
554:
553:
552:
539:
535:
531:
526:
520:
516:
512:
507:
503:
499:
496:
491:
487:
480:
477:
474:
471:
468:
465:
462:
459:
456:
453:
450:
447:
444:
441:
438:
435:
432:
429:
426:
423:
398:
394:
390:
385:
381:
377:
371:
368:
341:
338:
297:
293:
289:
284:
280:
276:
273:
270:
267:
248:
247:
236:
233:
230:
225:
221:
217:
212:
208:
205:
202:
197:
193:
189:
186:
183:
180:
175:
171:
164:
159:
155:
152:
149:
144:
140:
136:
133:
130:
127:
122:
118:
111:
106:
102:
99:
96:
91:
88:
85:
81:
74:
71:
68:
65:
62:
59:
13:
10:
9:
6:
4:
3:
2:
646:
635:
632:
630:
627:
626:
624:
615:
611:
608:
607:
603:
596:
595:0-201-07616-0
592:
588:
582:
579:
572:
568:
565:
563:
560:
559:
555:
537:
533:
529:
524:
518:
514:
510:
505:
501:
497:
494:
489:
485:
478:
475:
469:
463:
460:
457:
451:
445:
442:
439:
436:
430:
424:
421:
414:
413:
412:
396:
392:
388:
383:
379:
375:
366:
355:
339:
336:
328:
324:
320:
315:
313:
295:
291:
287:
282:
278:
274:
271:
268:
265:
257:
253:
231:
223:
219:
215:
210:
203:
195:
191:
187:
181:
173:
169:
162:
157:
150:
142:
138:
134:
128:
120:
116:
109:
97:
89:
86:
83:
79:
72:
66:
60:
57:
50:
49:
48:
46:
42:
38:
35:
31:
27:
23:
19:
586:
581:
316:
249:
21:
15:
567:L-estimator
321:'s work on
45:L-estimator
43:; it is an
623:Categories
573:References
319:John Tukey
41:midsummary
18:statistics
614:MathWorld
530:−
464:
458:−
446:
425:
370:~
288:−
256:quartiles
105:¯
61:
37:mid-range
26:quartiles
610:H-spread
556:See also
30:location
22:midhinge
327:trimean
39:or 25%
34:trimmed
593:
354:median
258:(i.e.
20:, the
629:Means
591:ISBN
612:at
461:med
16:In
625::
443:TM
422:MH
397:50
224:25
196:75
174:25
58:MH
47:.
538:2
534:Q
525:4
519:3
515:Q
511:+
506:2
502:Q
498:2
495:+
490:1
486:Q
479:2
476:=
473:)
470:X
467:(
455:)
452:X
449:(
440:2
437:=
434:)
431:X
428:(
393:P
389:=
384:2
380:Q
376:=
367:X
356:(
340:M
337:T
329:(
296:1
292:Q
283:3
279:Q
275:=
272:R
269:Q
266:I
235:)
232:X
229:(
220:M
216:=
211:2
207:)
204:X
201:(
192:P
188:+
185:)
182:X
179:(
170:P
163:=
158:2
154:)
151:X
148:(
143:3
139:Q
135:+
132:)
129:X
126:(
121:1
117:Q
110:=
101:)
98:X
95:(
90:3
87:,
84:1
80:Q
73:=
70:)
67:X
64:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.