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Statistical dispersion

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3317: 133: 3303: 36: 3341: 3329: 807:. A system of a large number of particles is characterized by the mean values of a relatively few number of macroscopic quantities such as temperature, energy, and density. The standard deviation is an important measure in fluctuation theory, which explains many physical phenomena, including why the sky is blue. 840:(MPS) is a change from one probability distribution A to another probability distribution B, where B is formed by spreading out one or more portions of A's probability density function while leaving the mean (the expected value) unchanged. The concept of a mean-preserving spread provides a 828:, that is, one and the same subject differing in tests taken at different times or in other differing conditions. Such types of variability are also seen in the arena of manufactured products; even there, the meticulous scientist finds variation. 581:: While the entropy of a discrete variable is location-invariant and scale-independent, and therefore not a measure of dispersion in the above sense, the entropy of a continuous variable is location invariant and additive in scale: If 844:
of probability distributions according to their dispersions: of two probability distributions, one may be ranked as having more dispersion than the other, or alternatively neither may be ranked as having more dispersion.
725: 470: 176:. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. 803:
in interpreting and reporting the measured results. One may assume that the quantity being measured is stable, and that the variation between measurements is due to
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being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include:
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Example of samples from two populations with the same mean but different dispersion. The blue population is much more dispersed than the red population.
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that is zero if all the data are the same and increases as the data become more diverse.
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All the above measures of statistical dispersion have the useful property that they are
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is stretched or squeezed. Common examples of measures of statistical dispersion are the
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Rothschild, Michael; Stiglitz, Joseph (1970). "Increasing risk I: A definition".
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Statistical property quantifying how much a collection of data is spread out
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can be used for applications where the noise disrupts convergence. The
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can be used to counteract linear frequency drift sensitivity.
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Some measures of dispersion have specialized purposes. The
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Autoregressive conditional heteroskedasticity (ARCH)
831: 60:. Unsourced material may be challenged and removed. 2406: 1005: 719: 657: 622: 602: 538: 518: 494: 464: 411: 391: 368: 330: 303: 914:NIST/SEMATECH e-Handbook of Statistical Methods. 3359: 2492:Multivariate adaptive regression splines (MARS) 934:"Allan Variance -- Overview by David W. Allan" 1047: 526:, that is, ignores a preceding negative sign 233:(also known as Gini mean absolute difference) 779:. One measure that does so is the discrete 1092: 1054: 1040: 273:are those unaffected by a small number of 202:Most measures of dispersion have the same 179:Dispersion is contrasted with location or 1705: 980: 254:These are frequently used (together with 120:Learn how and when to remove this message 916:"1.3.6.4. Location and Scale Parameters" 731:There are other measures of dispersion: 610:is the entropy of a continuous variable 131: 14: 3360: 3018:Kaplan–Meier estimator (product limit) 3091: 2658: 2405: 1704: 1474: 1091: 1035: 3368:Statistical deviation and dispersion 3328: 3028:Accelerated failure time (AFT) model 818:to the phenomenon: It may be due to 266:, in which capacity they are called 245:(or simply called average deviation) 58:adding citations to reliable sources 29: 3340: 2623:Analysis of variance (ANOVA, anova) 1475: 24: 2718:Cochran–Mantel–Haenszel statistics 1344:Pearson product-moment correlation 565:Quartile coefficient of dispersion 187:Measures of statistical dispersion 25: 3389: 720:{\displaystyle H(z)=H(x)+\log(a)} 549:Other measures of dispersion are 193:measure of statistical dispersion 3339: 3327: 3315: 3302: 3301: 3092: 832:A partial ordering of dispersion 34: 2977:Least-squares spectral analysis 752:is used and when this ratio is 277:, and include the IQR and MAD. 45:needs additional citations for 1958:Mean-unbiased minimum-variance 1061: 999: 974: 950: 926: 922:. U.S. Department of Commerce. 907: 714: 708: 696: 690: 681: 675: 597: 591: 488: 480: 465:{\displaystyle S_{Y}=|a|S_{X}} 448: 440: 13: 1: 3271:Geographic information system 2487:Simultaneous equations models 981:McQuarrie, Donald A. (1976). 900: 2454:Coefficient of determination 2065:Uniformly most powerful test 1022:10.1016/0022-0531(70)90038-4 870:Probability density function 825:intra-individual variability 820:inter-individual variability 7: 3023:Proportional hazards models 2967:Spectral density estimation 2949:Vector autoregression (VAR) 2383:Maximum posterior estimator 1615:Randomized controlled trial 848: 797:precise, i.e., reproducible 249:Distance standard deviation 160:) is the extent to which a 10: 3394: 2783:Multivariate distributions 1203:Average absolute deviation 1009:Journal of Economic Theory 799:, and there is additional 786: 243:Average absolute deviation 3297: 3251: 3188: 3141: 3104: 3100: 3087: 3059: 3041: 3008: 2999: 2957: 2904: 2865: 2814: 2805: 2771:Structural equation model 2726: 2683: 2679: 2654: 2613: 2579: 2533: 2500: 2462: 2429: 2425: 2401: 2341: 2250: 2169: 2133: 2124: 2107:Score/Lagrange multiplier 2092: 2045: 1990: 1916: 1907: 1717: 1713: 1700: 1659: 1633: 1585: 1540: 1522:Sample size determination 1487: 1483: 1470: 1374: 1329: 1303: 1285: 1241: 1193: 1113: 1104: 1100: 1087: 1069: 750:coefficient of dispersion 237:Median absolute deviation 3266:Environmental statistics 2788:Elliptical distributions 2581:Generalized linear model 2510:Simple linear regression 2280:Hodges–Lehmann estimator 1737:Probability distribution 1646:Stochastic approximation 1208:Coefficient of variation 985:. NY: Harper & Row. 890:Robust measures of scale 570:Relative mean difference 560:Coefficient of variation 271:Robust measures of scale 231:Mean absolute difference 69:"Statistical dispersion" 2926:Cross-correlation (XCF) 2534:Non-standard predictors 1968:Lehmann–ScheffĂ© theorem 1641:Adaptive clinical trial 880:Measurement uncertainty 801:inter-rater variability 419:should have dispersion 288:. This means that if a 18:Scattering (statistics) 3378:Accuracy and precision 3322:Mathematics portal 3143:Engineering statistics 3051:Nelson–Aalen estimator 2628:Analysis of covariance 2515:Ordinary least squares 2439:Pearson product-moment 1843:Statistical functional 1754:Empirical distribution 1587:Controlled experiments 1316:Frequency distribution 1094:Descriptive statistics 885:Precision (statistics) 838:mean-preserving spread 742:Variance-to-mean ratio 721: 659: 658:{\displaystyle z=ax+b} 624: 604: 540: 520: 496: 466: 413: 393: 370: 369:{\displaystyle Y=aX+b} 332: 305: 137: 3238:Population statistics 3180:System identification 2914:Autocorrelation (ACF) 2842:Exponential smoothing 2756:Discriminant analysis 2751:Canonical correlation 2615:Partition of variance 2477:Regression validation 2321:(Jonckheere–Terpstra) 2220:Likelihood-ratio test 1909:Frequentist inference 1821:Location–scale family 1742:Sampling distribution 1707:Statistical inference 1674:Cross-sectional study 1661:Observational studies 1620:Randomized experiment 1449:Stem-and-leaf display 1251:Central limit theorem 983:Statistical Mechanics 875:Qualitative variation 777:qualitative variation 773:categorical variables 722: 660: 625: 605: 572:, equal to twice the 541: 521: 497: 467: 414: 394: 371: 340:linear transformation 333: 331:{\displaystyle S_{X}} 306: 135: 3161:Probabilistic design 2746:Principal components 2589:Exponential families 2541:Nonlinear regression 2520:General linear model 2482:Mixed effects models 2472:Errors and residuals 2449:Confounding variable 2351:Bayesian probability 2329:Van der Waerden test 2319:Ordered alternative 2084:Multiple comparisons 1963:Rao–Blackwellization 1926:Estimating equations 1882:Statistical distance 1600:Factorial experiment 1133:Arithmetic-Geometric 669: 634: 614: 603:{\displaystyle H(z)} 585: 530: 510: 476: 423: 403: 383: 345: 315: 311:has a dispersion of 295: 54:improve this article 3233:Official statistics 3156:Methods engineering 2837:Seasonal adjustment 2605:Poisson regressions 2525:Bayesian regression 2464:Regression analysis 2444:Partial correlation 2416:Regression analysis 2015:Prediction interval 2010:Likelihood interval 2000:Confidence interval 1992:Interval estimation 1953:Unbiased estimators 1771:Model specification 1651:Up-and-down designs 1339:Partial correlation 1295:Index of dispersion 1213:Interquartile range 958:"Hadamard Variance" 860:Circular dispersion 812:biological sciences 805:observational error 495:{\displaystyle |a|} 268:estimates of scale. 220:Interquartile range 174:interquartile range 3373:Summary statistics 3253:Spatial statistics 3133:Medical statistics 3033:First hitting time 2987:Whittle likelihood 2638:Degrees of freedom 2633:Multivariate ANOVA 2566:Heteroscedasticity 2378:Bayesian estimator 2343:Bayesian inference 2192:Kolmogorov–Smirnov 2077:Randomization test 2047:Testing hypotheses 2020:Tolerance interval 1931:Maximum likelihood 1826:Exponential family 1759:Density estimation 1719:Statistical theory 1679:Natural experiment 1625:Scientific control 1542:Survey methodology 1228:Standard deviation 938:www.allanstime.com 895:Summary statistics 744:– mostly used for 717: 655: 620: 600: 536: 516: 492: 462: 409: 389: 366: 328: 301: 282:location-invariant 215:Standard deviation 170:standard deviation 138: 3355: 3354: 3293: 3292: 3289: 3288: 3228:National accounts 3198:Actuarial science 3190:Social statistics 3083: 3082: 3079: 3078: 3075: 3074: 3010:Survival function 2995: 2994: 2857:Granger causality 2698:Contingency table 2673:Survival analysis 2650: 2649: 2646: 2645: 2502:Linear regression 2397: 2396: 2393: 2392: 2368:Credible interval 2337: 2336: 2120: 2119: 1936:Method of moments 1805:Parametric family 1766:Statistical model 1696: 1695: 1692: 1691: 1610:Random assignment 1532:Statistical power 1466: 1465: 1462: 1461: 1311:Contingency table 1281: 1280: 1148:Generalized/power 865:Dispersion matrix 793:physical sciences 766:Hadamard variance 623:{\displaystyle z} 539:{\displaystyle -} 519:{\displaystyle a} 412:{\displaystyle b} 392:{\displaystyle a} 304:{\displaystyle X} 195:is a nonnegative 130: 129: 122: 104: 16:(Redirected from 3385: 3343: 3342: 3331: 3330: 3320: 3319: 3305: 3304: 3208:Crime statistics 3102: 3101: 3089: 3088: 3006: 3005: 2972:Fourier analysis 2959:Frequency domain 2939: 2886: 2852:Structural break 2812: 2811: 2761:Cluster analysis 2708:Log-linear model 2681: 2680: 2656: 2655: 2597: 2571:Homoscedasticity 2427: 2426: 2403: 2402: 2322: 2314: 2306: 2305:(Kruskal–Wallis) 2290: 2275: 2230:Cross validation 2215: 2197:Anderson–Darling 2144: 2131: 2130: 2102:Likelihood-ratio 2094:Parametric tests 2072:Permutation test 2055:1- & 2-tails 1946:Minimum distance 1918:Point estimation 1914: 1913: 1865:Optimal decision 1816: 1715: 1714: 1702: 1701: 1684:Quasi-experiment 1634:Adaptive designs 1485: 1484: 1472: 1471: 1349:Rank correlation 1111: 1110: 1102: 1101: 1089: 1088: 1056: 1049: 1042: 1033: 1032: 1026: 1025: 1003: 997: 996: 978: 972: 971: 969: 968: 954: 948: 947: 945: 944: 930: 924: 923: 920:www.itl.nist.gov 911: 842:partial ordering 726: 724: 723: 718: 664: 662: 661: 656: 629: 627: 626: 621: 609: 607: 606: 601: 574:Gini coefficient 545: 543: 542: 537: 525: 523: 522: 517: 501: 499: 498: 493: 491: 483: 471: 469: 468: 463: 461: 460: 451: 443: 435: 434: 418: 416: 415: 410: 398: 396: 395: 390: 375: 373: 372: 367: 337: 335: 334: 329: 327: 326: 310: 308: 307: 302: 264:scale parameters 181:central tendency 125: 118: 114: 111: 105: 103: 62: 38: 30: 21: 3393: 3392: 3388: 3387: 3386: 3384: 3383: 3382: 3358: 3357: 3356: 3351: 3314: 3285: 3247: 3184: 3170:quality control 3137: 3119:Clinical trials 3096: 3071: 3055: 3043:Hazard function 3037: 2991: 2953: 2937: 2900: 2896:Breusch–Godfrey 2884: 2861: 2801: 2776:Factor analysis 2722: 2703:Graphical model 2675: 2642: 2609: 2595: 2575: 2529: 2496: 2458: 2421: 2420: 2389: 2333: 2320: 2312: 2304: 2288: 2273: 2252:Rank statistics 2246: 2225:Model selection 2213: 2171:Goodness of fit 2165: 2142: 2116: 2088: 2041: 1986: 1975:Median unbiased 1903: 1814: 1747:Order statistic 1709: 1688: 1655: 1629: 1581: 1536: 1479: 1477:Data collection 1458: 1370: 1325: 1299: 1277: 1237: 1189: 1106:Continuous data 1096: 1083: 1065: 1060: 1030: 1029: 1004: 1000: 993: 979: 975: 966: 964: 956: 955: 951: 942: 940: 932: 931: 927: 912: 908: 903: 851: 834: 789: 670: 667: 666: 635: 632: 631: 615: 612: 611: 586: 583: 582: 531: 528: 527: 511: 508: 507: 487: 479: 477: 474: 473: 456: 452: 447: 439: 430: 426: 424: 421: 420: 404: 401: 400: 384: 381: 380: 346: 343: 342: 322: 318: 316: 313: 312: 296: 293: 292: 290:random variable 286:linear in scale 189: 126: 115: 109: 106: 63: 61: 51: 39: 28: 23: 22: 15: 12: 11: 5: 3391: 3381: 3380: 3375: 3370: 3353: 3352: 3350: 3349: 3337: 3325: 3311: 3298: 3295: 3294: 3291: 3290: 3287: 3286: 3284: 3283: 3278: 3273: 3268: 3263: 3257: 3255: 3249: 3248: 3246: 3245: 3240: 3235: 3230: 3225: 3220: 3215: 3210: 3205: 3200: 3194: 3192: 3186: 3185: 3183: 3182: 3177: 3172: 3163: 3158: 3153: 3147: 3145: 3139: 3138: 3136: 3135: 3130: 3125: 3116: 3114:Bioinformatics 3110: 3108: 3098: 3097: 3085: 3084: 3081: 3080: 3077: 3076: 3073: 3072: 3070: 3069: 3063: 3061: 3057: 3056: 3054: 3053: 3047: 3045: 3039: 3038: 3036: 3035: 3030: 3025: 3020: 3014: 3012: 3003: 2997: 2996: 2993: 2992: 2990: 2989: 2984: 2979: 2974: 2969: 2963: 2961: 2955: 2954: 2952: 2951: 2946: 2941: 2933: 2928: 2923: 2922: 2921: 2919:partial (PACF) 2910: 2908: 2902: 2901: 2899: 2898: 2893: 2888: 2880: 2875: 2869: 2867: 2866:Specific tests 2863: 2862: 2860: 2859: 2854: 2849: 2844: 2839: 2834: 2829: 2824: 2818: 2816: 2809: 2803: 2802: 2800: 2799: 2798: 2797: 2796: 2795: 2780: 2779: 2778: 2768: 2766:Classification 2763: 2758: 2753: 2748: 2743: 2738: 2732: 2730: 2724: 2723: 2721: 2720: 2715: 2713:McNemar's test 2710: 2705: 2700: 2695: 2689: 2687: 2677: 2676: 2652: 2651: 2648: 2647: 2644: 2643: 2641: 2640: 2635: 2630: 2625: 2619: 2617: 2611: 2610: 2608: 2607: 2591: 2585: 2583: 2577: 2576: 2574: 2573: 2568: 2563: 2558: 2553: 2551:Semiparametric 2548: 2543: 2537: 2535: 2531: 2530: 2528: 2527: 2522: 2517: 2512: 2506: 2504: 2498: 2497: 2495: 2494: 2489: 2484: 2479: 2474: 2468: 2466: 2460: 2459: 2457: 2456: 2451: 2446: 2441: 2435: 2433: 2423: 2422: 2419: 2418: 2413: 2407: 2399: 2398: 2395: 2394: 2391: 2390: 2388: 2387: 2386: 2385: 2375: 2370: 2365: 2364: 2363: 2358: 2347: 2345: 2339: 2338: 2335: 2334: 2332: 2331: 2326: 2325: 2324: 2316: 2308: 2292: 2289:(Mann–Whitney) 2284: 2283: 2282: 2269: 2268: 2267: 2256: 2254: 2248: 2247: 2245: 2244: 2243: 2242: 2237: 2232: 2222: 2217: 2214:(Shapiro–Wilk) 2209: 2204: 2199: 2194: 2189: 2181: 2175: 2173: 2167: 2166: 2164: 2163: 2155: 2146: 2134: 2128: 2126:Specific tests 2122: 2121: 2118: 2117: 2115: 2114: 2109: 2104: 2098: 2096: 2090: 2089: 2087: 2086: 2081: 2080: 2079: 2069: 2068: 2067: 2057: 2051: 2049: 2043: 2042: 2040: 2039: 2038: 2037: 2032: 2022: 2017: 2012: 2007: 2002: 1996: 1994: 1988: 1987: 1985: 1984: 1979: 1978: 1977: 1972: 1971: 1970: 1965: 1950: 1949: 1948: 1943: 1938: 1933: 1922: 1920: 1911: 1905: 1904: 1902: 1901: 1896: 1891: 1890: 1889: 1879: 1874: 1873: 1872: 1862: 1861: 1860: 1855: 1850: 1840: 1835: 1830: 1829: 1828: 1823: 1818: 1802: 1801: 1800: 1795: 1790: 1780: 1779: 1778: 1773: 1763: 1762: 1761: 1751: 1750: 1749: 1739: 1734: 1729: 1723: 1721: 1711: 1710: 1698: 1697: 1694: 1693: 1690: 1689: 1687: 1686: 1681: 1676: 1671: 1665: 1663: 1657: 1656: 1654: 1653: 1648: 1643: 1637: 1635: 1631: 1630: 1628: 1627: 1622: 1617: 1612: 1607: 1602: 1597: 1591: 1589: 1583: 1582: 1580: 1579: 1577:Standard error 1574: 1569: 1564: 1563: 1562: 1557: 1546: 1544: 1538: 1537: 1535: 1534: 1529: 1524: 1519: 1514: 1509: 1507:Optimal design 1504: 1499: 1493: 1491: 1481: 1480: 1468: 1467: 1464: 1463: 1460: 1459: 1457: 1456: 1451: 1446: 1441: 1436: 1431: 1426: 1421: 1416: 1411: 1406: 1401: 1396: 1391: 1386: 1380: 1378: 1372: 1371: 1369: 1368: 1363: 1362: 1361: 1356: 1346: 1341: 1335: 1333: 1327: 1326: 1324: 1323: 1318: 1313: 1307: 1305: 1304:Summary tables 1301: 1300: 1298: 1297: 1291: 1289: 1283: 1282: 1279: 1278: 1276: 1275: 1274: 1273: 1268: 1263: 1253: 1247: 1245: 1239: 1238: 1236: 1235: 1230: 1225: 1220: 1215: 1210: 1205: 1199: 1197: 1191: 1190: 1188: 1187: 1182: 1177: 1176: 1175: 1170: 1165: 1160: 1155: 1150: 1145: 1140: 1138:Contraharmonic 1135: 1130: 1119: 1117: 1108: 1098: 1097: 1085: 1084: 1082: 1081: 1076: 1070: 1067: 1066: 1059: 1058: 1051: 1044: 1036: 1028: 1027: 1016:(3): 225–243. 998: 991: 973: 962:www.wriley.com 949: 925: 905: 904: 902: 899: 898: 897: 892: 887: 882: 877: 872: 867: 862: 857: 850: 847: 833: 830: 788: 785: 762:Allan variance 758: 757: 748:when the term 739: 729: 728: 716: 713: 710: 707: 704: 701: 698: 695: 692: 689: 686: 683: 680: 677: 674: 654: 651: 648: 645: 642: 639: 619: 599: 596: 593: 590: 576: 567: 562: 535: 515: 504:absolute value 490: 486: 482: 459: 455: 450: 446: 442: 438: 433: 429: 408: 388: 365: 362: 359: 356: 353: 350: 325: 321: 300: 252: 251: 246: 240: 234: 228: 223: 217: 188: 185: 128: 127: 42: 40: 33: 26: 9: 6: 4: 3: 2: 3390: 3379: 3376: 3374: 3371: 3369: 3366: 3365: 3363: 3348: 3347: 3338: 3336: 3335: 3326: 3324: 3323: 3318: 3312: 3310: 3309: 3300: 3299: 3296: 3282: 3279: 3277: 3276:Geostatistics 3274: 3272: 3269: 3267: 3264: 3262: 3259: 3258: 3256: 3254: 3250: 3244: 3243:Psychometrics 3241: 3239: 3236: 3234: 3231: 3229: 3226: 3224: 3221: 3219: 3216: 3214: 3211: 3209: 3206: 3204: 3201: 3199: 3196: 3195: 3193: 3191: 3187: 3181: 3178: 3176: 3173: 3171: 3167: 3164: 3162: 3159: 3157: 3154: 3152: 3149: 3148: 3146: 3144: 3140: 3134: 3131: 3129: 3126: 3124: 3120: 3117: 3115: 3112: 3111: 3109: 3107: 3106:Biostatistics 3103: 3099: 3095: 3090: 3086: 3068: 3067:Log-rank test 3065: 3064: 3062: 3058: 3052: 3049: 3048: 3046: 3044: 3040: 3034: 3031: 3029: 3026: 3024: 3021: 3019: 3016: 3015: 3013: 3011: 3007: 3004: 3002: 2998: 2988: 2985: 2983: 2980: 2978: 2975: 2973: 2970: 2968: 2965: 2964: 2962: 2960: 2956: 2950: 2947: 2945: 2942: 2940: 2938:(Box–Jenkins) 2934: 2932: 2929: 2927: 2924: 2920: 2917: 2916: 2915: 2912: 2911: 2909: 2907: 2903: 2897: 2894: 2892: 2891:Durbin–Watson 2889: 2887: 2881: 2879: 2876: 2874: 2873:Dickey–Fuller 2871: 2870: 2868: 2864: 2858: 2855: 2853: 2850: 2848: 2847:Cointegration 2845: 2843: 2840: 2838: 2835: 2833: 2830: 2828: 2825: 2823: 2822:Decomposition 2820: 2819: 2817: 2813: 2810: 2808: 2804: 2794: 2791: 2790: 2789: 2786: 2785: 2784: 2781: 2777: 2774: 2773: 2772: 2769: 2767: 2764: 2762: 2759: 2757: 2754: 2752: 2749: 2747: 2744: 2742: 2739: 2737: 2734: 2733: 2731: 2729: 2725: 2719: 2716: 2714: 2711: 2709: 2706: 2704: 2701: 2699: 2696: 2694: 2693:Cohen's kappa 2691: 2690: 2688: 2686: 2682: 2678: 2674: 2670: 2666: 2662: 2657: 2653: 2639: 2636: 2634: 2631: 2629: 2626: 2624: 2621: 2620: 2618: 2616: 2612: 2606: 2602: 2598: 2592: 2590: 2587: 2586: 2584: 2582: 2578: 2572: 2569: 2567: 2564: 2562: 2559: 2557: 2554: 2552: 2549: 2547: 2546:Nonparametric 2544: 2542: 2539: 2538: 2536: 2532: 2526: 2523: 2521: 2518: 2516: 2513: 2511: 2508: 2507: 2505: 2503: 2499: 2493: 2490: 2488: 2485: 2483: 2480: 2478: 2475: 2473: 2470: 2469: 2467: 2465: 2461: 2455: 2452: 2450: 2447: 2445: 2442: 2440: 2437: 2436: 2434: 2432: 2428: 2424: 2417: 2414: 2412: 2409: 2408: 2404: 2400: 2384: 2381: 2380: 2379: 2376: 2374: 2371: 2369: 2366: 2362: 2359: 2357: 2354: 2353: 2352: 2349: 2348: 2346: 2344: 2340: 2330: 2327: 2323: 2317: 2315: 2309: 2307: 2301: 2300: 2299: 2296: 2295:Nonparametric 2293: 2291: 2285: 2281: 2278: 2277: 2276: 2270: 2266: 2265:Sample median 2263: 2262: 2261: 2258: 2257: 2255: 2253: 2249: 2241: 2238: 2236: 2233: 2231: 2228: 2227: 2226: 2223: 2221: 2218: 2216: 2210: 2208: 2205: 2203: 2200: 2198: 2195: 2193: 2190: 2188: 2186: 2182: 2180: 2177: 2176: 2174: 2172: 2168: 2162: 2160: 2156: 2154: 2152: 2147: 2145: 2140: 2136: 2135: 2132: 2129: 2127: 2123: 2113: 2110: 2108: 2105: 2103: 2100: 2099: 2097: 2095: 2091: 2085: 2082: 2078: 2075: 2074: 2073: 2070: 2066: 2063: 2062: 2061: 2058: 2056: 2053: 2052: 2050: 2048: 2044: 2036: 2033: 2031: 2028: 2027: 2026: 2023: 2021: 2018: 2016: 2013: 2011: 2008: 2006: 2003: 2001: 1998: 1997: 1995: 1993: 1989: 1983: 1980: 1976: 1973: 1969: 1966: 1964: 1961: 1960: 1959: 1956: 1955: 1954: 1951: 1947: 1944: 1942: 1939: 1937: 1934: 1932: 1929: 1928: 1927: 1924: 1923: 1921: 1919: 1915: 1912: 1910: 1906: 1900: 1897: 1895: 1892: 1888: 1885: 1884: 1883: 1880: 1878: 1875: 1871: 1870:loss function 1868: 1867: 1866: 1863: 1859: 1856: 1854: 1851: 1849: 1846: 1845: 1844: 1841: 1839: 1836: 1834: 1831: 1827: 1824: 1822: 1819: 1817: 1811: 1808: 1807: 1806: 1803: 1799: 1796: 1794: 1791: 1789: 1786: 1785: 1784: 1781: 1777: 1774: 1772: 1769: 1768: 1767: 1764: 1760: 1757: 1756: 1755: 1752: 1748: 1745: 1744: 1743: 1740: 1738: 1735: 1733: 1730: 1728: 1725: 1724: 1722: 1720: 1716: 1712: 1708: 1703: 1699: 1685: 1682: 1680: 1677: 1675: 1672: 1670: 1667: 1666: 1664: 1662: 1658: 1652: 1649: 1647: 1644: 1642: 1639: 1638: 1636: 1632: 1626: 1623: 1621: 1618: 1616: 1613: 1611: 1608: 1606: 1603: 1601: 1598: 1596: 1593: 1592: 1590: 1588: 1584: 1578: 1575: 1573: 1572:Questionnaire 1570: 1568: 1565: 1561: 1558: 1556: 1553: 1552: 1551: 1548: 1547: 1545: 1543: 1539: 1533: 1530: 1528: 1525: 1523: 1520: 1518: 1515: 1513: 1510: 1508: 1505: 1503: 1500: 1498: 1495: 1494: 1492: 1490: 1486: 1482: 1478: 1473: 1469: 1455: 1452: 1450: 1447: 1445: 1442: 1440: 1437: 1435: 1432: 1430: 1427: 1425: 1422: 1420: 1417: 1415: 1412: 1410: 1407: 1405: 1402: 1400: 1399:Control chart 1397: 1395: 1392: 1390: 1387: 1385: 1382: 1381: 1379: 1377: 1373: 1367: 1364: 1360: 1357: 1355: 1352: 1351: 1350: 1347: 1345: 1342: 1340: 1337: 1336: 1334: 1332: 1328: 1322: 1319: 1317: 1314: 1312: 1309: 1308: 1306: 1302: 1296: 1293: 1292: 1290: 1288: 1284: 1272: 1269: 1267: 1264: 1262: 1259: 1258: 1257: 1254: 1252: 1249: 1248: 1246: 1244: 1240: 1234: 1231: 1229: 1226: 1224: 1221: 1219: 1216: 1214: 1211: 1209: 1206: 1204: 1201: 1200: 1198: 1196: 1192: 1186: 1183: 1181: 1178: 1174: 1171: 1169: 1166: 1164: 1161: 1159: 1156: 1154: 1151: 1149: 1146: 1144: 1141: 1139: 1136: 1134: 1131: 1129: 1126: 1125: 1124: 1121: 1120: 1118: 1116: 1112: 1109: 1107: 1103: 1099: 1095: 1090: 1086: 1080: 1077: 1075: 1072: 1071: 1068: 1064: 1057: 1052: 1050: 1045: 1043: 1038: 1037: 1034: 1023: 1019: 1015: 1011: 1010: 1002: 994: 992:0-06-044366-9 988: 984: 977: 963: 959: 953: 939: 935: 929: 921: 917: 910: 906: 896: 893: 891: 888: 886: 883: 881: 878: 876: 873: 871: 868: 866: 863: 861: 858: 856: 853: 852: 846: 843: 839: 829: 827: 826: 821: 817: 813: 808: 806: 802: 798: 794: 784: 782: 778: 774: 769: 767: 763: 755: 754:dimensionless 751: 747: 743: 740: 737: 734: 733: 732: 711: 705: 702: 699: 693: 687: 684: 678: 672: 652: 649: 646: 643: 640: 637: 617: 594: 588: 580: 577: 575: 571: 568: 566: 563: 561: 558: 557: 556: 554: 553: 552:dimensionless 547: 533: 513: 505: 484: 457: 453: 444: 436: 431: 427: 406: 386: 379: 363: 360: 357: 354: 351: 348: 341: 323: 319: 298: 291: 287: 283: 278: 276: 272: 269: 265: 261: 257: 256:scale factors 250: 247: 244: 241: 238: 235: 232: 229: 227: 224: 221: 218: 216: 213: 212: 211: 209: 205: 200: 198: 194: 184: 182: 177: 175: 171: 167: 163: 159: 155: 151: 148:(also called 147: 143: 134: 124: 121: 113: 110:December 2010 102: 99: 95: 92: 88: 85: 81: 78: 74: 71: â€“  70: 66: 65:Find sources: 59: 55: 49: 48: 43:This article 41: 37: 32: 31: 19: 3344: 3332: 3313: 3306: 3218:Econometrics 3168: / 3151:Chemometrics 3128:Epidemiology 3121: / 3094:Applications 2936:ARIMA model 2883:Q-statistic 2832:Stationarity 2728:Multivariate 2671: / 2667: / 2665:Multivariate 2663: / 2603: / 2599: / 2373:Bayes factor 2272:Signed rank 2184: 2158: 2150: 2138: 1833:Completeness 1669:Cohort study 1567:Opinion poll 1502:Missing data 1489:Study design 1444:Scatter plot 1366:Scatter plot 1359:Spearman's ρ 1321:Grouped data 1194: 1013: 1007: 1001: 982: 976: 965:. Retrieved 961: 952: 941:. Retrieved 937: 928: 919: 909: 835: 824: 823: 819: 815: 809: 790: 770: 759: 730: 550: 548: 285: 281: 279: 267: 253: 201: 192: 190: 178: 162:distribution 157: 153: 149: 145: 139: 116: 107: 97: 90: 83: 76: 64: 52:Please help 47:verification 44: 3346:WikiProject 3261:Cartography 3223:Jurimetrics 3175:Reliability 2906:Time domain 2885:(Ljung–Box) 2807:Time-series 2685:Categorical 2669:Time-series 2661:Categorical 2596:(Bernoulli) 2431:Correlation 2411:Correlation 2207:Jarque–Bera 2179:Chi-squared 1941:M-estimator 1894:Asymptotics 1838:Sufficiency 1605:Interaction 1517:Replication 1497:Effect size 1454:Violin plot 1434:Radar chart 1414:Forest plot 1404:Correlogram 1354:Kendall's τ 197:real number 150:variability 3362:Categories 3213:Demography 2931:ARMA model 2736:Regression 2313:(Friedman) 2274:(Wilcoxon) 2212:Normality 2202:Lilliefors 2149:Student's 2025:Resampling 1899:Robustness 1887:divergence 1877:Efficiency 1815:(monotone) 1810:Likelihood 1727:Population 1560:Stratified 1512:Population 1331:Dependence 1287:Count data 1218:Percentile 1195:Dispersion 1128:Arithmetic 1063:Statistics 967:2021-09-16 943:2021-09-16 901:References 746:count data 260:estimators 146:dispersion 142:statistics 80:newspapers 2594:Logistic 2361:posterior 2287:Rank sum 2035:Jackknife 2030:Bootstrap 1848:Bootstrap 1783:Parameter 1732:Statistic 1527:Statistic 1439:Run chart 1424:Pie chart 1419:Histogram 1409:Fan chart 1384:Bar chart 1266:L-moments 1153:Geometric 816:intrinsic 706:⁡ 534:− 3308:Category 3001:Survival 2878:Johansen 2601:Binomial 2556:Isotonic 2143:(normal) 1788:location 1595:Blocking 1550:Sampling 1429:Q–Q plot 1394:Box plot 1376:Graphics 1271:Skewness 1261:Kurtosis 1233:Variance 1163:Heronian 1158:Harmonic 849:See also 736:Variance 472:, where 275:outliers 208:quantity 166:variance 3334:Commons 3281:Kriging 3166:Process 3123:studies 2982:Wavelet 2815:General 1982:Plug-in 1776:L space 1555:Cluster 1256:Moments 1074:Outline 855:Average 810:In the 791:In the 787:Sources 781:entropy 665:, then 579:Entropy 502:is the 338:then a 206:as the 154:scatter 94:scholar 3203:Census 2793:Normal 2741:Manova 2561:Robust 2311:2-way 2303:1-way 2141:-test 1812:  1389:Biplot 1180:Median 1173:Lehmer 1115:Center 989:  172:, and 158:spread 96:  89:  82:  75:  67:  2827:Trend 2356:prior 2298:anova 2187:-test 2161:-test 2153:-test 2060:Power 2005:Pivot 1798:shape 1793:scale 1243:Shape 1223:Range 1168:Heinz 1143:Cubic 1079:Index 258:) as 239:(MAD) 226:Range 222:(IQR) 204:units 156:, or 101:JSTOR 87:books 3060:Test 2260:Sign 2112:Wald 1185:Mode 1123:Mean 987:ISBN 771:For 630:and 399:and 378:real 376:for 284:and 73:news 2240:BIC 2235:AIC 1018:doi 703:log 506:of 262:of 140:In 56:by 3364:: 1012:. 960:. 936:. 918:. 836:A 783:. 546:. 191:A 168:, 152:, 144:, 2185:G 2159:F 2151:t 2139:Z 1858:V 1853:U 1055:e 1048:t 1041:v 1024:. 1020:: 1014:2 995:. 970:. 946:. 727:. 715:) 712:a 709:( 700:+ 697:) 694:x 691:( 688:H 685:= 682:) 679:z 676:( 673:H 653:b 650:+ 647:x 644:a 641:= 638:z 618:z 598:) 595:z 592:( 589:H 514:a 489:| 485:a 481:| 458:X 454:S 449:| 445:a 441:| 437:= 432:Y 428:S 407:b 387:a 364:b 361:+ 358:X 355:a 352:= 349:Y 324:X 320:S 299:X 123:) 117:( 112:) 108:( 98:· 91:· 84:· 77:· 50:. 20:)

Index

Scattering (statistics)

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"Statistical dispersion"
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statistics
distribution
variance
standard deviation
interquartile range
central tendency
real number
units
quantity
Standard deviation
Interquartile range
Range
Mean absolute difference
Median absolute deviation
Average absolute deviation
Distance standard deviation
scale factors

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