3658:
1040:
3644:
27:
3682:
3670:
1362:
1026:
is not normally distributed. However, a normal distribution can be trivially perturbed to maintain its Q1 and Q2 std. scores at 0.67 and â0.67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as
464:+âââââ+â+ * |âââââââââââ| | |âââââââââââ| +âââââ+â+ +âââ+âââ+âââ+âââ+âââ+âââ+âââ+âââ+âââ+âââ+âââ+âââ+ Number line 0 1 2 3 4 5 6 7 8 9 10 11 12
1017:
946:
1054:
in data. Outliers here are defined as observations that fall below Q1 â 1.5 IQR or above Q3 + 1.5 IQR. In a boxplot, the highest and lowest occurring value within this limit are indicated by
712:
652:
542:
Pattern of latter two bullet points: If there are no data points at the true quartiles, use data points slightly "inland" (closer to the median) from the actual quartiles.
866:
107:(also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR =
2779:
3284:
1046:
with four mild outliers and one extreme outlier. In this chart, outliers are defined as mild above Q3 + 1.5 IQR and extreme above Q3 + 3 IQR.
3434:
546:
This means the 1.5*IQR whiskers can be uneven in lengths. The median, minimum, maximum, and the first and third quartile constitute the
3058:
1699:
2832:
3271:
1239:
1209:
1136:
1694:
1394:
1366:
134:, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. It is also used as a
2298:
1446:
1153:
957:
886:
3081:
2973:
1187:
1163:
660:
600:
3686:
3259:
3133:
563:
3317:
2978:
2723:
2094:
1684:
1058:
of the box (frequently with an additional bar at the end of the whisker) and any outliers as individual points.
3368:
2580:
2387:
2276:
2234:
1324:
2308:
3611:
2570:
1473:
3162:
3111:
3096:
3086:
2955:
2827:
2794:
2620:
2575:
2405:
559:
34:
3674:
3506:
3307:
3231:
2532:
2286:
1955:
1419:
3391:
3363:
3358:
3106:
2865:
2771:
2751:
2659:
2370:
2188:
1671:
1543:
1022:
If the actual values of the first or third quartiles differ substantially from the calculated values,
3708:
3123:
2891:
2612:
2537:
2466:
2395:
2315:
2303:
2173:
2161:
2154:
1862:
1583:
184:
3606:
3373:
3236:
2921:
2886:
2850:
2635:
2077:
1986:
1945:
1857:
1548:
1387:
1313:
Beta mathematics handbook : concepts, theorems, methods, algorithms, formulas, graphs, tables
1087:
224:
The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q
166:
135:
3515:
3128:
3068:
3005:
2643:
2627:
2365:
2227:
2217:
2067:
1981:
1292:
539:+ 1.5 * IQR = 9 + 3 = 12. (If there is no data point at 12, then the highest point less than 12.)
1117:
Dekking, Frederik Michel; Kraaikamp, Cornelis; LopuhaÀ, Hen Paul; Meester, Ludolf Erwin (2005).
842:
529:- 1.5 * IQR = 7 - 3 = 4. (If there is no data point at 4, then the lowest point greater than 4.)
3553:
3483:
3276:
3213:
2968:
2855:
1852:
1749:
1656:
1535:
1434:
1264:
58:
46:
3578:
3520:
3463:
3289:
3182:
3091:
2817:
2701:
2560:
2552:
2442:
2434:
2249:
2145:
2123:
2082:
2047:
2014:
1960:
1935:
1890:
1829:
1789:
1591:
1414:
85:, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q
3501:
3076:
3025:
3001:
2963:
2881:
2860:
2812:
2691:
2669:
2638:
2547:
2424:
2375:
2293:
2266:
2222:
2178:
1940:
1716:
1596:
1043:
754:
20:
558:
The interquartile range of a continuous distribution can be calculated by integrating the
8:
3648:
3573:
3496:
3177:
2941:
2934:
2896:
2804:
2784:
2756:
2489:
2355:
2350:
2340:
2332:
2150:
2111:
2001:
1991:
1900:
1679:
1635:
1478:
1380:
810:
774:
741:
547:
3662:
3473:
3327:
3223:
3172:
3048:
2945:
2929:
2906:
2683:
2417:
2400:
2360:
2271:
2166:
2128:
2099:
2059:
2019:
1965:
1882:
1568:
1563:
1286:
798:
151:
131:
294:
The following table has 13 rows, and follows the rules for the odd number of entries.
3657:
3568:
3538:
3530:
3350:
3341:
3266:
3197:
3053:
3038:
3013:
2901:
2842:
2708:
2696:
2322:
2239:
2183:
2106:
1950:
1872:
1651:
1525:
1330:
1320:
1316:
1245:
1235:
1205:
1183:
1159:
1132:
1067:
718:
127:
1039:
3593:
3548:
3312:
3299:
3192:
3167:
3101:
3033:
2911:
2519:
2412:
2345:
2258:
2205:
2024:
1895:
1689:
1573:
1488:
1455:
1124:
195:
3510:
3254:
3116:
3043:
2718:
2592:
2565:
2542:
2511:
2138:
2133:
2087:
1817:
1468:
1118:
155:
3000:
724:
The interquartile range and median of some common distributions are shown below
3459:
3454:
1917:
1847:
1493:
1082:
818:
216:
The quartile deviation or semi-interquartile range is defined as half the IQR.
3702:
3616:
3583:
3446:
3407:
3218:
3187:
2651:
2605:
2210:
1912:
1739:
1503:
1498:
1249:
566:âany other means of calculating the CDF will also work). The lower quartile,
1334:
3558:
3491:
3468:
3383:
2713:
2009:
1907:
1842:
1784:
1769:
1706:
1661:
1028:
594:
equals 0.75; in terms of the CDF, the quartiles can be defined as follows:
1229:
1128:
3601:
3563:
3246:
3147:
3009:
2822:
2789:
2281:
2198:
2193:
1837:
1794:
1774:
1754:
1744:
1513:
788:
183:, the average of the first and third quartiles), half the IQR equals the
78:
2447:
1927:
1627:
1558:
1508:
1483:
1403:
2600:
2452:
2072:
1867:
1779:
1764:
1759:
1724:
2116:
1734:
1611:
1606:
1601:
1073:
468:
210:
180:
162:
139:
82:
61:, which is the spread of the data. The IQR may also be called the
3621:
3322:
1051:
202:
30:
26:
81:
of the data. To calculate the IQR, the data set is divided into
3543:
2524:
2498:
2478:
1729:
1520:
1361:
1263:
Rousseeuw, Peter J.; Croux, Christophe (1992). Y. Dodge (ed.).
191:
173:
97:
1116:
1372:
448:
For the data in this table the interquartile range is IQR = Q
1463:
1180:
CRC Standard
Probability and Statistics Tables and Formulae
1090: â Statistical indicators of the deviation of a sample
794:
828:, is â0.67, and the standard score of the third quartile,
179:
For a symmetric distribution (where the median equals the
77:
It is defined as the difference between the 75th and 25th
1123:. Springer Texts in Statistics. London: Springer London.
573:, is a number such that integral of the PDF from -â to
158:
of 25% and is thus often preferred to the total range.
1347:
Dekking, Kraaikamp, LopuhaĂ€ & Meester, pp. 235â237
789:
Interquartile range test for normality of distribution
1265:"Explicit Scale Estimators with High Breakdown Point"
960:
889:
845:
663:
603:
3285:
Autoregressive conditional heteroskedasticity (ARCH)
1078:
Pages displaying wikidata descriptions as a fallback
459:
172:
The IQR is used in businesses as a marker for their
1120:
232:. Each quartile is a median calculated as follows.
2747:
1011:
940:
860:
706:
646:
1012:{\displaystyle Q_{3}=(\sigma \,z_{3})+{\bar {P}}}
941:{\displaystyle Q_{1}=(\sigma \,z_{1})+{\bar {P}}}
3700:
1076: â average of the first and third quartiles
587:, is such a number that the integral from -â to
2833:Multivariate adaptive regression splines (MARS)
805:can be used in a simple test of whether or not
1262:
1204:. Burlington, MA: Elsevier. pp. 103â104.
1050:The interquartile range is often used to find
707:{\displaystyle Q_{3}={\text{CDF}}^{-1}(0.75),}
647:{\displaystyle Q_{1}={\text{CDF}}^{-1}(0.25),}
1388:
138:It can be clearly visualized by the box on a
880:is normally distributed, the first quartile
1288:An Introduction to the Theory of Statistics
1274:. Amsterdam: North-Holland. pp. 77â92.
1272:L1-Statistical Analysis and Related Methods
1433:
1395:
1381:
1227:
19:"IQR" redirects here. For other uses, see
2046:
1151:
980:
909:
402:(median of upper half, from row 8 to 13)
1291:. Charles Griffin and Company. pp.
1038:
335:(median of lower half, from row 1 to 6)
165:, simple graphical representations of a
25:
1310:
1158:. Oxford University Press. p. 55.
580:equals 0.25, while the upper quartile,
3701:
3359:KaplanâMeier estimator (product limit)
289:
3432:
2999:
2746:
2045:
1815:
1432:
1376:
3669:
3369:Accelerated failure time (AFT) model
1306:
1304:
1302:
1284:
1223:
1221:
1199:
1145:
1112:
1110:
1108:
1106:
1104:
281:is the same as the ordinary median.
33:(with an interquartile range) and a
3681:
2964:Analysis of variance (ANOVA, anova)
1816:
1278:
1178:Zwillinger, D., Kokoska, S. (2000)
13:
3059:CochranâMantelâHaenszel statistics
1685:Pearson product-moment correlation
817:is normally distributed, then the
89:(also called the lower quartile),
14:
3720:
1354:
1299:
1228:Kaltenbach, Hans-Michael (2012).
1218:
1172:
1152:Upton, Graham; Cook, Ian (1996).
1101:
460:Data set in a plain-text box plot
209:). The IQR also may indicate the
16:Measure of statistical dispersion
3680:
3668:
3656:
3643:
3642:
3433:
1360:
564:cumulative distribution function
553:
201:The IQR can be used to identify
194:is the corresponding measure of
154:, the interquartile range has a
3318:Least-squares spectral analysis
749:2 Ί(0.75)Ï â 1.349Ï â (27/20)Ï
2299:Mean-unbiased minimum-variance
1402:
1341:
1256:
1193:
1003:
991:
974:
932:
920:
903:
852:
698:
692:
638:
632:
1:
3612:Geographic information system
2828:Simultaneous equations models
1231:A concise guide to statistics
1094:
206:
130:, defined as the 25% trimmed
2795:Coefficient of determination
2406:Uniformly most powerful test
1311:Bertil., Westergren (1988).
560:probability density function
219:
35:probability density function
7:
3364:Proportional hazards models
3308:Spectral density estimation
3290:Vector autoregression (VAR)
2724:Maximum posterior estimator
1956:Randomized controlled trial
1070: â Statistical measure
1061:
1034:
505:Interquartile range, IQR =
284:
126:The IQR is an example of a
10:
3725:
3124:Multivariate distributions
1544:Average absolute deviation
861:{\displaystyle {\bar {P}}}
319:
302:
299:
18:
3638:
3592:
3529:
3482:
3445:
3441:
3428:
3400:
3382:
3349:
3340:
3298:
3245:
3206:
3155:
3146:
3112:Structural equation model
3067:
3024:
3020:
2995:
2954:
2920:
2874:
2841:
2803:
2770:
2766:
2742:
2682:
2591:
2510:
2474:
2465:
2448:Score/Lagrange multiplier
2433:
2386:
2331:
2257:
2248:
2058:
2054:
2041:
2000:
1974:
1926:
1881:
1863:Sample size determination
1828:
1824:
1811:
1715:
1670:
1644:
1626:
1582:
1534:
1454:
1445:
1441:
1428:
1410:
1031:would be indicated here.
485:Median (second quartile)
467:For the data set in this
395:
328:
185:median absolute deviation
161:The IQR is used to build
3607:Environmental statistics
3129:Elliptical distributions
2922:Generalized linear model
2851:Simple linear regression
2621:HodgesâLehmann estimator
2078:Probability distribution
1987:Stochastic approximation
1549:Coefficient of variation
1234:. Heidelberg: Springer.
1155:Understanding Statistics
1088:Robust measures of scale
532:Upper 1.5*IQR whisker =
522:Lower 1.5*IQR whisker =
326:(median of whole table)
167:probability distribution
3267:Cross-correlation (XCF)
2875:Non-standard predictors
2309:LehmannâScheffĂ© theorem
1982:Adaptive clinical trial
1202:Introductory Statistics
951:and the third quartile
870:standard deviation
821:of the first quartile,
495:Upper (third) quartile
475:Lower (first) quartile
136:robust measure of scale
3663:Mathematics portal
3484:Engineering statistics
3392:NelsonâAalen estimator
2969:Analysis of covariance
2856:Ordinary least squares
2780:Pearson product-moment
2184:Statistical functional
2095:Empirical distribution
1928:Controlled experiments
1657:Frequency distribution
1435:Descriptive statistics
1285:Yule, G. Udny (1911).
1200:Ross, Sheldon (2010).
1047:
1013:
942:
862:
708:
648:
145:
59:statistical dispersion
47:descriptive statistics
42:
3579:Population statistics
3521:System identification
3255:Autocorrelation (ACF)
3183:Exponential smoothing
3097:Discriminant analysis
3092:Canonical correlation
2956:Partition of variance
2818:Regression validation
2662:(JonckheereâTerpstra)
2561:Likelihood-ratio test
2250:Frequentist inference
2162:Locationâscale family
2083:Sampling distribution
2048:Statistical inference
2015:Cross-sectional study
2002:Observational studies
1961:Randomized experiment
1790:Stem-and-leaf display
1592:Central limit theorem
1129:10.1007/1-84628-168-7
1042:
1014:
943:
863:
709:
649:
29:
3502:Probabilistic design
3087:Principal components
2930:Exponential families
2882:Nonlinear regression
2861:General linear model
2823:Mixed effects models
2813:Errors and residuals
2790:Confounding variable
2692:Bayesian probability
2670:Van der Waerden test
2660:Ordered alternative
2425:Multiple comparisons
2304:RaoâBlackwellization
2267:Estimating equations
2223:Statistical distance
1941:Factorial experiment
1474:Arithmetic-Geometric
1369:at Wikimedia Commons
1044:Box-and-whisker plot
958:
887:
843:
811:normally distributed
661:
601:
21:IQR (disambiguation)
3574:Official statistics
3497:Methods engineering
3178:Seasonal adjustment
2946:Poisson regressions
2866:Bayesian regression
2805:Regression analysis
2785:Partial correlation
2757:Regression analysis
2356:Prediction interval
2351:Likelihood interval
2341:Confidence interval
2333:Interval estimation
2294:Unbiased estimators
2112:Model specification
1992:Up-and-down designs
1680:Partial correlation
1636:Index of dispersion
1554:Interquartile range
1367:Interquartile range
872: = Ï for
766: ln(2) â 1.386
548:Five-number summary
290:Data set in a table
51:interquartile range
3594:Spatial statistics
3474:Medical statistics
3374:First hitting time
3328:Whittle likelihood
2979:Degrees of freedom
2974:Multivariate ANOVA
2907:Heteroscedasticity
2719:Bayesian estimator
2684:Bayesian inference
2533:KolmogorovâSmirnov
2418:Randomization test
2388:Testing hypotheses
2361:Tolerance interval
2272:Maximum likelihood
2167:Exponential family
2100:Density estimation
2060:Statistical theory
2020:Natural experiment
1966:Scientific control
1883:Survey methodology
1569:Standard deviation
1048:
1009:
938:
858:
835:, is +0.67. Given
813:, or Gaussian. If
799:standard deviation
704:
644:
562:(which yields the
57:) is a measure of
43:
37:(pdf) of a Normal
3696:
3695:
3634:
3633:
3630:
3629:
3569:National accounts
3539:Actuarial science
3531:Social statistics
3424:
3423:
3420:
3419:
3416:
3415:
3351:Survival function
3336:
3335:
3198:Granger causality
3039:Contingency table
3014:Survival analysis
2991:
2990:
2987:
2986:
2843:Linear regression
2738:
2737:
2734:
2733:
2709:Credible interval
2678:
2677:
2461:
2460:
2277:Method of moments
2146:Parametric family
2107:Statistical model
2037:
2036:
2033:
2032:
1951:Random assignment
1873:Statistical power
1807:
1806:
1803:
1802:
1652:Contingency table
1622:
1621:
1489:Generalized/power
1365:Media related to
1317:Studentlitteratur
1241:978-3-642-23502-3
1211:978-0-12-374388-6
1138:978-1-85233-896-1
1068:Interdecile range
1006:
935:
855:
786:
785:
719:quantile function
717:where CDF is the
681:
621:
456:= 119 - 31 = 88.
446:
445:
276:second quartile Q
243:number of values
128:trimmed estimator
3716:
3709:Scale statistics
3684:
3683:
3672:
3671:
3661:
3660:
3646:
3645:
3549:Crime statistics
3443:
3442:
3430:
3429:
3347:
3346:
3313:Fourier analysis
3300:Frequency domain
3280:
3227:
3193:Structural break
3153:
3152:
3102:Cluster analysis
3049:Log-linear model
3022:
3021:
2997:
2996:
2938:
2912:Homoscedasticity
2768:
2767:
2744:
2743:
2663:
2655:
2647:
2646:(KruskalâWallis)
2631:
2616:
2571:Cross validation
2556:
2538:AndersonâDarling
2485:
2472:
2471:
2443:Likelihood-ratio
2435:Parametric tests
2413:Permutation test
2396:1- & 2-tails
2287:Minimum distance
2259:Point estimation
2255:
2254:
2206:Optimal decision
2157:
2056:
2055:
2043:
2042:
2025:Quasi-experiment
1975:Adaptive designs
1826:
1825:
1813:
1812:
1690:Rank correlation
1452:
1451:
1443:
1442:
1430:
1429:
1397:
1390:
1383:
1374:
1373:
1364:
1348:
1345:
1339:
1338:
1308:
1297:
1296:
1282:
1276:
1275:
1269:
1260:
1254:
1253:
1225:
1216:
1215:
1197:
1191:
1176:
1170:
1169:
1149:
1143:
1142:
1114:
1079:
1018:
1016:
1015:
1010:
1008:
1007:
999:
990:
989:
970:
969:
947:
945:
944:
939:
937:
936:
928:
919:
918:
899:
898:
867:
865:
864:
859:
857:
856:
848:
801:of a population
727:
726:
713:
711:
710:
705:
691:
690:
682:
679:
673:
672:
653:
651:
650:
645:
631:
630:
622:
619:
613:
612:
297:
296:
266:= median of the
261:third quartile Q
253:= median of the
248:first quartile Q
213:of the dataset.
196:central tendency
40:
3724:
3723:
3719:
3718:
3717:
3715:
3714:
3713:
3699:
3698:
3697:
3692:
3655:
3626:
3588:
3525:
3511:quality control
3478:
3460:Clinical trials
3437:
3412:
3396:
3384:Hazard function
3378:
3332:
3294:
3278:
3241:
3237:BreuschâGodfrey
3225:
3202:
3142:
3117:Factor analysis
3063:
3044:Graphical model
3016:
2983:
2950:
2936:
2916:
2870:
2837:
2799:
2762:
2761:
2730:
2674:
2661:
2653:
2645:
2629:
2614:
2593:Rank statistics
2587:
2566:Model selection
2554:
2512:Goodness of fit
2506:
2483:
2457:
2429:
2382:
2327:
2316:Median unbiased
2244:
2155:
2088:Order statistic
2050:
2029:
1996:
1970:
1922:
1877:
1820:
1818:Data collection
1799:
1711:
1666:
1640:
1618:
1578:
1530:
1447:Continuous data
1437:
1424:
1406:
1401:
1357:
1352:
1351:
1346:
1342:
1327:
1319:. p. 348.
1309:
1300:
1283:
1279:
1267:
1261:
1257:
1242:
1226:
1219:
1212:
1198:
1194:
1177:
1173:
1166:
1150:
1146:
1139:
1115:
1102:
1097:
1077:
1064:
1037:
998:
997:
985:
981:
965:
961:
959:
956:
955:
927:
926:
914:
910:
894:
890:
888:
885:
884:
847:
846:
844:
841:
840:
834:
827:
791:
683:
678:
677:
668:
664:
662:
659:
658:
623:
618:
617:
608:
604:
602:
599:
598:
593:
586:
579:
572:
556:
538:
528:
518:
511:
501:
491:
481:
465:
462:
455:
451:
401:
399:
334:
332:
325:
323:
292:
287:
279:
264:
257:smallest values
251:
231:
227:
222:
156:breakdown point
148:
123:
120:
113:
106:
95:
88:
38:
24:
17:
12:
11:
5:
3722:
3712:
3711:
3694:
3693:
3691:
3690:
3678:
3666:
3652:
3639:
3636:
3635:
3632:
3631:
3628:
3627:
3625:
3624:
3619:
3614:
3609:
3604:
3598:
3596:
3590:
3589:
3587:
3586:
3581:
3576:
3571:
3566:
3561:
3556:
3551:
3546:
3541:
3535:
3533:
3527:
3526:
3524:
3523:
3518:
3513:
3504:
3499:
3494:
3488:
3486:
3480:
3479:
3477:
3476:
3471:
3466:
3457:
3455:Bioinformatics
3451:
3449:
3439:
3438:
3426:
3425:
3422:
3421:
3418:
3417:
3414:
3413:
3411:
3410:
3404:
3402:
3398:
3397:
3395:
3394:
3388:
3386:
3380:
3379:
3377:
3376:
3371:
3366:
3361:
3355:
3353:
3344:
3338:
3337:
3334:
3333:
3331:
3330:
3325:
3320:
3315:
3310:
3304:
3302:
3296:
3295:
3293:
3292:
3287:
3282:
3274:
3269:
3264:
3263:
3262:
3260:partial (PACF)
3251:
3249:
3243:
3242:
3240:
3239:
3234:
3229:
3221:
3216:
3210:
3208:
3207:Specific tests
3204:
3203:
3201:
3200:
3195:
3190:
3185:
3180:
3175:
3170:
3165:
3159:
3157:
3150:
3144:
3143:
3141:
3140:
3139:
3138:
3137:
3136:
3121:
3120:
3119:
3109:
3107:Classification
3104:
3099:
3094:
3089:
3084:
3079:
3073:
3071:
3065:
3064:
3062:
3061:
3056:
3054:McNemar's test
3051:
3046:
3041:
3036:
3030:
3028:
3018:
3017:
2993:
2992:
2989:
2988:
2985:
2984:
2982:
2981:
2976:
2971:
2966:
2960:
2958:
2952:
2951:
2949:
2948:
2932:
2926:
2924:
2918:
2917:
2915:
2914:
2909:
2904:
2899:
2894:
2892:Semiparametric
2889:
2884:
2878:
2876:
2872:
2871:
2869:
2868:
2863:
2858:
2853:
2847:
2845:
2839:
2838:
2836:
2835:
2830:
2825:
2820:
2815:
2809:
2807:
2801:
2800:
2798:
2797:
2792:
2787:
2782:
2776:
2774:
2764:
2763:
2760:
2759:
2754:
2748:
2740:
2739:
2736:
2735:
2732:
2731:
2729:
2728:
2727:
2726:
2716:
2711:
2706:
2705:
2704:
2699:
2688:
2686:
2680:
2679:
2676:
2675:
2673:
2672:
2667:
2666:
2665:
2657:
2649:
2633:
2630:(MannâWhitney)
2625:
2624:
2623:
2610:
2609:
2608:
2597:
2595:
2589:
2588:
2586:
2585:
2584:
2583:
2578:
2573:
2563:
2558:
2555:(ShapiroâWilk)
2550:
2545:
2540:
2535:
2530:
2522:
2516:
2514:
2508:
2507:
2505:
2504:
2496:
2487:
2475:
2469:
2467:Specific tests
2463:
2462:
2459:
2458:
2456:
2455:
2450:
2445:
2439:
2437:
2431:
2430:
2428:
2427:
2422:
2421:
2420:
2410:
2409:
2408:
2398:
2392:
2390:
2384:
2383:
2381:
2380:
2379:
2378:
2373:
2363:
2358:
2353:
2348:
2343:
2337:
2335:
2329:
2328:
2326:
2325:
2320:
2319:
2318:
2313:
2312:
2311:
2306:
2291:
2290:
2289:
2284:
2279:
2274:
2263:
2261:
2252:
2246:
2245:
2243:
2242:
2237:
2232:
2231:
2230:
2220:
2215:
2214:
2213:
2203:
2202:
2201:
2196:
2191:
2181:
2176:
2171:
2170:
2169:
2164:
2159:
2143:
2142:
2141:
2136:
2131:
2121:
2120:
2119:
2114:
2104:
2103:
2102:
2092:
2091:
2090:
2080:
2075:
2070:
2064:
2062:
2052:
2051:
2039:
2038:
2035:
2034:
2031:
2030:
2028:
2027:
2022:
2017:
2012:
2006:
2004:
1998:
1997:
1995:
1994:
1989:
1984:
1978:
1976:
1972:
1971:
1969:
1968:
1963:
1958:
1953:
1948:
1943:
1938:
1932:
1930:
1924:
1923:
1921:
1920:
1918:Standard error
1915:
1910:
1905:
1904:
1903:
1898:
1887:
1885:
1879:
1878:
1876:
1875:
1870:
1865:
1860:
1855:
1850:
1848:Optimal design
1845:
1840:
1834:
1832:
1822:
1821:
1809:
1808:
1805:
1804:
1801:
1800:
1798:
1797:
1792:
1787:
1782:
1777:
1772:
1767:
1762:
1757:
1752:
1747:
1742:
1737:
1732:
1727:
1721:
1719:
1713:
1712:
1710:
1709:
1704:
1703:
1702:
1697:
1687:
1682:
1676:
1674:
1668:
1667:
1665:
1664:
1659:
1654:
1648:
1646:
1645:Summary tables
1642:
1641:
1639:
1638:
1632:
1630:
1624:
1623:
1620:
1619:
1617:
1616:
1615:
1614:
1609:
1604:
1594:
1588:
1586:
1580:
1579:
1577:
1576:
1571:
1566:
1561:
1556:
1551:
1546:
1540:
1538:
1532:
1531:
1529:
1528:
1523:
1518:
1517:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1479:Contraharmonic
1476:
1471:
1460:
1458:
1449:
1439:
1438:
1426:
1425:
1423:
1422:
1417:
1411:
1408:
1407:
1400:
1399:
1392:
1385:
1377:
1371:
1370:
1356:
1355:External links
1353:
1350:
1349:
1340:
1325:
1298:
1277:
1255:
1240:
1217:
1210:
1192:
1171:
1164:
1144:
1137:
1099:
1098:
1096:
1093:
1092:
1091:
1085:
1083:Probable error
1080:
1071:
1063:
1060:
1036:
1033:
1020:
1019:
1005:
1002:
996:
993:
988:
984:
979:
976:
973:
968:
964:
949:
948:
934:
931:
925:
922:
917:
913:
908:
905:
902:
897:
893:
854:
851:
832:
825:
819:standard score
790:
787:
784:
783:
780:
777:
771:
770:
760:
757:
751:
750:
747:
744:
738:
737:
734:
731:
715:
714:
703:
700:
697:
694:
689:
686:
676:
671:
667:
655:
654:
643:
640:
637:
634:
629:
626:
616:
611:
607:
591:
584:
577:
570:
555:
552:
544:
543:
540:
536:
530:
526:
520:
516:
509:
503:
499:
493:
489:
483:
479:
463:
461:
458:
453:
449:
444:
443:
440:
436:
435:
432:
428:
427:
424:
420:
419:
416:
412:
411:
408:
404:
403:
397:
394:
391:
387:
386:
384:
381:
377:
376:
373:
369:
368:
365:
361:
360:
357:
353:
352:
349:
345:
344:
341:
337:
336:
330:
327:
321:
318:
315:
311:
310:
307:
304:
301:
291:
288:
286:
283:
277:
272:
271:
270:largest values
262:
258:
249:
235:Given an even
229:
225:
221:
218:
147:
144:
121:
118:
111:
104:
93:
86:
15:
9:
6:
4:
3:
2:
3721:
3710:
3707:
3706:
3704:
3689:
3688:
3679:
3677:
3676:
3667:
3665:
3664:
3659:
3653:
3651:
3650:
3641:
3640:
3637:
3623:
3620:
3618:
3617:Geostatistics
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3599:
3597:
3595:
3591:
3585:
3584:Psychometrics
3582:
3580:
3577:
3575:
3572:
3570:
3567:
3565:
3562:
3560:
3557:
3555:
3552:
3550:
3547:
3545:
3542:
3540:
3537:
3536:
3534:
3532:
3528:
3522:
3519:
3517:
3514:
3512:
3508:
3505:
3503:
3500:
3498:
3495:
3493:
3490:
3489:
3487:
3485:
3481:
3475:
3472:
3470:
3467:
3465:
3461:
3458:
3456:
3453:
3452:
3450:
3448:
3447:Biostatistics
3444:
3440:
3436:
3431:
3427:
3409:
3408:Log-rank test
3406:
3405:
3403:
3399:
3393:
3390:
3389:
3387:
3385:
3381:
3375:
3372:
3370:
3367:
3365:
3362:
3360:
3357:
3356:
3354:
3352:
3348:
3345:
3343:
3339:
3329:
3326:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3305:
3303:
3301:
3297:
3291:
3288:
3286:
3283:
3281:
3279:(BoxâJenkins)
3275:
3273:
3270:
3268:
3265:
3261:
3258:
3257:
3256:
3253:
3252:
3250:
3248:
3244:
3238:
3235:
3233:
3232:DurbinâWatson
3230:
3228:
3222:
3220:
3217:
3215:
3214:DickeyâFuller
3212:
3211:
3209:
3205:
3199:
3196:
3194:
3191:
3189:
3188:Cointegration
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3163:Decomposition
3161:
3160:
3158:
3154:
3151:
3149:
3145:
3135:
3132:
3131:
3130:
3127:
3126:
3125:
3122:
3118:
3115:
3114:
3113:
3110:
3108:
3105:
3103:
3100:
3098:
3095:
3093:
3090:
3088:
3085:
3083:
3080:
3078:
3075:
3074:
3072:
3070:
3066:
3060:
3057:
3055:
3052:
3050:
3047:
3045:
3042:
3040:
3037:
3035:
3034:Cohen's kappa
3032:
3031:
3029:
3027:
3023:
3019:
3015:
3011:
3007:
3003:
2998:
2994:
2980:
2977:
2975:
2972:
2970:
2967:
2965:
2962:
2961:
2959:
2957:
2953:
2947:
2943:
2939:
2933:
2931:
2928:
2927:
2925:
2923:
2919:
2913:
2910:
2908:
2905:
2903:
2900:
2898:
2895:
2893:
2890:
2888:
2887:Nonparametric
2885:
2883:
2880:
2879:
2877:
2873:
2867:
2864:
2862:
2859:
2857:
2854:
2852:
2849:
2848:
2846:
2844:
2840:
2834:
2831:
2829:
2826:
2824:
2821:
2819:
2816:
2814:
2811:
2810:
2808:
2806:
2802:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2777:
2775:
2773:
2769:
2765:
2758:
2755:
2753:
2750:
2749:
2745:
2741:
2725:
2722:
2721:
2720:
2717:
2715:
2712:
2710:
2707:
2703:
2700:
2698:
2695:
2694:
2693:
2690:
2689:
2687:
2685:
2681:
2671:
2668:
2664:
2658:
2656:
2650:
2648:
2642:
2641:
2640:
2637:
2636:Nonparametric
2634:
2632:
2626:
2622:
2619:
2618:
2617:
2611:
2607:
2606:Sample median
2604:
2603:
2602:
2599:
2598:
2596:
2594:
2590:
2582:
2579:
2577:
2574:
2572:
2569:
2568:
2567:
2564:
2562:
2559:
2557:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2527:
2523:
2521:
2518:
2517:
2515:
2513:
2509:
2503:
2501:
2497:
2495:
2493:
2488:
2486:
2481:
2477:
2476:
2473:
2470:
2468:
2464:
2454:
2451:
2449:
2446:
2444:
2441:
2440:
2438:
2436:
2432:
2426:
2423:
2419:
2416:
2415:
2414:
2411:
2407:
2404:
2403:
2402:
2399:
2397:
2394:
2393:
2391:
2389:
2385:
2377:
2374:
2372:
2369:
2368:
2367:
2364:
2362:
2359:
2357:
2354:
2352:
2349:
2347:
2344:
2342:
2339:
2338:
2336:
2334:
2330:
2324:
2321:
2317:
2314:
2310:
2307:
2305:
2302:
2301:
2300:
2297:
2296:
2295:
2292:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2269:
2268:
2265:
2264:
2262:
2260:
2256:
2253:
2251:
2247:
2241:
2238:
2236:
2233:
2229:
2226:
2225:
2224:
2221:
2219:
2216:
2212:
2211:loss function
2209:
2208:
2207:
2204:
2200:
2197:
2195:
2192:
2190:
2187:
2186:
2185:
2182:
2180:
2177:
2175:
2172:
2168:
2165:
2163:
2160:
2158:
2152:
2149:
2148:
2147:
2144:
2140:
2137:
2135:
2132:
2130:
2127:
2126:
2125:
2122:
2118:
2115:
2113:
2110:
2109:
2108:
2105:
2101:
2098:
2097:
2096:
2093:
2089:
2086:
2085:
2084:
2081:
2079:
2076:
2074:
2071:
2069:
2066:
2065:
2063:
2061:
2057:
2053:
2049:
2044:
2040:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2007:
2005:
2003:
1999:
1993:
1990:
1988:
1985:
1983:
1980:
1979:
1977:
1973:
1967:
1964:
1962:
1959:
1957:
1954:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1933:
1931:
1929:
1925:
1919:
1916:
1914:
1913:Questionnaire
1911:
1909:
1906:
1902:
1899:
1897:
1894:
1893:
1892:
1889:
1888:
1886:
1884:
1880:
1874:
1871:
1869:
1866:
1864:
1861:
1859:
1856:
1854:
1851:
1849:
1846:
1844:
1841:
1839:
1836:
1835:
1833:
1831:
1827:
1823:
1819:
1814:
1810:
1796:
1793:
1791:
1788:
1786:
1783:
1781:
1778:
1776:
1773:
1771:
1768:
1766:
1763:
1761:
1758:
1756:
1753:
1751:
1748:
1746:
1743:
1741:
1740:Control chart
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1722:
1720:
1718:
1714:
1708:
1705:
1701:
1698:
1696:
1693:
1692:
1691:
1688:
1686:
1683:
1681:
1678:
1677:
1675:
1673:
1669:
1663:
1660:
1658:
1655:
1653:
1650:
1649:
1647:
1643:
1637:
1634:
1633:
1631:
1629:
1625:
1613:
1610:
1608:
1605:
1603:
1600:
1599:
1598:
1595:
1593:
1590:
1589:
1587:
1585:
1581:
1575:
1572:
1570:
1567:
1565:
1562:
1560:
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1541:
1539:
1537:
1533:
1527:
1524:
1522:
1519:
1515:
1512:
1510:
1507:
1505:
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1497:
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1480:
1477:
1475:
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1444:
1440:
1436:
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1427:
1421:
1418:
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1413:
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1379:
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1368:
1363:
1359:
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1344:
1336:
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1328:
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1318:
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1307:
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1294:
1290:
1289:
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1273:
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1259:
1251:
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1237:
1233:
1232:
1224:
1222:
1213:
1207:
1203:
1196:
1189:
1188:1-58488-059-7
1185:
1182:, CRC Press.
1181:
1175:
1167:
1165:0-19-914391-9
1161:
1157:
1156:
1148:
1140:
1134:
1130:
1126:
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1121:
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1111:
1109:
1107:
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1100:
1089:
1086:
1084:
1081:
1075:
1072:
1069:
1066:
1065:
1059:
1057:
1053:
1045:
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1032:
1030:
1025:
1000:
994:
986:
982:
977:
971:
966:
962:
954:
953:
952:
929:
923:
915:
911:
906:
900:
895:
891:
883:
882:
881:
879:
875:
871:
849:
839: =
838:
831:
824:
820:
816:
812:
808:
804:
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796:
781:
778:
776:
773:
772:
769:
765:
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758:
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753:
752:
748:
745:
743:
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739:
735:
732:
730:Distribution
729:
728:
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722:
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701:
695:
687:
684:
674:
669:
665:
657:
656:
641:
635:
627:
624:
614:
609:
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583:
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569:
565:
561:
554:Distributions
551:
549:
541:
535:
531:
525:
521:
515:
508:
504:
498:
494:
488:
484:
478:
474:
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470:
457:
441:
438:
437:
433:
430:
429:
425:
422:
421:
417:
414:
413:
409:
406:
405:
392:
389:
388:
385:
382:
379:
378:
374:
371:
370:
366:
363:
362:
358:
355:
354:
350:
347:
346:
342:
339:
338:
316:
313:
312:
308:
305:
298:
295:
282:
280:
269:
265:
259:
256:
252:
246:
245:
244:
242:
238:
233:
217:
214:
212:
208:
204:
199:
197:
193:
188:
186:
182:
177:
175:
170:
168:
164:
159:
157:
153:
150:Unlike total
143:
141:
137:
133:
129:
124:
117:
110:
103:
99:
92:
84:
80:
76:
72:
71:fourth spread
68:
64:
60:
56:
52:
48:
36:
32:
28:
22:
3685:
3673:
3654:
3647:
3559:Econometrics
3509: /
3492:Chemometrics
3469:Epidemiology
3462: /
3435:Applications
3277:ARIMA model
3224:Q-statistic
3173:Stationarity
3069:Multivariate
3012: /
3008: /
3006:Multivariate
3004: /
2944: /
2940: /
2714:Bayes factor
2613:Signed rank
2525:
2499:
2491:
2479:
2174:Completeness
2010:Cohort study
1908:Opinion poll
1843:Missing data
1830:Study design
1785:Scatter plot
1707:Scatter plot
1700:Spearman's Ï
1662:Grouped data
1553:
1343:
1312:
1287:
1280:
1271:
1258:
1230:
1201:
1195:
1179:
1174:
1154:
1147:
1119:
1055:
1049:
1023:
1021:
950:
877:
873:
869:
836:
829:
822:
814:
806:
802:
792:
767:
763:
723:
716:
588:
581:
574:
567:
557:
545:
533:
523:
513:
506:
496:
486:
476:
466:
447:
293:
275:
273:
267:
260:
254:
247:
240:
236:
234:
223:
215:
200:
189:
178:
171:
160:
149:
125:
115:
108:
101:
90:
74:
70:
66:
62:
54:
50:
44:
3687:WikiProject
3602:Cartography
3564:Jurimetrics
3516:Reliability
3247:Time domain
3226:(LjungâBox)
3148:Time-series
3026:Categorical
3010:Time-series
3002:Categorical
2937:(Bernoulli)
2772:Correlation
2752:Correlation
2548:JarqueâBera
2520:Chi-squared
2282:M-estimator
2235:Asymptotics
2179:Sufficiency
1946:Interaction
1858:Replication
1838:Effect size
1795:Violin plot
1775:Radar chart
1755:Forest plot
1745:Correlogram
1695:Kendall's Ï
79:percentiles
3554:Demography
3272:ARMA model
3077:Regression
2654:(Friedman)
2615:(Wilcoxon)
2553:Normality
2543:Lilliefors
2490:Student's
2366:Resampling
2240:Robustness
2228:divergence
2218:Efficiency
2156:(monotone)
2151:Likelihood
2068:Population
1901:Stratified
1853:Population
1672:Dependence
1628:Count data
1559:Percentile
1536:Dispersion
1469:Arithmetic
1404:Statistics
1326:9144250517
1095:References
67:middle 50%
41:Population
2935:Logistic
2702:posterior
2628:Rank sum
2376:Jackknife
2371:Bootstrap
2189:Bootstrap
2124:Parameter
2073:Statistic
1868:Statistic
1780:Run chart
1765:Pie chart
1760:Histogram
1750:Fan chart
1725:Bar chart
1607:L-moments
1494:Geometric
1250:763157853
1004:¯
978:σ
933:¯
907:σ
853:¯
793:The IQR,
685:−
625:−
452:− Q
309:Quartile
220:Algorithm
163:box plots
83:quartiles
75:Hâspread.
63:midspread
3703:Category
3649:Category
3342:Survival
3219:Johansen
2942:Binomial
2897:Isotonic
2484:(normal)
2129:location
1936:Blocking
1891:Sampling
1770:QâQ plot
1735:Box plot
1717:Graphics
1612:Skewness
1602:Kurtosis
1574:Variance
1504:Heronian
1499:Harmonic
1335:18454776
1190:page 18.
1074:Midhinge
1062:See also
1056:whiskers
1052:outliers
1035:Outliers
1029:QâQ plot
469:box plot
285:Examples
211:skewness
203:outliers
181:midhinge
140:box plot
114:â
3675:Commons
3622:Kriging
3507:Process
3464:studies
3323:Wavelet
3156:General
2323:Plug-in
2117:L space
1896:Cluster
1597:Moments
1415:Outline
755:Laplace
733:Median
306:Median
239:or odd
187:(MAD).
176:rates.
100:), and
31:Boxplot
3544:Census
3134:Normal
3082:Manova
2902:Robust
2652:2-way
2644:1-way
2482:-test
2153:
1730:Biplot
1521:Median
1514:Lehmer
1456:Center
1333:
1323:
1248:
1238:
1208:
1186:
1162:
1135:
797:, and
775:Cauchy
742:Normal
192:median
174:income
98:median
49:, the
39:N(0,Ï)
3168:Trend
2697:prior
2639:anova
2528:-test
2502:-test
2494:-test
2401:Power
2346:Pivot
2139:shape
2134:scale
1584:Shape
1564:Range
1509:Heinz
1484:Cubic
1420:Index
1295:â148.
1268:(PDF)
876:, if
492:= 8.5
228:and Q
207:below
205:(see
152:range
132:range
96:(the
73:, or
3401:Test
2601:Sign
2453:Wald
1526:Mode
1464:Mean
1331:OCLC
1321:ISBN
1246:OCLC
1236:ISBN
1206:ISBN
1184:ISBN
1160:ISBN
1133:ISBN
868:and
837:mean
795:mean
736:IQR
696:0.75
636:0.25
442:177
434:155
426:119
418:119
410:116
400:=119
393:115
274:The
241:2n+1
190:The
2581:BIC
2576:AIC
1293:147
1125:doi
809:is
782:2Îł
680:CDF
620:CDF
519:= 2
502:= 9
482:= 7
439:13
431:12
423:11
415:10
383:87
375:75
367:47
359:31
351:31
333:=31
324:=87
146:Use
55:IQR
45:In
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