3669:
1051:
3655:
38:
3693:
3681:
1373:
1037:
is not normally distributed. However, a normal distribution can be trivially perturbed to maintain its Q1 and Q2 std. scores at 0.67 and −0.67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as
475:+−−−−−+−+ * |−−−−−−−−−−−| | |−−−−−−−−−−−| +−−−−−+−+ +−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+ Number line 0 1 2 3 4 5 6 7 8 9 10 11 12
1028:
957:
1065:
in data. Outliers here are defined as observations that fall below Q1 − 1.5 IQR or above Q3 + 1.5 IQR. In a boxplot, the highest and lowest occurring value within this limit are indicated by
723:
663:
553:
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.
877:
2790:
3295:
118:(also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR =
3445:
3069:
1710:
2843:
3282:
1250:
1220:
1147:
1057:
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.
1705:
1405:
2309:
1457:
557:
This means the 1.5*IQR whiskers can be uneven in lengths. The median, minimum, maximum, and the first and third quartile constitute the
3092:
2984:
1198:
1174:
3697:
3270:
3144:
574:
3328:
2989:
2734:
2105:
1695:
2319:
3379:
2591:
2398:
2287:
2245:
1335:
1484:
1377:
3622:
2581:
145:, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. It is also used as a
2631:
3173:
3122:
3107:
3097:
2966:
2838:
2805:
2586:
2416:
570:
45:
3242:
2543:
1164:
968:
897:
3517:
3318:
2297:
1966:
1430:
3402:
3369:
671:
611:
3374:
3117:
2876:
2782:
2762:
2670:
2381:
2199:
1682:
1554:
2548:
2314:
2172:
3719:
3134:
2902:
2623:
2477:
2406:
2326:
2184:
2165:
1873:
1594:
195:
3247:
1069:
of the box (frequently with an additional bar at the end of the whisker) and any outliers as individual points.
3617:
3384:
2932:
2897:
2861:
2646:
2088:
1997:
1956:
1868:
1559:
1398:
1098:
177:
146:
2654:
2638:
3526:
3139:
3079:
3016:
2376:
2238:
2228:
2078:
1992:
3287:
3224:
3564:
3494:
2979:
2866:
1863:
1760:
1667:
1546:
1445:
69:
57:
3685:
2563:
3589:
3531:
3474:
3300:
3193:
3102:
2828:
2712:
2571:
2453:
2445:
2260:
2156:
2134:
2093:
2058:
2025:
1971:
1946:
1901:
1840:
1800:
1602:
1425:
3668:
2558:
1050:
1033:
If the actual values of the first or third quartiles differ substantially from the calculated values,
3512:
3087:
3036:
3012:
2974:
2892:
2871:
2823:
2702:
2680:
2649:
2435:
2386:
2304:
2277:
2233:
2189:
1951:
1727:
1607:
1054:
765:
31:
3659:
3584:
3507:
3188:
2952:
2945:
2907:
2815:
2795:
2767:
2500:
2366:
2361:
2351:
2343:
2161:
2122:
2012:
2002:
1911:
1690:
1646:
1489:
1391:
1324:
Beta mathematics handbook : concepts, theorems, methods, algorithms, formulas, graphs, tables
821:
785:
752:
558:
235:
The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q
3234:
3673:
3484:
3338:
3183:
3059:
2956:
2940:
2917:
2694:
2428:
2411:
2371:
2282:
2177:
2139:
2110:
2070:
2030:
1976:
1893:
1579:
1574:
1303:
809:
550:+ 1.5 * IQR = 9 + 3 = 12. (If there is no data point at 12, then the highest point less than 12.)
162:
142:
1128:
Dekking, Frederik Michel; Kraaikamp, Cornelis; Lopuhaä, Hen Paul; Meester, Ludolf Erwin (2005).
853:
540:- 1.5 * IQR = 7 - 3 = 4. (If there is no data point at 4, then the lowest point greater than 4.)
1275:
3579:
3549:
3541:
3361:
3352:
3277:
3208:
3064:
3049:
3024:
2912:
2853:
2719:
2707:
2333:
2250:
2194:
2117:
1961:
1883:
1662:
1536:
1341:
1331:
1327:
1256:
1246:
1216:
1194:
1170:
1143:
1078:
729:
138:
3604:
3559:
3323:
3310:
3203:
3178:
3112:
3044:
2922:
2530:
2423:
2356:
2269:
2216:
2035:
1906:
1700:
1499:
1466:
1135:
206:
96:, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q
3521:
3265:
3127:
3054:
2729:
2603:
2576:
2553:
2522:
2149:
2144:
2098:
1828:
1479:
569:
The interquartile range of a continuous distribution can be calculated by integrating the
166:
3470:
3465:
1928:
1858:
1504:
1297:
1093:
829:
305:
The following table has 13 rows, and follows the rules for the odd number of entries.
3713:
3627:
3594:
3457:
3418:
3229:
3198:
2662:
2616:
2221:
1923:
1750:
1514:
1509:
1780:
1039:
17:
3569:
3502:
3479:
3394:
2724:
2020:
1918:
1853:
1795:
1717:
1672:
1129:
3612:
3574:
3257:
3158:
3020:
2833:
2800:
2292:
2209:
2204:
1848:
1805:
1785:
1765:
1755:
1524:
735:
The interquartile range and median of some common distributions are shown below
89:
227:
The quartile deviation or semi-interquartile range is defined as half the IQR.
2458:
1938:
1638:
1569:
1519:
1494:
1414:
1260:
577:—any other means of calculating the CDF will also work). The lower quartile,
2611:
2463:
2083:
1878:
1790:
1775:
1770:
1735:
1345:
37:
605:
equals 0.75; in terms of the CDF, the quartiles can be defined as follows:
1372:
1240:
1139:
2127:
1745:
1622:
1617:
1612:
1584:
1084:
479:
221:
194:, the average of the first and third quartiles), half the IQR equals the
191:
173:
150:
93:
3632:
3333:
1062:
213:
41:
3554:
2535:
2509:
2489:
1740:
1531:
202:
184:
108:
1049:
72:, which is the spread of the data. The IQR may also be called the
1474:
805:
92:
of the data. To calculate the IQR, the data set is divided into
3443:
3010:
2757:
2056:
1826:
1443:
1387:
1274:
Rousseeuw, Peter J.; Croux, Christophe (1992). Y. Dodge (ed.).
1383:
459:
For the data in this table the interquartile range is IQR = Q
1191:
CRC Standard
Probability and Statistics Tables and Formulae
1101: – Statistical indicators of the deviation of a sample
839:, is −0.67, and the standard score of the third quartile,
190:
For a symmetric distribution (where the median equals the
88:
It is defined as the difference between the 75th and 25th
1134:. Springer Texts in Statistics. London: Springer London.
584:, is a number such that integral of the PDF from -∞ to
169:
of 25% and is thus often preferred to the total range.
1358:
Dekking, Kraaikamp, Lopuhaä & Meester, pp. 235–237
800:
Interquartile range test for normality of distribution
1276:"Explicit Scale Estimators with High Breakdown Point"
971:
900:
856:
674:
614:
3296:
Autoregressive conditional heteroskedasticity (ARCH)
1089:
Pages displaying wikidata descriptions as a fallback
183:
The IQR is used in businesses as a marker for their
3603:
3540:
3493:
3456:
3411:
3393:
3360:
3351:
3309:
3256:
3217:
3166:
3157:
3078:
3035:
2965:
2931:
2885:
2852:
2814:
2781:
2693:
2602:
2521:
2476:
2444:
2397:
2342:
2268:
2259:
2069:
2011:
1985:
1937:
1892:
1839:
1726:
1681:
1655:
1637:
1593:
1545:
1465:
1456:
1131:
243:. Each quartile is a median calculated as follows.
1022:
951:
871:
717:
657:
1023:{\displaystyle Q_{3}=(\sigma \,z_{3})+{\bar {P}}}
952:{\displaystyle Q_{1}=(\sigma \,z_{1})+{\bar {P}}}
1087: – average of the first and third quartiles
598:, is such a number that the integral from -∞ to
2844:Multivariate adaptive regression splines (MARS)
816:can be used in a simple test of whether or not
1215:. Burlington, MA: Elsevier. pp. 103–104.
1061:The interquartile range is often used to find
718:{\displaystyle Q_{3}={\text{CDF}}^{-1}(0.75),}
658:{\displaystyle Q_{1}={\text{CDF}}^{-1}(0.25),}
1399:
149:It can be clearly visualized by the box on a
8:
891:is normally distributed, the first quartile
1299:An Introduction to the Theory of Statistics
1285:. Amsterdam: North-Holland. pp. 77–92.
1283:L1-Statistical Analysis and Related Methods
3453:
3440:
3357:
3163:
3032:
3007:
2778:
2754:
2482:
2265:
2066:
2053:
1836:
1823:
1462:
1453:
1440:
1406:
1392:
1384:
30:"IQR" redirects here. For other uses, see
1009:
1008:
996:
991:
976:
970:
938:
937:
925:
920:
905:
899:
858:
857:
855:
694:
689:
679:
673:
634:
629:
619:
613:
413:(median of upper half, from row 8 to 13)
1302:. Charles Griffin and Company. pp.
737:
346:(median of lower half, from row 1 to 6)
307:
176:, simple graphical representations of a
36:
1169:. Oxford University Press. p. 55.
1111:
591:equals 0.25, while the upper quartile,
3370:Kaplan–Meier estimator (product limit)
7:
3680:
3380:Accelerated failure time (AFT) model
1317:
1315:
1313:
1234:
1232:
1123:
1121:
1119:
1117:
1115:
292:is the same as the ordinary median.
44:(with an interquartile range) and a
3692:
2975:Analysis of variance (ANOVA, anova)
1189:Zwillinger, D., Kokoska, S. (2000)
3070:Cochran–Mantel–Haenszel statistics
1696:Pearson product-moment correlation
828:is normally distributed, then the
100:(also called the lower quartile),
25:
1239:Kaltenbach, Hans-Michael (2012).
1163:Upton, Graham; Cook, Ian (1996).
471:Data set in a plain-text box plot
220:). The IQR also may indicate the
27:Measure of statistical dispersion
3691:
3679:
3667:
3654:
3653:
1371:
575:cumulative distribution function
212:The IQR can be used to identify
205:is the corresponding measure of
165:, the interquartile range has a
3329:Least-squares spectral analysis
760:2 Φ(0.75)σ ≈ 1.349σ ≈ (27/20)σ
2310:Mean-unbiased minimum-variance
1014:
1002:
985:
943:
931:
914:
863:
709:
703:
649:
643:
1:
3623:Geographic information system
2839:Simultaneous equations models
1242:A concise guide to statistics
217:
141:, defined as the 25% trimmed
2806:Coefficient of determination
2417:Uniformly most powerful test
1322:Bertil., Westergren (1988).
571:probability density function
46:probability density function
3375:Proportional hazards models
3319:Spectral density estimation
3301:Vector autoregression (VAR)
2735:Maximum posterior estimator
1967:Randomized controlled trial
1081: – Statistical measure
516:Interquartile range, IQR =
137:The IQR is an example of a
3736:
3135:Multivariate distributions
1555:Average absolute deviation
872:{\displaystyle {\bar {P}}}
330:
313:
310:
29:
3649:
3452:
3439:
3123:Structural equation model
3031:
3006:
2777:
2753:
2485:
2459:Score/Lagrange multiplier
2065:
2052:
1874:Sample size determination
1835:
1822:
1452:
1439:
1421:
1042:would be indicated here.
496:Median (second quartile)
478:For the data set in this
406:
339:
196:median absolute deviation
172:The IQR is used to build
3618:Environmental statistics
3140:Elliptical distributions
2933:Generalized linear model
2862:Simple linear regression
2632:Hodges–Lehmann estimator
2089:Probability distribution
1998:Stochastic approximation
1560:Coefficient of variation
1245:. Heidelberg: Springer.
1166:Understanding Statistics
1099:Robust measures of scale
543:Upper 1.5*IQR whisker =
533:Lower 1.5*IQR whisker =
337:(median of whole table)
178:probability distribution
3278:Cross-correlation (XCF)
2886:Non-standard predictors
2320:Lehmann–Scheffé theorem
1993:Adaptive clinical trial
1213:Introductory Statistics
962:and the third quartile
881:standard deviation
832:of the first quartile,
506:Upper (third) quartile
486:Lower (first) quartile
147:robust measure of scale
3674:Mathematics portal
3495:Engineering statistics
3403:Nelson–Aalen estimator
2980:Analysis of covariance
2867:Ordinary least squares
2791:Pearson product-moment
2195:Statistical functional
2106:Empirical distribution
1939:Controlled experiments
1668:Frequency distribution
1446:Descriptive statistics
1296:Yule, G. Udny (1911).
1211:Ross, Sheldon (2010).
1058:
1024:
953:
873:
719:
659:
70:statistical dispersion
58:descriptive statistics
53:
3590:Population statistics
3532:System identification
3266:Autocorrelation (ACF)
3194:Exponential smoothing
3108:Discriminant analysis
3103:Canonical correlation
2967:Partition of variance
2829:Regression validation
2673:(Jonckheere–Terpstra)
2572:Likelihood-ratio test
2261:Frequentist inference
2173:Location–scale family
2094:Sampling distribution
2059:Statistical inference
2026:Cross-sectional study
2013:Observational studies
1972:Randomized experiment
1801:Stem-and-leaf display
1603:Central limit theorem
1140:10.1007/1-84628-168-7
1053:
1025:
954:
874:
720:
660:
40:
3513:Probabilistic design
3098:Principal components
2941:Exponential families
2893:Nonlinear regression
2872:General linear model
2834:Mixed effects models
2824:Errors and residuals
2801:Confounding variable
2703:Bayesian probability
2681:Van der Waerden test
2671:Ordered alternative
2436:Multiple comparisons
2315:Rao–Blackwellization
2278:Estimating equations
2234:Statistical distance
1952:Factorial experiment
1485:Arithmetic-Geometric
1380:at Wikimedia Commons
1055:Box-and-whisker plot
969:
898:
854:
822:normally distributed
672:
612:
32:IQR (disambiguation)
18:Inter-quartile range
3585:Official statistics
3508:Methods engineering
3189:Seasonal adjustment
2957:Poisson regressions
2877:Bayesian regression
2816:Regression analysis
2796:Partial correlation
2768:Regression analysis
2367:Prediction interval
2362:Likelihood interval
2352:Confidence interval
2344:Interval estimation
2305:Unbiased estimators
2123:Model specification
2003:Up-and-down designs
1691:Partial correlation
1647:Index of dispersion
1565:Interquartile range
1378:Interquartile range
883: = σ for
777: ln(2) ≈ 1.386
559:Five-number summary
301:Data set in a table
62:interquartile range
3605:Spatial statistics
3485:Medical statistics
3385:First hitting time
3339:Whittle likelihood
2990:Degrees of freedom
2985:Multivariate ANOVA
2918:Heteroscedasticity
2730:Bayesian estimator
2695:Bayesian inference
2544:Kolmogorov–Smirnov
2429:Randomization test
2399:Testing hypotheses
2372:Tolerance interval
2283:Maximum likelihood
2178:Exponential family
2111:Density estimation
2071:Statistical theory
2031:Natural experiment
1977:Scientific control
1894:Survey methodology
1580:Standard deviation
1059:
1020:
949:
869:
846:, is +0.67. Given
824:, or Gaussian. If
810:standard deviation
715:
655:
573:(which yields the
68:) is a measure of
54:
48:(pdf) of a Normal
3707:
3706:
3645:
3644:
3641:
3640:
3580:National accounts
3550:Actuarial science
3542:Social statistics
3435:
3434:
3431:
3430:
3427:
3426:
3362:Survival function
3347:
3346:
3209:Granger causality
3050:Contingency table
3025:Survival analysis
3002:
3001:
2998:
2997:
2854:Linear regression
2749:
2748:
2745:
2744:
2720:Credible interval
2689:
2688:
2472:
2471:
2288:Method of moments
2157:Parametric family
2118:Statistical model
2048:
2047:
2044:
2043:
1962:Random assignment
1884:Statistical power
1818:
1817:
1814:
1813:
1663:Contingency table
1633:
1632:
1500:Generalized/power
1376:Media related to
1328:Studentlitteratur
1252:978-3-642-23502-3
1222:978-0-12-374388-6
1149:978-1-85233-896-1
1079:Interdecile range
1017:
946:
866:
797:
796:
730:quantile function
728:where CDF is the
692:
632:
467:= 119 - 31 = 88.
457:
456:
287:second quartile Q
254:number of values
139:trimmed estimator
16:(Redirected from
3727:
3720:Scale statistics
3695:
3694:
3683:
3682:
3672:
3671:
3657:
3656:
3560:Crime statistics
3454:
3441:
3358:
3324:Fourier analysis
3311:Frequency domain
3291:
3238:
3204:Structural break
3164:
3113:Cluster analysis
3060:Log-linear model
3033:
3008:
2949:
2923:Homoscedasticity
2779:
2755:
2674:
2666:
2658:
2657:(Kruskal–Wallis)
2642:
2627:
2582:Cross validation
2567:
2549:Anderson–Darling
2496:
2483:
2454:Likelihood-ratio
2446:Parametric tests
2424:Permutation test
2407:1- & 2-tails
2298:Minimum distance
2270:Point estimation
2266:
2217:Optimal decision
2168:
2067:
2054:
2036:Quasi-experiment
1986:Adaptive designs
1837:
1824:
1701:Rank correlation
1463:
1454:
1441:
1408:
1401:
1394:
1385:
1375:
1359:
1356:
1350:
1349:
1319:
1308:
1307:
1293:
1287:
1286:
1280:
1271:
1265:
1264:
1236:
1227:
1226:
1208:
1202:
1187:
1181:
1180:
1160:
1154:
1153:
1125:
1090:
1029:
1027:
1026:
1021:
1019:
1018:
1010:
1001:
1000:
981:
980:
958:
956:
955:
950:
948:
947:
939:
930:
929:
910:
909:
878:
876:
875:
870:
868:
867:
859:
812:of a population
738:
724:
722:
721:
716:
702:
701:
693:
690:
684:
683:
664:
662:
661:
656:
642:
641:
633:
630:
624:
623:
308:
277:= median of the
272:third quartile Q
264:= median of the
259:first quartile Q
224:of the dataset.
207:central tendency
51:
21:
3735:
3734:
3730:
3729:
3728:
3726:
3725:
3724:
3710:
3709:
3708:
3703:
3666:
3637:
3599:
3536:
3522:quality control
3489:
3471:Clinical trials
3448:
3423:
3407:
3395:Hazard function
3389:
3343:
3305:
3289:
3252:
3248:Breusch–Godfrey
3236:
3213:
3153:
3128:Factor analysis
3074:
3055:Graphical model
3027:
2994:
2961:
2947:
2927:
2881:
2848:
2810:
2773:
2772:
2741:
2685:
2672:
2664:
2656:
2640:
2625:
2604:Rank statistics
2598:
2577:Model selection
2565:
2523:Goodness of fit
2517:
2494:
2468:
2440:
2393:
2338:
2327:Median unbiased
2255:
2166:
2099:Order statistic
2061:
2040:
2007:
1981:
1933:
1888:
1831:
1829:Data collection
1810:
1722:
1677:
1651:
1629:
1589:
1541:
1458:Continuous data
1448:
1435:
1417:
1412:
1368:
1363:
1362:
1357:
1353:
1338:
1330:. p. 348.
1321:
1320:
1311:
1295:
1294:
1290:
1278:
1273:
1272:
1268:
1253:
1238:
1237:
1230:
1223:
1210:
1209:
1205:
1188:
1184:
1177:
1162:
1161:
1157:
1150:
1127:
1126:
1113:
1108:
1088:
1075:
1048:
992:
972:
967:
966:
921:
901:
896:
895:
852:
851:
845:
838:
802:
688:
675:
670:
669:
628:
615:
610:
609:
604:
597:
590:
583:
567:
549:
539:
529:
522:
512:
502:
492:
476:
473:
466:
462:
412:
410:
345:
343:
336:
334:
303:
298:
290:
275:
268:smallest values
262:
242:
238:
233:
167:breakdown point
159:
134:
131:
124:
117:
106:
99:
49:
35:
28:
23:
22:
15:
12:
11:
5:
3733:
3731:
3723:
3722:
3712:
3711:
3705:
3704:
3702:
3701:
3689:
3677:
3663:
3650:
3647:
3646:
3643:
3642:
3639:
3638:
3636:
3635:
3630:
3625:
3620:
3615:
3609:
3607:
3601:
3600:
3598:
3597:
3592:
3587:
3582:
3577:
3572:
3567:
3562:
3557:
3552:
3546:
3544:
3538:
3537:
3535:
3534:
3529:
3524:
3515:
3510:
3505:
3499:
3497:
3491:
3490:
3488:
3487:
3482:
3477:
3468:
3466:Bioinformatics
3462:
3460:
3450:
3449:
3444:
3437:
3436:
3433:
3432:
3429:
3428:
3425:
3424:
3422:
3421:
3415:
3413:
3409:
3408:
3406:
3405:
3399:
3397:
3391:
3390:
3388:
3387:
3382:
3377:
3372:
3366:
3364:
3355:
3349:
3348:
3345:
3344:
3342:
3341:
3336:
3331:
3326:
3321:
3315:
3313:
3307:
3306:
3304:
3303:
3298:
3293:
3285:
3280:
3275:
3274:
3273:
3271:partial (PACF)
3262:
3260:
3254:
3253:
3251:
3250:
3245:
3240:
3232:
3227:
3221:
3219:
3218:Specific tests
3215:
3214:
3212:
3211:
3206:
3201:
3196:
3191:
3186:
3181:
3176:
3170:
3168:
3161:
3155:
3154:
3152:
3151:
3150:
3149:
3148:
3147:
3132:
3131:
3130:
3120:
3118:Classification
3115:
3110:
3105:
3100:
3095:
3090:
3084:
3082:
3076:
3075:
3073:
3072:
3067:
3065:McNemar's test
3062:
3057:
3052:
3047:
3041:
3039:
3029:
3028:
3011:
3004:
3003:
3000:
2999:
2996:
2995:
2993:
2992:
2987:
2982:
2977:
2971:
2969:
2963:
2962:
2960:
2959:
2943:
2937:
2935:
2929:
2928:
2926:
2925:
2920:
2915:
2910:
2905:
2903:Semiparametric
2900:
2895:
2889:
2887:
2883:
2882:
2880:
2879:
2874:
2869:
2864:
2858:
2856:
2850:
2849:
2847:
2846:
2841:
2836:
2831:
2826:
2820:
2818:
2812:
2811:
2809:
2808:
2803:
2798:
2793:
2787:
2785:
2775:
2774:
2771:
2770:
2765:
2759:
2758:
2751:
2750:
2747:
2746:
2743:
2742:
2740:
2739:
2738:
2737:
2727:
2722:
2717:
2716:
2715:
2710:
2699:
2697:
2691:
2690:
2687:
2686:
2684:
2683:
2678:
2677:
2676:
2668:
2660:
2644:
2641:(Mann–Whitney)
2636:
2635:
2634:
2621:
2620:
2619:
2608:
2606:
2600:
2599:
2597:
2596:
2595:
2594:
2589:
2584:
2574:
2569:
2566:(Shapiro–Wilk)
2561:
2556:
2551:
2546:
2541:
2533:
2527:
2525:
2519:
2518:
2516:
2515:
2507:
2498:
2486:
2480:
2478:Specific tests
2474:
2473:
2470:
2469:
2467:
2466:
2461:
2456:
2450:
2448:
2442:
2441:
2439:
2438:
2433:
2432:
2431:
2421:
2420:
2419:
2409:
2403:
2401:
2395:
2394:
2392:
2391:
2390:
2389:
2384:
2374:
2369:
2364:
2359:
2354:
2348:
2346:
2340:
2339:
2337:
2336:
2331:
2330:
2329:
2324:
2323:
2322:
2317:
2302:
2301:
2300:
2295:
2290:
2285:
2274:
2272:
2263:
2257:
2256:
2254:
2253:
2248:
2243:
2242:
2241:
2231:
2226:
2225:
2224:
2214:
2213:
2212:
2207:
2202:
2192:
2187:
2182:
2181:
2180:
2175:
2170:
2154:
2153:
2152:
2147:
2142:
2132:
2131:
2130:
2125:
2115:
2114:
2113:
2103:
2102:
2101:
2091:
2086:
2081:
2075:
2073:
2063:
2062:
2057:
2050:
2049:
2046:
2045:
2042:
2041:
2039:
2038:
2033:
2028:
2023:
2017:
2015:
2009:
2008:
2006:
2005:
2000:
1995:
1989:
1987:
1983:
1982:
1980:
1979:
1974:
1969:
1964:
1959:
1954:
1949:
1943:
1941:
1935:
1934:
1932:
1931:
1929:Standard error
1926:
1921:
1916:
1915:
1914:
1909:
1898:
1896:
1890:
1889:
1887:
1886:
1881:
1876:
1871:
1866:
1861:
1859:Optimal design
1856:
1851:
1845:
1843:
1833:
1832:
1827:
1820:
1819:
1816:
1815:
1812:
1811:
1809:
1808:
1803:
1798:
1793:
1788:
1783:
1778:
1773:
1768:
1763:
1758:
1753:
1748:
1743:
1738:
1732:
1730:
1724:
1723:
1721:
1720:
1715:
1714:
1713:
1708:
1698:
1693:
1687:
1685:
1679:
1678:
1676:
1675:
1670:
1665:
1659:
1657:
1656:Summary tables
1653:
1652:
1650:
1649:
1643:
1641:
1635:
1634:
1631:
1630:
1628:
1627:
1626:
1625:
1620:
1615:
1605:
1599:
1597:
1591:
1590:
1588:
1587:
1582:
1577:
1572:
1567:
1562:
1557:
1551:
1549:
1543:
1542:
1540:
1539:
1534:
1529:
1528:
1527:
1522:
1517:
1512:
1507:
1502:
1497:
1492:
1490:Contraharmonic
1487:
1482:
1471:
1469:
1460:
1450:
1449:
1444:
1437:
1436:
1434:
1433:
1428:
1422:
1419:
1418:
1413:
1411:
1410:
1403:
1396:
1388:
1382:
1381:
1367:
1366:External links
1364:
1361:
1360:
1351:
1336:
1309:
1288:
1266:
1251:
1228:
1221:
1203:
1182:
1175:
1155:
1148:
1110:
1109:
1107:
1104:
1103:
1102:
1096:
1094:Probable error
1091:
1082:
1074:
1071:
1047:
1044:
1031:
1030:
1016:
1013:
1007:
1004:
999:
995:
990:
987:
984:
979:
975:
960:
959:
945:
942:
936:
933:
928:
924:
919:
916:
913:
908:
904:
865:
862:
843:
836:
830:standard score
801:
798:
795:
794:
791:
788:
782:
781:
771:
768:
762:
761:
758:
755:
749:
748:
745:
742:
726:
725:
714:
711:
708:
705:
700:
697:
687:
682:
678:
666:
665:
654:
651:
648:
645:
640:
637:
627:
622:
618:
602:
595:
588:
581:
566:
563:
555:
554:
551:
547:
541:
537:
531:
527:
520:
514:
510:
504:
500:
494:
490:
474:
472:
469:
464:
460:
455:
454:
451:
447:
446:
443:
439:
438:
435:
431:
430:
427:
423:
422:
419:
415:
414:
408:
405:
402:
398:
397:
395:
392:
388:
387:
384:
380:
379:
376:
372:
371:
368:
364:
363:
360:
356:
355:
352:
348:
347:
341:
338:
332:
329:
326:
322:
321:
318:
315:
312:
302:
299:
297:
294:
288:
283:
282:
281:largest values
273:
269:
260:
246:Given an even
240:
236:
232:
229:
158:
155:
132:
129:
122:
115:
104:
97:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3732:
3721:
3718:
3717:
3715:
3700:
3699:
3690:
3688:
3687:
3678:
3676:
3675:
3670:
3664:
3662:
3661:
3652:
3651:
3648:
3634:
3631:
3629:
3628:Geostatistics
3626:
3624:
3621:
3619:
3616:
3614:
3611:
3610:
3608:
3606:
3602:
3596:
3595:Psychometrics
3593:
3591:
3588:
3586:
3583:
3581:
3578:
3576:
3573:
3571:
3568:
3566:
3563:
3561:
3558:
3556:
3553:
3551:
3548:
3547:
3545:
3543:
3539:
3533:
3530:
3528:
3525:
3523:
3519:
3516:
3514:
3511:
3509:
3506:
3504:
3501:
3500:
3498:
3496:
3492:
3486:
3483:
3481:
3478:
3476:
3472:
3469:
3467:
3464:
3463:
3461:
3459:
3458:Biostatistics
3455:
3451:
3447:
3442:
3438:
3420:
3419:Log-rank test
3417:
3416:
3414:
3410:
3404:
3401:
3400:
3398:
3396:
3392:
3386:
3383:
3381:
3378:
3376:
3373:
3371:
3368:
3367:
3365:
3363:
3359:
3356:
3354:
3350:
3340:
3337:
3335:
3332:
3330:
3327:
3325:
3322:
3320:
3317:
3316:
3314:
3312:
3308:
3302:
3299:
3297:
3294:
3292:
3290:(Box–Jenkins)
3286:
3284:
3281:
3279:
3276:
3272:
3269:
3268:
3267:
3264:
3263:
3261:
3259:
3255:
3249:
3246:
3244:
3243:Durbin–Watson
3241:
3239:
3233:
3231:
3228:
3226:
3225:Dickey–Fuller
3223:
3222:
3220:
3216:
3210:
3207:
3205:
3202:
3200:
3199:Cointegration
3197:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3174:Decomposition
3172:
3171:
3169:
3165:
3162:
3160:
3156:
3146:
3143:
3142:
3141:
3138:
3137:
3136:
3133:
3129:
3126:
3125:
3124:
3121:
3119:
3116:
3114:
3111:
3109:
3106:
3104:
3101:
3099:
3096:
3094:
3091:
3089:
3086:
3085:
3083:
3081:
3077:
3071:
3068:
3066:
3063:
3061:
3058:
3056:
3053:
3051:
3048:
3046:
3045:Cohen's kappa
3043:
3042:
3040:
3038:
3034:
3030:
3026:
3022:
3018:
3014:
3009:
3005:
2991:
2988:
2986:
2983:
2981:
2978:
2976:
2973:
2972:
2970:
2968:
2964:
2958:
2954:
2950:
2944:
2942:
2939:
2938:
2936:
2934:
2930:
2924:
2921:
2919:
2916:
2914:
2911:
2909:
2906:
2904:
2901:
2899:
2898:Nonparametric
2896:
2894:
2891:
2890:
2888:
2884:
2878:
2875:
2873:
2870:
2868:
2865:
2863:
2860:
2859:
2857:
2855:
2851:
2845:
2842:
2840:
2837:
2835:
2832:
2830:
2827:
2825:
2822:
2821:
2819:
2817:
2813:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2788:
2786:
2784:
2780:
2776:
2769:
2766:
2764:
2761:
2760:
2756:
2752:
2736:
2733:
2732:
2731:
2728:
2726:
2723:
2721:
2718:
2714:
2711:
2709:
2706:
2705:
2704:
2701:
2700:
2698:
2696:
2692:
2682:
2679:
2675:
2669:
2667:
2661:
2659:
2653:
2652:
2651:
2648:
2647:Nonparametric
2645:
2643:
2637:
2633:
2630:
2629:
2628:
2622:
2618:
2617:Sample median
2615:
2614:
2613:
2610:
2609:
2607:
2605:
2601:
2593:
2590:
2588:
2585:
2583:
2580:
2579:
2578:
2575:
2573:
2570:
2568:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2538:
2534:
2532:
2529:
2528:
2526:
2524:
2520:
2514:
2512:
2508:
2506:
2504:
2499:
2497:
2492:
2488:
2487:
2484:
2481:
2479:
2475:
2465:
2462:
2460:
2457:
2455:
2452:
2451:
2449:
2447:
2443:
2437:
2434:
2430:
2427:
2426:
2425:
2422:
2418:
2415:
2414:
2413:
2410:
2408:
2405:
2404:
2402:
2400:
2396:
2388:
2385:
2383:
2380:
2379:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2349:
2347:
2345:
2341:
2335:
2332:
2328:
2325:
2321:
2318:
2316:
2313:
2312:
2311:
2308:
2307:
2306:
2303:
2299:
2296:
2294:
2291:
2289:
2286:
2284:
2281:
2280:
2279:
2276:
2275:
2273:
2271:
2267:
2264:
2262:
2258:
2252:
2249:
2247:
2244:
2240:
2237:
2236:
2235:
2232:
2230:
2227:
2223:
2222:loss function
2220:
2219:
2218:
2215:
2211:
2208:
2206:
2203:
2201:
2198:
2197:
2196:
2193:
2191:
2188:
2186:
2183:
2179:
2176:
2174:
2171:
2169:
2163:
2160:
2159:
2158:
2155:
2151:
2148:
2146:
2143:
2141:
2138:
2137:
2136:
2133:
2129:
2126:
2124:
2121:
2120:
2119:
2116:
2112:
2109:
2108:
2107:
2104:
2100:
2097:
2096:
2095:
2092:
2090:
2087:
2085:
2082:
2080:
2077:
2076:
2074:
2072:
2068:
2064:
2060:
2055:
2051:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2019:
2018:
2016:
2014:
2010:
2004:
2001:
1999:
1996:
1994:
1991:
1990:
1988:
1984:
1978:
1975:
1973:
1970:
1968:
1965:
1963:
1960:
1958:
1955:
1953:
1950:
1948:
1945:
1944:
1942:
1940:
1936:
1930:
1927:
1925:
1924:Questionnaire
1922:
1920:
1917:
1913:
1910:
1908:
1905:
1904:
1903:
1900:
1899:
1897:
1895:
1891:
1885:
1882:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1860:
1857:
1855:
1852:
1850:
1847:
1846:
1844:
1842:
1838:
1834:
1830:
1825:
1821:
1807:
1804:
1802:
1799:
1797:
1794:
1792:
1789:
1787:
1784:
1782:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1757:
1754:
1752:
1751:Control chart
1749:
1747:
1744:
1742:
1739:
1737:
1734:
1733:
1731:
1729:
1725:
1719:
1716:
1712:
1709:
1707:
1704:
1703:
1702:
1699:
1697:
1694:
1692:
1689:
1688:
1686:
1684:
1680:
1674:
1671:
1669:
1666:
1664:
1661:
1660:
1658:
1654:
1648:
1645:
1644:
1642:
1640:
1636:
1624:
1621:
1619:
1616:
1614:
1611:
1610:
1609:
1606:
1604:
1601:
1600:
1598:
1596:
1592:
1586:
1583:
1581:
1578:
1576:
1573:
1571:
1568:
1566:
1563:
1561:
1558:
1556:
1553:
1552:
1550:
1548:
1544:
1538:
1535:
1533:
1530:
1526:
1523:
1521:
1518:
1516:
1513:
1511:
1508:
1506:
1503:
1501:
1498:
1496:
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1455:
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1416:
1409:
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1397:
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1389:
1386:
1379:
1374:
1370:
1369:
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1355:
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1347:
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1333:
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1325:
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1301:
1300:
1292:
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1284:
1277:
1270:
1267:
1262:
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1243:
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1233:
1229:
1224:
1218:
1214:
1207:
1204:
1200:
1199:1-58488-059-7
1196:
1193:, CRC Press.
1192:
1186:
1183:
1178:
1176:0-19-914391-9
1172:
1168:
1167:
1159:
1156:
1151:
1145:
1141:
1137:
1133:
1132:
1124:
1122:
1120:
1118:
1116:
1112:
1105:
1100:
1097:
1095:
1092:
1086:
1083:
1080:
1077:
1076:
1072:
1070:
1068:
1064:
1056:
1052:
1045:
1043:
1041:
1036:
1011:
1005:
997:
993:
988:
982:
977:
973:
965:
964:
963:
940:
934:
926:
922:
917:
911:
906:
902:
894:
893:
892:
890:
886:
882:
860:
850: =
849:
842:
835:
831:
827:
823:
819:
815:
811:
807:
799:
792:
789:
787:
784:
783:
780:
776:
772:
769:
767:
764:
763:
759:
756:
754:
751:
750:
746:
743:
741:Distribution
740:
739:
736:
733:
731:
712:
706:
698:
695:
685:
680:
676:
668:
667:
652:
646:
638:
635:
625:
620:
616:
608:
607:
606:
601:
594:
587:
580:
576:
572:
565:Distributions
564:
562:
560:
552:
546:
542:
536:
532:
526:
519:
515:
509:
505:
499:
495:
489:
485:
484:
483:
481:
470:
468:
452:
449:
448:
444:
441:
440:
436:
433:
432:
428:
425:
424:
420:
417:
416:
403:
400:
399:
396:
393:
390:
389:
385:
382:
381:
377:
374:
373:
369:
366:
365:
361:
358:
357:
353:
350:
349:
327:
324:
323:
319:
316:
309:
306:
300:
295:
293:
291:
280:
276:
270:
267:
263:
257:
256:
255:
253:
249:
244:
230:
228:
225:
223:
219:
215:
210:
208:
204:
199:
197:
193:
188:
186:
181:
179:
175:
170:
168:
164:
161:Unlike total
156:
154:
152:
148:
144:
140:
135:
128:
121:
114:
110:
103:
95:
91:
87:
83:
82:fourth spread
79:
75:
71:
67:
63:
59:
47:
43:
39:
33:
19:
3696:
3684:
3665:
3658:
3570:Econometrics
3520: /
3503:Chemometrics
3480:Epidemiology
3473: /
3446:Applications
3288:ARIMA model
3235:Q-statistic
3184:Stationarity
3080:Multivariate
3023: /
3019: /
3017:Multivariate
3015: /
2955: /
2951: /
2725:Bayes factor
2624:Signed rank
2536:
2510:
2502:
2490:
2185:Completeness
2021:Cohort study
1919:Opinion poll
1854:Missing data
1841:Study design
1796:Scatter plot
1718:Scatter plot
1711:Spearman's ρ
1673:Grouped data
1564:
1354:
1323:
1298:
1291:
1282:
1269:
1241:
1212:
1206:
1190:
1185:
1165:
1158:
1130:
1066:
1060:
1034:
1032:
961:
888:
884:
880:
847:
840:
833:
825:
817:
813:
803:
778:
774:
734:
727:
599:
592:
585:
578:
568:
556:
544:
534:
524:
517:
507:
497:
487:
477:
458:
304:
286:
284:
278:
271:
265:
258:
251:
247:
245:
234:
226:
211:
200:
189:
182:
171:
160:
136:
126:
119:
112:
101:
85:
81:
77:
73:
65:
61:
55:
3698:WikiProject
3613:Cartography
3575:Jurimetrics
3527:Reliability
3258:Time domain
3237:(Ljung–Box)
3159:Time-series
3037:Categorical
3021:Time-series
3013:Categorical
2948:(Bernoulli)
2783:Correlation
2763:Correlation
2559:Jarque–Bera
2531:Chi-squared
2293:M-estimator
2246:Asymptotics
2190:Sufficiency
1957:Interaction
1869:Replication
1849:Effect size
1806:Violin plot
1786:Radar chart
1766:Forest plot
1756:Correlogram
1706:Kendall's τ
90:percentiles
3565:Demography
3283:ARMA model
3088:Regression
2665:(Friedman)
2626:(Wilcoxon)
2564:Normality
2554:Lilliefors
2501:Student's
2377:Resampling
2251:Robustness
2239:divergence
2229:Efficiency
2167:(monotone)
2162:Likelihood
2079:Population
1912:Stratified
1864:Population
1683:Dependence
1639:Count data
1570:Percentile
1547:Dispersion
1480:Arithmetic
1415:Statistics
1337:9144250517
1106:References
78:middle 50%
52:Population
2946:Logistic
2713:posterior
2639:Rank sum
2387:Jackknife
2382:Bootstrap
2200:Bootstrap
2135:Parameter
2084:Statistic
1879:Statistic
1791:Run chart
1776:Pie chart
1771:Histogram
1761:Fan chart
1736:Bar chart
1618:L-moments
1505:Geometric
1261:763157853
1015:¯
989:σ
944:¯
918:σ
864:¯
804:The IQR,
696:−
636:−
463:− Q
320:Quartile
231:Algorithm
174:box plots
94:quartiles
86:H‑spread.
74:midspread
3714:Category
3660:Category
3353:Survival
3230:Johansen
2953:Binomial
2908:Isotonic
2495:(normal)
2140:location
1947:Blocking
1902:Sampling
1781:Q–Q plot
1746:Box plot
1728:Graphics
1623:Skewness
1613:Kurtosis
1585:Variance
1515:Heronian
1510:Harmonic
1346:18454776
1201:page 18.
1085:Midhinge
1073:See also
1067:whiskers
1063:outliers
1046:Outliers
1040:Q–Q plot
480:box plot
296:Examples
222:skewness
214:outliers
192:midhinge
151:box plot
125:−
3686:Commons
3633:Kriging
3518:Process
3475:studies
3334:Wavelet
3167:General
2334:Plug-in
2128:L space
1907:Cluster
1608:Moments
1426:Outline
766:Laplace
744:Median
317:Median
250:or odd
198:(MAD).
187:rates.
111:), and
42:Boxplot
3555:Census
3145:Normal
3093:Manova
2913:Robust
2663:2-way
2655:1-way
2493:-test
2164:
1741:Biplot
1532:Median
1525:Lehmer
1467:Center
1344:
1334:
1259:
1249:
1219:
1197:
1173:
1146:
808:, and
786:Cauchy
753:Normal
203:median
185:income
109:median
60:, the
50:N(0,σ)
3179:Trend
2708:prior
2650:anova
2539:-test
2513:-test
2505:-test
2412:Power
2357:Pivot
2150:shape
2145:scale
1595:Shape
1575:Range
1520:Heinz
1495:Cubic
1431:Index
1306:–148.
1279:(PDF)
887:, if
503:= 8.5
239:and Q
218:below
216:(see
163:range
143:range
107:(the
84:, or
3412:Test
2612:Sign
2464:Wald
1537:Mode
1475:Mean
1342:OCLC
1332:ISBN
1257:OCLC
1247:ISBN
1217:ISBN
1195:ISBN
1171:ISBN
1144:ISBN
879:and
848:mean
806:mean
747:IQR
707:0.75
647:0.25
453:177
445:155
437:119
429:119
421:116
411:=119
404:115
285:The
252:2n+1
201:The
2592:BIC
2587:AIC
1304:147
1136:doi
820:is
793:2γ
691:CDF
631:CDF
530:= 2
513:= 9
493:= 7
450:13
442:12
434:11
426:10
394:87
386:75
378:47
370:31
362:31
344:=31
335:=87
157:Use
66:IQR
56:In
3716::
1340:.
1326:.
1312:^
1281:.
1255:.
1231:^
1142:.
1114:^
790:μ
770:μ
757:μ
732:.
561:.
523:-
482::
418:9
401:8
391:7
383:6
375:5
367:4
359:3
354:7
351:2
328:7
325:1
314:x
311:i
248:2n
209:.
180:.
153:.
80:,
76:,
2537:G
2511:F
2503:t
2491:Z
2210:V
2205:U
1407:e
1400:t
1393:v
1348:.
1263:.
1225:.
1179:.
1152:.
1138::
1035:P
1012:P
1006:+
1003:)
998:3
994:z
986:(
983:=
978:3
974:Q
941:P
935:+
932:)
927:1
923:z
915:(
912:=
907:1
903:Q
889:P
885:P
861:P
844:3
841:z
837:1
834:z
826:P
818:P
814:P
779:b
775:b
773:2
713:,
710:)
704:(
699:1
686:=
681:3
677:Q
653:,
650:)
644:(
639:1
626:=
621:1
617:Q
603:3
600:Q
596:3
593:Q
589:1
586:Q
582:1
579:Q
548:3
545:Q
538:1
535:Q
528:1
525:Q
521:3
518:Q
511:3
508:Q
501:2
498:Q
491:1
488:Q
465:1
461:3
409:3
407:Q
342:1
340:Q
333:2
331:Q
289:2
279:n
274:3
266:n
261:1
241:1
237:3
133:.
130:1
127:Q
123:3
120:Q
116:3
113:Q
105:2
102:Q
98:1
64:(
34:.
20:)
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