4941:
4889:
2095:
1959:
1828:
4875:
4913:
4901:
1854:
across this range, even when the naive probability for a sample number taking one certain value from infinitely many is zero. In this context, the analog of a weighted average, in which there are infinitely many possibilities for the precise value of the variable in each range, is called the
1954:
In general application, such an oversight will lead to the average value artificially moving towards the middle of the numerical range. A solution to this problem is to use the optimization formulation (that is, define the mean as the central point: the point about which one has the lowest
1866:; it has the property that all measures of its central tendency, including not just the mean but also the median mentioned above and the mode (the three Ms), are equal. This equality does not hold for other probability distributions, as illustrated for the log-normal distribution here.
386:
1745:, the former being twice the latter. The arithmetic mean (sometimes called the "unweighted average" or "equally weighted average") can be interpreted as a special case of a weighted average in which all weights are equal to the same number (
1264:
1625:
mean in which the first number receives, for example, twice as much weight as the second (perhaps because it is assumed to appear twice as often in the general population from which these numbers were sampled) would be calculated as
588:
949:
is the distance from a given number to the mean, one way to interpret this property is by saying that the numbers to the left of the mean are balanced by the numbers to the right. The mean is the only number for which the
1689:
496:
199:
The arithmetic mean of a set of observed data is equal to the sum of the numerical values of each observation, divided by the total number of observations. Symbolically, for a data set consisting of the values
905:
1619:
1482:
A weighted average, or weighted mean, is an average in which some data points count more heavily than others in that they are given more weight in the calculation. For example, the arithmetic mean of
1463:
There are applications of this phenomenon in many fields. For example, since the 1980s, the median income in the United States has increased more slowly than the arithmetic average of income.
187:
for which a few people's incomes are substantially higher than most people's, the arithmetic mean may not coincide with one's notion of "middle". In that case, robust statistics, such as the
1032:
252:
1136:
1081:
782:
1561:
244:
947:
681:
1797:
1770:
1743:
1716:
1418:
1266:
So, for example, calculating a mean of liters and then converting to gallons is the same as converting to gallons first and then calculating the mean. This is also called
1348:
2054:
811:
125:(when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an
1933:
1913:
1154:
624:
1438:
1368:
416:
1817:
1520:
1500:
1458:
976:
720:
654:
1955:
dispersion) and redefine the difference as a modular distance (i.e., the distance on the circle: so the modular distance between 1° and 359° is 2°, not 358°).
504:
137:. The term "arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as
1846:
If a numerical property, and any sample of data from it, can take on any value from a continuous range instead of, for example, just integers, then the
1629:
4010:
1302:. The median is defined such that no more than half the values are larger, and no more than half are smaller than it. If elements in the data
4515:
1083:, then the arithmetic mean of the numbers does this best since it minimizes the sum of squared deviations from the typical value: the sum of
2530:
2209:
421:
4665:
4289:
2930:
1283:
The arithmetic mean of any amount of equal-sized number groups together is the arithmetic mean of the arithmetic means of each group.
816:
4063:
1566:
4502:
734:
The arithmetic mean has several properties that make it interesting, especially as a measure of central tendency. These include:
2577:
597:(i.e., consists of every possible observation and not just a subset of them), then the mean of that population is called the
2925:
2625:
2505:
3529:
2677:
1851:
1939:). Thus, these could easily be called 1° and -1°, or 361° and 719°, since each one of them produces a different average.
951:
4312:
4204:
2444:
2388:
100:
2461:
981:
4917:
4490:
4364:
1370:, as is the median. However, when we consider a sample that cannot be arranged to increase arithmetically, such as
1306:
when placed in some order, then the median and arithmetic average are equal. For example, consider the data sample
687:
17:
381:{\displaystyle {\bar {x}}={\frac {1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)={\frac {x_{1}+x_{2}+\dots +x_{n}}{n}}}
4548:
4209:
3954:
3325:
2915:
1460:. The average value can vary considerably from most values in the sample and can be larger or smaller than most.
4599:
3811:
3618:
3507:
3465:
3539:
4842:
3801:
2704:
1086:
4393:
4342:
4327:
4317:
4186:
4058:
4025:
3851:
3806:
3636:
4905:
4737:
4538:
4462:
3763:
3517:
3186:
2650:
1875:
1040:
741:
1525:
203:
4931:
4622:
4594:
4589:
4337:
4096:
4002:
3982:
3890:
3601:
3419:
2902:
2774:
2224:
2214:
1420:, the median and arithmetic average can differ significantly. In this case, the arithmetic average is
910:
4354:
4122:
3843:
3768:
3697:
3626:
3546:
3534:
3404:
3392:
3385:
3093:
2814:
954:(deviations from the estimate) sum to zero. This can also be interpreted as saying that the mean is
659:
2071:
symbol "xĚ" combines two codes â the base letter "x" plus a code for the line above ( ̄ or ÂŻ).
1775:
1748:
1721:
1694:
1373:
4837:
4604:
4467:
4152:
4117:
4081:
3866:
3308:
3217:
3176:
3088:
2779:
2618:
1858:
4746:
4359:
4299:
4236:
3874:
3858:
3596:
3458:
3448:
3298:
3212:
1832:
1309:
1280:
The arithmetic mean of a sample is always between the largest and smallest values in that sample.
1139:
2538:
2030:
1142:. If the arithmetic mean of a population of numbers is desired, then the estimate of it that is
787:
4784:
4714:
4507:
4444:
4199:
4086:
3083:
2980:
2887:
2766:
2665:
2275:
1986:
1947:
1303:
955:
594:
184:
4809:
4751:
4694:
4520:
4413:
4322:
4048:
3932:
3791:
3783:
3673:
3665:
3480:
3376:
3354:
3313:
3278:
3245:
3191:
3166:
3121:
3060:
3020:
2822:
2645:
1259:{\displaystyle {\text{avg}}(ca_{1},\cdots ,ca_{n})=c\cdot {\text{avg}}(a_{1},\cdots ,a_{n}).}
627:
4732:
4307:
4256:
4232:
4194:
4112:
4091:
4043:
3922:
3900:
3869:
3778:
3655:
3606:
3524:
3497:
3453:
3409:
3171:
2947:
2827:
1967:
1918:
1895:
1267:
1151:
The arithmetic mean is independent of scale of the units of measurement, in the sense that
691:
2598:
609:
8:
4879:
4804:
4727:
4408:
4172:
4165:
4127:
4035:
4015:
3987:
3720:
3586:
3581:
3571:
3563:
3381:
3342:
3232:
3222:
3131:
2910:
2866:
2784:
2709:
2611:
2099:
1990:
1962:
1863:
1850:
of a number falling into some range of possible values can be described by integrating a
1423:
1353:
1037:
If it is required to use a single number as a "typical" value for a set of known numbers
180:
134:
130:
401:
4945:
4893:
4704:
4558:
4454:
4403:
4279:
4176:
4160:
4137:
3914:
3648:
3631:
3591:
3502:
3397:
3359:
3330:
3290:
3250:
3196:
3113:
2799:
2794:
2593:
2229:
2219:
2024:
1802:
1505:
1485:
1443:
961:
705:
699:
639:
31:
2594:
Calculations and comparisons between arithmetic mean and geometric mean of two numbers
2094:
4940:
4888:
4799:
4769:
4761:
4581:
4572:
4497:
4428:
4284:
4269:
4244:
4132:
4073:
3939:
3927:
3553:
3470:
3414:
3337:
3181:
3103:
2882:
2756:
2573:
2566:
2440:
2384:
2299:
2020:
1840:
1143:
161:
148:
In addition to mathematics and statistics, the arithmetic mean is frequently used in
2405:
583:{\displaystyle {\frac {2500+2700+2400+2300+2550+2650+2750+2450+2600+2400}{10}}=2530}
4824:
4779:
4543:
4530:
4423:
4398:
4332:
4264:
4142:
3750:
3643:
3576:
3489:
3436:
3255:
3126:
2920:
2804:
2719:
2686:
2462:"The Rich, the Right, and the Facts: Deconstructing the Income Distribution Debate"
2204:
2119:
1950:
about it (the points are both 1° from it and 179° from 180°, the putative average).
1477:
172:
168:
59:
4741:
4485:
4347:
4274:
3949:
3823:
3796:
3773:
3742:
3369:
3364:
3318:
3048:
2434:
2060:
1892:
Firstly, angle measurements are only defined up to an additive constant of 360° (
599:
4231:
2199:
1958:
4961:
4690:
4685:
3148:
3078:
2724:
2152:
2130:
2083:
1994:
1885:
604:
138:
2288:
Using
Pythagoras' theorem, OC² = OG² + GC² ∴ GC = √
1827:
1138:. The sample mean is also the best single predictor because it has the lowest
4955:
4847:
4814:
4677:
4638:
4449:
4418:
3882:
3836:
3441:
3143:
2970:
2734:
2729:
2380:
2163:
142:
4789:
4722:
4699:
4614:
3944:
3240:
3138:
3073:
3015:
3000:
2937:
2892:
1684:{\displaystyle 3\cdot {\frac {2}{3}}+5\cdot {\frac {1}{3}}={\frac {11}{3}}}
723:
153:
2479:
4832:
4794:
4477:
4378:
4240:
4053:
4020:
3512:
3429:
3424:
3068:
3025:
3005:
2985:
2975:
2744:
2064:
1847:
632:
45:
3678:
3158:
2858:
2789:
2739:
2714:
2634:
2079:
126:
49:
3831:
3683:
3303:
3098:
3010:
2995:
2990:
2955:
1862:. The most widely encountered probability distribution is called the
491:{\displaystyle \{2500,2700,2400,2300,2550,2650,2750,2450,2600,2400\}}
392:
149:
1942:
Secondly, in this situation, 0° (or 360°) is geometrically a better
1880:
Particular care is needed when using cyclic data, such as phases or
3347:
2965:
2842:
2837:
2832:
1973:
PR is the diameter of a circle centered on O; its radius AO is the
1836:
695:
1884:. Taking the arithmetic mean of 1° and 359° yields a result of 180
4852:
4553:
176:
157:
121:
2599:
Calculate the arithmetic mean of a series of numbers on fxSolver
4774:
3755:
3729:
3709:
2960:
2751:
2506:"The Three M's of Statistics: Mode, Median, Mean June 30, 2010"
1936:
1299:
1293:
900:{\displaystyle (x_{1}-{\bar {x}})+\dotsb +(x_{n}-{\bar {x}})=0}
188:
160:, and almost every academic field to some extent. For example,
2067:) may not display the "xĚ" symbol correctly. For example, the
2603:
1881:
1614:{\displaystyle 3\cdot {\frac {1}{2}}+5\cdot {\frac {1}{2}}=4}
1146:
is the arithmetic mean of a sample drawn from the population.
74:
2694:
2068:
164:
is the arithmetic average income of a nation's population.
115:
83:
38:
2503:
2075:
89:
71:
65:
191:, may provide a better description of central tendency.
1822:
1691:. Here the weights, which necessarily sum to one, are
179:(values much larger or smaller than most others). For
4929:
2278:, QC² = QO² + OC² ∴ QC = √
2033:
1921:
1898:
1805:
1778:
1751:
1724:
1697:
1632:
1569:
1528:
1508:
1488:
1446:
1426:
1376:
1356:
1312:
1157:
1089:
1043:
984:
964:
913:
819:
790:
744:
708:
662:
642:
612:
507:
424:
404:
255:
206:
101:
92:
62:
4516:
Autoregressive conditional heteroskedasticity (ARCH)
86:
68:
698:. More generally, because the arithmetic mean is a
391:(For an explanation of the summation operator, see
80:
77:
3978:
2565:
2048:
1927:
1907:
1811:
1791:
1764:
1737:
1710:
1683:
1613:
1555:
1514:
1494:
1452:
1432:
1412:
1362:
1342:
1258:
1130:
1075:
1026:
970:
941:
899:
805:
776:
714:
675:
648:
618:
582:
490:
410:
380:
238:
167:While the arithmetic mean is often used to report
2082:) symbol when copied to a text processor such as
686:The arithmetic mean can be similarly defined for
246:, the arithmetic mean is defined by the formula:
4953:
4064:Multivariate adaptive regression splines (MARS)
2019:The arithmetic mean is often denoted by a bar (
1298:The arithmetic mean may be contrasted with the
630:(a subset of the population), it is called the
1027:{\displaystyle {\overline {x+a}}={\bar {x}}+a}
2619:
2210:Inequality of arithmetic and geometric means
1407:
1377:
1337:
1313:
485:
425:
30:"XĚ" redirects here. For the character, see
2664:
2626:
2612:
2504:Thinkmap Visual Thesaurus (30 June 2010).
27:Type of average of a collection of numbers
3277:
2439:. New Age International. pp. 53â58.
2436:Statistical Methods: An Introductory Text
2093:
2078:), the symbol may be replaced by a "¢" (
1957:
1826:
1274:
729:
398:For example, if the monthly salaries of
37:For broader coverage of this topic, see
2459:
2014:
1287:
694:values; this is often referred to as a
14:
4954:
4590:KaplanâMeier estimator (product limit)
2497:
2374:
1131:{\displaystyle (x_{i}-{\bar {x}})^{2}}
958:in the sense that for any real number
4663:
4230:
3977:
3276:
3046:
2663:
2607:
2432:
2403:
1888:. This is incorrect for two reasons:
4900:
4600:Accelerated failure time (AFT) model
2563:
2428:
2426:
1823:Continuous probability distributions
4912:
4195:Analysis of variance (ANOVA, anova)
3047:
2531:"Notes on Unicode for Stat Symbols"
1852:continuous probability distribution
1471:
1076:{\displaystyle x_{1},\dotsc ,x_{n}}
777:{\displaystyle x_{1},\dotsc ,x_{n}}
24:
4290:CochranâMantelâHaenszel statistics
2916:Pearson product-moment correlation
2557:
2074:In some document formats (such as
1556:{\displaystyle {\frac {3+5}{2}}=4}
1466:
239:{\displaystyle x_{1},\dots ,x_{n}}
25:
4973:
2587:
2423:
2187:of two distinct positive numbers
1839:, resulting in various means and
1835:with equal median, but different
702:(meaning its coefficients sum to
690:in multiple dimensions, not only
4939:
4911:
4899:
4887:
4874:
4873:
4664:
942:{\displaystyle x_{i}-{\bar {x}}}
58:
4549:Least-squares spectral analysis
676:{\displaystyle {\overline {X}}}
498:, then the arithmetic mean is:
3530:Mean-unbiased minimum-variance
2633:
2523:
2472:
2460:Krugman, Paul (4 June 2014) .
2453:
2397:
2368:
2242:
2040:
1792:{\displaystyle {\frac {1}{n}}}
1765:{\displaystyle {\frac {1}{2}}}
1738:{\displaystyle {\frac {1}{3}}}
1711:{\displaystyle {\frac {2}{3}}}
1413:{\displaystyle \{1,2,4,8,16\}}
1250:
1218:
1201:
1163:
1119:
1112:
1090:
1012:
933:
888:
882:
860:
848:
842:
820:
797:
262:
175:: it is greatly influenced by
13:
1:
4843:Geographic information system
4059:Simultaneous equations models
2377:Mathematics: A Human Endeavor
2361:
194:
4026:Coefficient of determination
3637:Uniformly most powerful test
998:
668:
7:
4595:Proportional hazards models
4539:Spectral density estimation
4521:Vector autoregression (VAR)
3955:Maximum posterior estimator
3187:Randomized controlled trial
2433:Medhi, Jyotiprasad (1992).
2089:
1876:Mean of circular quantities
1343:{\displaystyle \{1,2,3,4\}}
726:, not only a vector space.
10:
4978:
4355:Multivariate distributions
2775:Average absolute deviation
2568:How to Lie with Statistics
2375:Jacobs, Harold R. (1994).
2225:Standard error of the mean
2215:Sample mean and covariance
2049:{\displaystyle {\bar {x}}}
1873:
1475:
1291:
806:{\displaystyle {\bar {x}}}
722:), it can be defined on a
36:
29:
4869:
4823:
4760:
4713:
4676:
4672:
4659:
4631:
4613:
4580:
4571:
4529:
4476:
4437:
4386:
4377:
4343:Structural equation model
4298:
4255:
4251:
4226:
4185:
4151:
4105:
4072:
4034:
4001:
3997:
3973:
3913:
3822:
3741:
3705:
3696:
3679:Score/Lagrange multiplier
3664:
3617:
3562:
3488:
3479:
3289:
3285:
3272:
3231:
3205:
3157:
3112:
3094:Sample size determination
3059:
3055:
3042:
2946:
2901:
2875:
2857:
2813:
2765:
2685:
2676:
2672:
2659:
2641:
2290:OC² − OG²
1869:
1819:numbers being averaged).
1772:in the above example and
956:translationally invariant
4838:Environmental statistics
4360:Elliptical distributions
4153:Generalized linear model
4082:Simple linear regression
3852:HodgesâLehmann estimator
3309:Probability distribution
3218:Stochastic approximation
2780:Coefficient of variation
2235:
1859:probability distribution
1833:log-normal distributions
4498:Cross-correlation (XCF)
4106:Non-standard predictors
3540:LehmannâScheffĂŠ theorem
3213:Adaptive clinical trial
2510:www.visualthesaurus.com
2484:Encyclopedia Britannica
1304:increase arithmetically
1268:first order homogeneity
1140:root mean squared error
626:. If the data set is a
4894:Mathematics portal
4715:Engineering statistics
4623:NelsonâAalen estimator
4200:Analysis of covariance
4087:Ordinary least squares
4011:Pearson product-moment
3415:Statistical functional
3326:Empirical distribution
3159:Controlled experiments
2888:Frequency distribution
2666:Descriptive statistics
2564:Huff, Darrell (1993).
2195:
2050:
2011:
1987:geometric mean theorem
1946:value: there is lower
1929:
1909:
1843:
1813:
1793:
1766:
1739:
1712:
1685:
1615:
1557:
1516:
1496:
1454:
1440:, while the median is
1434:
1414:
1364:
1344:
1260:
1132:
1077:
1028:
972:
943:
901:
807:
778:
716:
677:
650:
636:(which for a data set
620:
595:statistical population
584:
492:
412:
382:
306:
240:
185:distribution of income
4810:Population statistics
4752:System identification
4486:Autocorrelation (ACF)
4414:Exponential smoothing
4328:Discriminant analysis
4323:Canonical correlation
4187:Partition of variance
4049:Regression validation
3893:(JonckheereâTerpstra)
3792:Likelihood-ratio test
3481:Frequentist inference
3393:Locationâscale family
3314:Sampling distribution
3279:Statistical inference
3246:Cross-sectional study
3233:Observational studies
3192:Randomized experiment
3021:Stem-and-leaf display
2823:Central limit theorem
2466:The American Prospect
2410:mathworld.wolfram.com
2097:
2051:
1961:
1930:
1928:{\displaystyle \tau }
1910:
1908:{\displaystyle 2\pi }
1830:
1814:
1794:
1767:
1740:
1713:
1686:
1616:
1558:
1517:
1497:
1455:
1435:
1415:
1365:
1345:
1275:Additional properties
1261:
1133:
1078:
1029:
973:
944:
902:
808:
779:
730:Motivating properties
717:
678:
651:
621:
593:If the data set is a
585:
493:
413:
383:
286:
241:
4733:Probabilistic design
4318:Principal components
4161:Exponential families
4113:Nonlinear regression
4092:General linear model
4054:Mixed effects models
4044:Errors and residuals
4021:Confounding variable
3923:Bayesian probability
3901:Van der Waerden test
3891:Ordered alternative
3656:Multiple comparisons
3535:RaoâBlackwellization
3498:Estimating equations
3454:Statistical distance
3172:Factorial experiment
2705:Arithmetic-Geometric
2535:www.personal.psu.edu
2480:"Mean | mathematics"
2031:
2015:Symbols and encoding
1919:
1896:
1803:
1799:in a situation with
1776:
1749:
1722:
1695:
1630:
1567:
1526:
1506:
1486:
1444:
1424:
1374:
1354:
1310:
1288:Contrast with median
1155:
1087:
1041:
982:
962:
911:
817:
788:
742:
706:
660:
640:
619:{\displaystyle \mu }
610:
505:
422:
402:
253:
204:
181:skewed distributions
4805:Official statistics
4728:Methods engineering
4409:Seasonal adjustment
4177:Poisson regressions
4097:Bayesian regression
4036:Regression analysis
4016:Partial correlation
3988:Regression analysis
3587:Prediction interval
3582:Likelihood interval
3572:Confidence interval
3564:Interval estimation
3525:Unbiased estimators
3343:Model specification
3223:Up-and-down designs
2911:Partial correlation
2867:Index of dispersion
2785:Interquartile range
2404:Weisstein, Eric W.
2280:QO² + OC²
2276:Pythagoras' theorem
2100:proof without words
1963:Proof without words
1864:normal distribution
1433:{\displaystyle 6.2}
1363:{\displaystyle 2.5}
603:and denoted by the
131:observational study
4825:Spatial statistics
4705:Medical statistics
4605:First hitting time
4559:Whittle likelihood
4210:Degrees of freedom
4205:Multivariate ANOVA
4138:Heteroscedasticity
3950:Bayesian estimator
3915:Bayesian inference
3764:KolmogorovâSmirnov
3649:Randomization test
3619:Testing hypotheses
3592:Tolerance interval
3503:Maximum likelihood
3398:Exponential family
3331:Density estimation
3291:Statistical theory
3251:Natural experiment
3197:Scientific control
3114:Survey methodology
2800:Standard deviation
2379:(Third ed.).
2230:Summary statistics
2220:Standard deviation
2196:
2046:
2012:
1935:, if measuring in
1925:
1905:
1844:
1831:Comparison of two
1809:
1789:
1762:
1735:
1708:
1681:
1611:
1563:, or equivalently
1553:
1512:
1492:
1450:
1430:
1410:
1360:
1340:
1256:
1128:
1073:
1024:
968:
939:
897:
803:
774:
712:
700:convex combination
673:
646:
628:statistical sample
616:
580:
488:
411:{\displaystyle 10}
408:
378:
236:
169:central tendencies
111:arithmetic average
32:macron (diacritic)
4927:
4926:
4865:
4864:
4861:
4860:
4800:National accounts
4770:Actuarial science
4762:Social statistics
4655:
4654:
4651:
4650:
4647:
4646:
4582:Survival function
4567:
4566:
4429:Granger causality
4270:Contingency table
4245:Survival analysis
4222:
4221:
4218:
4217:
4074:Linear regression
3969:
3968:
3965:
3964:
3940:Credible interval
3909:
3908:
3692:
3691:
3508:Method of moments
3377:Parametric family
3338:Statistical model
3268:
3267:
3264:
3263:
3182:Random assignment
3104:Statistical power
3038:
3037:
3034:
3033:
2883:Contingency table
2853:
2852:
2720:Generalized/power
2579:978-0-393-31072-6
2406:"Arithmetic Mean"
2300:similar triangles
2043:
1989:, triangle PGR's
1812:{\displaystyle n}
1787:
1760:
1733:
1706:
1679:
1666:
1647:
1621:. In contrast, a
1603:
1584:
1545:
1515:{\displaystyle 5}
1495:{\displaystyle 3}
1453:{\displaystyle 4}
1216:
1161:
1115:
1015:
1001:
971:{\displaystyle a}
936:
885:
845:
800:
715:{\displaystyle 1}
671:
649:{\displaystyle X}
572:
376:
279:
265:
162:per capita income
16:(Redirected from
4969:
4944:
4943:
4935:
4915:
4914:
4903:
4902:
4892:
4891:
4877:
4876:
4780:Crime statistics
4674:
4673:
4661:
4660:
4578:
4577:
4544:Fourier analysis
4531:Frequency domain
4511:
4458:
4424:Structural break
4384:
4383:
4333:Cluster analysis
4280:Log-linear model
4253:
4252:
4228:
4227:
4169:
4143:Homoscedasticity
3999:
3998:
3975:
3974:
3894:
3886:
3878:
3877:(KruskalâWallis)
3862:
3847:
3802:Cross validation
3787:
3769:AndersonâDarling
3716:
3703:
3702:
3674:Likelihood-ratio
3666:Parametric tests
3644:Permutation test
3627:1- & 2-tails
3518:Minimum distance
3490:Point estimation
3486:
3485:
3437:Optimal decision
3388:
3287:
3286:
3274:
3273:
3256:Quasi-experiment
3206:Adaptive designs
3057:
3056:
3044:
3043:
2921:Rank correlation
2683:
2682:
2674:
2673:
2661:
2660:
2628:
2621:
2614:
2605:
2604:
2583:
2572:. W. W. Norton.
2571:
2551:
2550:
2548:
2546:
2541:on 31 March 2022
2537:. Archived from
2527:
2521:
2520:
2518:
2516:
2501:
2495:
2494:
2492:
2490:
2476:
2470:
2469:
2457:
2451:
2450:
2430:
2421:
2420:
2418:
2416:
2401:
2395:
2394:
2372:
2355:
2349:
2347:
2346:
2343:
2340:
2333:
2331:
2330:
2327:
2324:
2317:
2315:
2314:
2311:
2308:
2291:
2281:
2246:
2205:Generalized mean
2186:
2171:
2160:
2149:
2138:
2127:
2120:root mean square
2116:
2055:
2053:
2052:
2047:
2045:
2044:
2036:
2010:
2007:
1997:. For any ratio
1971:
1968:AMâGM inequality
1934:
1932:
1931:
1926:
1914:
1912:
1911:
1906:
1818:
1816:
1815:
1810:
1798:
1796:
1795:
1790:
1788:
1780:
1771:
1769:
1768:
1763:
1761:
1753:
1744:
1742:
1741:
1736:
1734:
1726:
1717:
1715:
1714:
1709:
1707:
1699:
1690:
1688:
1687:
1682:
1680:
1672:
1667:
1659:
1648:
1640:
1620:
1618:
1617:
1612:
1604:
1596:
1585:
1577:
1562:
1560:
1559:
1554:
1546:
1541:
1530:
1521:
1519:
1518:
1513:
1501:
1499:
1498:
1493:
1478:Weighted average
1472:Weighted average
1459:
1457:
1456:
1451:
1439:
1437:
1436:
1431:
1419:
1417:
1416:
1411:
1369:
1367:
1366:
1361:
1349:
1347:
1346:
1341:
1265:
1263:
1262:
1257:
1249:
1248:
1230:
1229:
1217:
1214:
1200:
1199:
1178:
1177:
1162:
1159:
1137:
1135:
1134:
1129:
1127:
1126:
1117:
1116:
1108:
1102:
1101:
1082:
1080:
1079:
1074:
1072:
1071:
1053:
1052:
1033:
1031:
1030:
1025:
1017:
1016:
1008:
1002:
997:
986:
977:
975:
974:
969:
948:
946:
945:
940:
938:
937:
929:
923:
922:
906:
904:
903:
898:
887:
886:
878:
872:
871:
847:
846:
838:
832:
831:
812:
810:
809:
804:
802:
801:
793:
783:
781:
780:
775:
773:
772:
754:
753:
721:
719:
718:
713:
682:
680:
679:
674:
672:
664:
655:
653:
652:
647:
625:
623:
622:
617:
589:
587:
586:
581:
573:
568:
509:
497:
495:
494:
489:
417:
415:
414:
409:
387:
385:
384:
379:
377:
372:
371:
370:
352:
351:
339:
338:
328:
323:
319:
318:
317:
316:
305:
300:
280:
272:
267:
266:
258:
245:
243:
242:
237:
235:
234:
216:
215:
173:robust statistic
105:
99:
98:
95:
94:
91:
88:
85:
82:
79:
76:
73:
70:
67:
64:
21:
18:Arithmetic means
4977:
4976:
4972:
4971:
4970:
4968:
4967:
4966:
4952:
4951:
4950:
4938:
4930:
4928:
4923:
4886:
4857:
4819:
4756:
4742:quality control
4709:
4691:Clinical trials
4668:
4643:
4627:
4615:Hazard function
4609:
4563:
4525:
4509:
4472:
4468:BreuschâGodfrey
4456:
4433:
4373:
4348:Factor analysis
4294:
4275:Graphical model
4247:
4214:
4181:
4167:
4147:
4101:
4068:
4030:
3993:
3992:
3961:
3905:
3892:
3884:
3876:
3860:
3845:
3824:Rank statistics
3818:
3797:Model selection
3785:
3743:Goodness of fit
3737:
3714:
3688:
3660:
3613:
3558:
3547:Median unbiased
3475:
3386:
3319:Order statistic
3281:
3260:
3227:
3201:
3153:
3108:
3051:
3049:Data collection
3030:
2942:
2897:
2871:
2849:
2809:
2761:
2678:Continuous data
2668:
2655:
2637:
2632:
2590:
2580:
2560:
2558:Further reading
2555:
2554:
2544:
2542:
2529:
2528:
2524:
2514:
2512:
2502:
2498:
2488:
2486:
2478:
2477:
2473:
2458:
2454:
2447:
2431:
2424:
2414:
2412:
2402:
2398:
2391:
2383:. p. 547.
2373:
2369:
2364:
2359:
2358:
2344:
2341:
2338:
2337:
2335:
2328:
2325:
2322:
2321:
2319:
2312:
2309:
2306:
2305:
2303:
2297:
2289:
2287:
2279:
2273:
2247:
2243:
2238:
2173:
2162:
2151:
2142:arithmetic mean
2140:
2129:
2118:
2103:
2092:
2061:text processors
2059:Some software (
2035:
2034:
2032:
2029:
2028:
2017:
2008:
1998:
1975:arithmetic mean
1966:
1920:
1917:
1916:
1897:
1894:
1893:
1878:
1872:
1825:
1804:
1801:
1800:
1779:
1777:
1774:
1773:
1752:
1750:
1747:
1746:
1725:
1723:
1720:
1719:
1698:
1696:
1693:
1692:
1671:
1658:
1639:
1631:
1628:
1627:
1595:
1576:
1568:
1565:
1564:
1531:
1529:
1527:
1524:
1523:
1507:
1504:
1503:
1487:
1484:
1483:
1480:
1474:
1469:
1467:Generalizations
1445:
1442:
1441:
1425:
1422:
1421:
1375:
1372:
1371:
1355:
1352:
1351:
1311:
1308:
1307:
1296:
1290:
1277:
1244:
1240:
1225:
1221:
1213:
1195:
1191:
1173:
1169:
1158:
1156:
1153:
1152:
1122:
1118:
1107:
1106:
1097:
1093:
1088:
1085:
1084:
1067:
1063:
1048:
1044:
1042:
1039:
1038:
1007:
1006:
987:
985:
983:
980:
979:
963:
960:
959:
928:
927:
918:
914:
912:
909:
908:
877:
876:
867:
863:
837:
836:
827:
823:
818:
815:
814:
792:
791:
789:
786:
785:
768:
764:
749:
745:
743:
740:
739:
732:
707:
704:
703:
663:
661:
658:
657:
641:
638:
637:
611:
608:
607:
600:population mean
510:
508:
506:
503:
502:
423:
420:
419:
403:
400:
399:
366:
362:
347:
343:
334:
330:
329:
327:
312:
308:
307:
301:
290:
285:
281:
271:
257:
256:
254:
251:
250:
230:
226:
211:
207:
205:
202:
201:
197:
103:
61:
57:
54:arithmetic mean
42:
35:
28:
23:
22:
15:
12:
11:
5:
4975:
4965:
4964:
4949:
4948:
4925:
4924:
4922:
4921:
4909:
4897:
4883:
4870:
4867:
4866:
4863:
4862:
4859:
4858:
4856:
4855:
4850:
4845:
4840:
4835:
4829:
4827:
4821:
4820:
4818:
4817:
4812:
4807:
4802:
4797:
4792:
4787:
4782:
4777:
4772:
4766:
4764:
4758:
4757:
4755:
4754:
4749:
4744:
4735:
4730:
4725:
4719:
4717:
4711:
4710:
4708:
4707:
4702:
4697:
4688:
4686:Bioinformatics
4682:
4680:
4670:
4669:
4657:
4656:
4653:
4652:
4649:
4648:
4645:
4644:
4642:
4641:
4635:
4633:
4629:
4628:
4626:
4625:
4619:
4617:
4611:
4610:
4608:
4607:
4602:
4597:
4592:
4586:
4584:
4575:
4569:
4568:
4565:
4564:
4562:
4561:
4556:
4551:
4546:
4541:
4535:
4533:
4527:
4526:
4524:
4523:
4518:
4513:
4505:
4500:
4495:
4494:
4493:
4491:partial (PACF)
4482:
4480:
4474:
4473:
4471:
4470:
4465:
4460:
4452:
4447:
4441:
4439:
4438:Specific tests
4435:
4434:
4432:
4431:
4426:
4421:
4416:
4411:
4406:
4401:
4396:
4390:
4388:
4381:
4375:
4374:
4372:
4371:
4370:
4369:
4368:
4367:
4352:
4351:
4350:
4340:
4338:Classification
4335:
4330:
4325:
4320:
4315:
4310:
4304:
4302:
4296:
4295:
4293:
4292:
4287:
4285:McNemar's test
4282:
4277:
4272:
4267:
4261:
4259:
4249:
4248:
4224:
4223:
4220:
4219:
4216:
4215:
4213:
4212:
4207:
4202:
4197:
4191:
4189:
4183:
4182:
4180:
4179:
4163:
4157:
4155:
4149:
4148:
4146:
4145:
4140:
4135:
4130:
4125:
4123:Semiparametric
4120:
4115:
4109:
4107:
4103:
4102:
4100:
4099:
4094:
4089:
4084:
4078:
4076:
4070:
4069:
4067:
4066:
4061:
4056:
4051:
4046:
4040:
4038:
4032:
4031:
4029:
4028:
4023:
4018:
4013:
4007:
4005:
3995:
3994:
3991:
3990:
3985:
3979:
3971:
3970:
3967:
3966:
3963:
3962:
3960:
3959:
3958:
3957:
3947:
3942:
3937:
3936:
3935:
3930:
3919:
3917:
3911:
3910:
3907:
3906:
3904:
3903:
3898:
3897:
3896:
3888:
3880:
3864:
3861:(MannâWhitney)
3856:
3855:
3854:
3841:
3840:
3839:
3828:
3826:
3820:
3819:
3817:
3816:
3815:
3814:
3809:
3804:
3794:
3789:
3786:(ShapiroâWilk)
3781:
3776:
3771:
3766:
3761:
3753:
3747:
3745:
3739:
3738:
3736:
3735:
3727:
3718:
3706:
3700:
3698:Specific tests
3694:
3693:
3690:
3689:
3687:
3686:
3681:
3676:
3670:
3668:
3662:
3661:
3659:
3658:
3653:
3652:
3651:
3641:
3640:
3639:
3629:
3623:
3621:
3615:
3614:
3612:
3611:
3610:
3609:
3604:
3594:
3589:
3584:
3579:
3574:
3568:
3566:
3560:
3559:
3557:
3556:
3551:
3550:
3549:
3544:
3543:
3542:
3537:
3522:
3521:
3520:
3515:
3510:
3505:
3494:
3492:
3483:
3477:
3476:
3474:
3473:
3468:
3463:
3462:
3461:
3451:
3446:
3445:
3444:
3434:
3433:
3432:
3427:
3422:
3412:
3407:
3402:
3401:
3400:
3395:
3390:
3374:
3373:
3372:
3367:
3362:
3352:
3351:
3350:
3345:
3335:
3334:
3333:
3323:
3322:
3321:
3311:
3306:
3301:
3295:
3293:
3283:
3282:
3270:
3269:
3266:
3265:
3262:
3261:
3259:
3258:
3253:
3248:
3243:
3237:
3235:
3229:
3228:
3226:
3225:
3220:
3215:
3209:
3207:
3203:
3202:
3200:
3199:
3194:
3189:
3184:
3179:
3174:
3169:
3163:
3161:
3155:
3154:
3152:
3151:
3149:Standard error
3146:
3141:
3136:
3135:
3134:
3129:
3118:
3116:
3110:
3109:
3107:
3106:
3101:
3096:
3091:
3086:
3081:
3079:Optimal design
3076:
3071:
3065:
3063:
3053:
3052:
3040:
3039:
3036:
3035:
3032:
3031:
3029:
3028:
3023:
3018:
3013:
3008:
3003:
2998:
2993:
2988:
2983:
2978:
2973:
2968:
2963:
2958:
2952:
2950:
2944:
2943:
2941:
2940:
2935:
2934:
2933:
2928:
2918:
2913:
2907:
2905:
2899:
2898:
2896:
2895:
2890:
2885:
2879:
2877:
2876:Summary tables
2873:
2872:
2870:
2869:
2863:
2861:
2855:
2854:
2851:
2850:
2848:
2847:
2846:
2845:
2840:
2835:
2825:
2819:
2817:
2811:
2810:
2808:
2807:
2802:
2797:
2792:
2787:
2782:
2777:
2771:
2769:
2763:
2762:
2760:
2759:
2754:
2749:
2748:
2747:
2742:
2737:
2732:
2727:
2722:
2717:
2712:
2710:Contraharmonic
2707:
2702:
2691:
2689:
2680:
2670:
2669:
2657:
2656:
2654:
2653:
2648:
2642:
2639:
2638:
2631:
2630:
2623:
2616:
2608:
2602:
2601:
2596:
2589:
2588:External links
2586:
2585:
2584:
2578:
2559:
2556:
2553:
2552:
2522:
2496:
2471:
2452:
2445:
2422:
2396:
2389:
2366:
2365:
2363:
2360:
2357:
2356:
2240:
2239:
2237:
2234:
2233:
2232:
2227:
2222:
2217:
2212:
2207:
2202:
2153:geometric mean
2131:quadratic mean
2091:
2088:
2084:Microsoft Word
2042:
2039:
2016:
2013:
2009:AO ≥ GQ.
1995:geometric mean
1972:
1952:
1951:
1940:
1924:
1904:
1901:
1874:Main article:
1871:
1868:
1824:
1821:
1808:
1786:
1783:
1759:
1756:
1732:
1729:
1705:
1702:
1678:
1675:
1670:
1665:
1662:
1657:
1654:
1651:
1646:
1643:
1638:
1635:
1610:
1607:
1602:
1599:
1594:
1591:
1588:
1583:
1580:
1575:
1572:
1552:
1549:
1544:
1540:
1537:
1534:
1511:
1491:
1476:Main article:
1473:
1470:
1468:
1465:
1449:
1429:
1409:
1406:
1403:
1400:
1397:
1394:
1391:
1388:
1385:
1382:
1379:
1359:
1350:. The mean is
1339:
1336:
1333:
1330:
1327:
1324:
1321:
1318:
1315:
1292:Main article:
1289:
1286:
1285:
1284:
1281:
1276:
1273:
1272:
1271:
1255:
1252:
1247:
1243:
1239:
1236:
1233:
1228:
1224:
1220:
1212:
1209:
1206:
1203:
1198:
1194:
1190:
1187:
1184:
1181:
1176:
1172:
1168:
1165:
1148:
1147:
1125:
1121:
1114:
1111:
1105:
1100:
1096:
1092:
1070:
1066:
1062:
1059:
1056:
1051:
1047:
1035:
1023:
1020:
1014:
1011:
1005:
1000:
996:
993:
990:
967:
935:
932:
926:
921:
917:
896:
893:
890:
884:
881:
875:
870:
866:
862:
859:
856:
853:
850:
844:
841:
835:
830:
826:
822:
799:
796:
771:
767:
763:
760:
757:
752:
748:
731:
728:
711:
670:
667:
656:is denoted as
645:
615:
591:
590:
579:
576:
571:
567:
564:
561:
558:
555:
552:
549:
546:
543:
540:
537:
534:
531:
528:
525:
522:
519:
516:
513:
487:
484:
481:
478:
475:
472:
469:
466:
463:
460:
457:
454:
451:
448:
445:
442:
439:
436:
433:
430:
427:
418:employees are
407:
389:
388:
375:
369:
365:
361:
358:
355:
350:
346:
342:
337:
333:
326:
322:
315:
311:
304:
299:
296:
293:
289:
284:
278:
275:
270:
264:
261:
233:
229:
225:
222:
219:
214:
210:
196:
193:
183:, such as the
171:, it is not a
113:, or just the
26:
9:
6:
4:
3:
2:
4974:
4963:
4960:
4959:
4957:
4947:
4942:
4937:
4936:
4933:
4920:
4919:
4910:
4908:
4907:
4898:
4896:
4895:
4890:
4884:
4882:
4881:
4872:
4871:
4868:
4854:
4851:
4849:
4848:Geostatistics
4846:
4844:
4841:
4839:
4836:
4834:
4831:
4830:
4828:
4826:
4822:
4816:
4815:Psychometrics
4813:
4811:
4808:
4806:
4803:
4801:
4798:
4796:
4793:
4791:
4788:
4786:
4783:
4781:
4778:
4776:
4773:
4771:
4768:
4767:
4765:
4763:
4759:
4753:
4750:
4748:
4745:
4743:
4739:
4736:
4734:
4731:
4729:
4726:
4724:
4721:
4720:
4718:
4716:
4712:
4706:
4703:
4701:
4698:
4696:
4692:
4689:
4687:
4684:
4683:
4681:
4679:
4678:Biostatistics
4675:
4671:
4667:
4662:
4658:
4640:
4639:Log-rank test
4637:
4636:
4634:
4630:
4624:
4621:
4620:
4618:
4616:
4612:
4606:
4603:
4601:
4598:
4596:
4593:
4591:
4588:
4587:
4585:
4583:
4579:
4576:
4574:
4570:
4560:
4557:
4555:
4552:
4550:
4547:
4545:
4542:
4540:
4537:
4536:
4534:
4532:
4528:
4522:
4519:
4517:
4514:
4512:
4510:(BoxâJenkins)
4506:
4504:
4501:
4499:
4496:
4492:
4489:
4488:
4487:
4484:
4483:
4481:
4479:
4475:
4469:
4466:
4464:
4463:DurbinâWatson
4461:
4459:
4453:
4451:
4448:
4446:
4445:DickeyâFuller
4443:
4442:
4440:
4436:
4430:
4427:
4425:
4422:
4420:
4419:Cointegration
4417:
4415:
4412:
4410:
4407:
4405:
4402:
4400:
4397:
4395:
4394:Decomposition
4392:
4391:
4389:
4385:
4382:
4380:
4376:
4366:
4363:
4362:
4361:
4358:
4357:
4356:
4353:
4349:
4346:
4345:
4344:
4341:
4339:
4336:
4334:
4331:
4329:
4326:
4324:
4321:
4319:
4316:
4314:
4311:
4309:
4306:
4305:
4303:
4301:
4297:
4291:
4288:
4286:
4283:
4281:
4278:
4276:
4273:
4271:
4268:
4266:
4265:Cohen's kappa
4263:
4262:
4260:
4258:
4254:
4250:
4246:
4242:
4238:
4234:
4229:
4225:
4211:
4208:
4206:
4203:
4201:
4198:
4196:
4193:
4192:
4190:
4188:
4184:
4178:
4174:
4170:
4164:
4162:
4159:
4158:
4156:
4154:
4150:
4144:
4141:
4139:
4136:
4134:
4131:
4129:
4126:
4124:
4121:
4119:
4118:Nonparametric
4116:
4114:
4111:
4110:
4108:
4104:
4098:
4095:
4093:
4090:
4088:
4085:
4083:
4080:
4079:
4077:
4075:
4071:
4065:
4062:
4060:
4057:
4055:
4052:
4050:
4047:
4045:
4042:
4041:
4039:
4037:
4033:
4027:
4024:
4022:
4019:
4017:
4014:
4012:
4009:
4008:
4006:
4004:
4000:
3996:
3989:
3986:
3984:
3981:
3980:
3976:
3972:
3956:
3953:
3952:
3951:
3948:
3946:
3943:
3941:
3938:
3934:
3931:
3929:
3926:
3925:
3924:
3921:
3920:
3918:
3916:
3912:
3902:
3899:
3895:
3889:
3887:
3881:
3879:
3873:
3872:
3871:
3868:
3867:Nonparametric
3865:
3863:
3857:
3853:
3850:
3849:
3848:
3842:
3838:
3837:Sample median
3835:
3834:
3833:
3830:
3829:
3827:
3825:
3821:
3813:
3810:
3808:
3805:
3803:
3800:
3799:
3798:
3795:
3793:
3790:
3788:
3782:
3780:
3777:
3775:
3772:
3770:
3767:
3765:
3762:
3760:
3758:
3754:
3752:
3749:
3748:
3746:
3744:
3740:
3734:
3732:
3728:
3726:
3724:
3719:
3717:
3712:
3708:
3707:
3704:
3701:
3699:
3695:
3685:
3682:
3680:
3677:
3675:
3672:
3671:
3669:
3667:
3663:
3657:
3654:
3650:
3647:
3646:
3645:
3642:
3638:
3635:
3634:
3633:
3630:
3628:
3625:
3624:
3622:
3620:
3616:
3608:
3605:
3603:
3600:
3599:
3598:
3595:
3593:
3590:
3588:
3585:
3583:
3580:
3578:
3575:
3573:
3570:
3569:
3567:
3565:
3561:
3555:
3552:
3548:
3545:
3541:
3538:
3536:
3533:
3532:
3531:
3528:
3527:
3526:
3523:
3519:
3516:
3514:
3511:
3509:
3506:
3504:
3501:
3500:
3499:
3496:
3495:
3493:
3491:
3487:
3484:
3482:
3478:
3472:
3469:
3467:
3464:
3460:
3457:
3456:
3455:
3452:
3450:
3447:
3443:
3442:loss function
3440:
3439:
3438:
3435:
3431:
3428:
3426:
3423:
3421:
3418:
3417:
3416:
3413:
3411:
3408:
3406:
3403:
3399:
3396:
3394:
3391:
3389:
3383:
3380:
3379:
3378:
3375:
3371:
3368:
3366:
3363:
3361:
3358:
3357:
3356:
3353:
3349:
3346:
3344:
3341:
3340:
3339:
3336:
3332:
3329:
3328:
3327:
3324:
3320:
3317:
3316:
3315:
3312:
3310:
3307:
3305:
3302:
3300:
3297:
3296:
3294:
3292:
3288:
3284:
3280:
3275:
3271:
3257:
3254:
3252:
3249:
3247:
3244:
3242:
3239:
3238:
3236:
3234:
3230:
3224:
3221:
3219:
3216:
3214:
3211:
3210:
3208:
3204:
3198:
3195:
3193:
3190:
3188:
3185:
3183:
3180:
3178:
3175:
3173:
3170:
3168:
3165:
3164:
3162:
3160:
3156:
3150:
3147:
3145:
3144:Questionnaire
3142:
3140:
3137:
3133:
3130:
3128:
3125:
3124:
3123:
3120:
3119:
3117:
3115:
3111:
3105:
3102:
3100:
3097:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3075:
3072:
3070:
3067:
3066:
3064:
3062:
3058:
3054:
3050:
3045:
3041:
3027:
3024:
3022:
3019:
3017:
3014:
3012:
3009:
3007:
3004:
3002:
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2977:
2974:
2972:
2971:Control chart
2969:
2967:
2964:
2962:
2959:
2957:
2954:
2953:
2951:
2949:
2945:
2939:
2936:
2932:
2929:
2927:
2924:
2923:
2922:
2919:
2917:
2914:
2912:
2909:
2908:
2906:
2904:
2900:
2894:
2891:
2889:
2886:
2884:
2881:
2880:
2878:
2874:
2868:
2865:
2864:
2862:
2860:
2856:
2844:
2841:
2839:
2836:
2834:
2831:
2830:
2829:
2826:
2824:
2821:
2820:
2818:
2816:
2812:
2806:
2803:
2801:
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2776:
2773:
2772:
2770:
2768:
2764:
2758:
2755:
2753:
2750:
2746:
2743:
2741:
2738:
2736:
2733:
2731:
2728:
2726:
2723:
2721:
2718:
2716:
2713:
2711:
2708:
2706:
2703:
2701:
2698:
2697:
2696:
2693:
2692:
2690:
2688:
2684:
2681:
2679:
2675:
2671:
2667:
2662:
2658:
2652:
2649:
2647:
2644:
2643:
2640:
2636:
2629:
2624:
2622:
2617:
2615:
2610:
2609:
2606:
2600:
2597:
2595:
2592:
2591:
2581:
2575:
2570:
2569:
2562:
2561:
2540:
2536:
2532:
2526:
2511:
2507:
2500:
2485:
2481:
2475:
2467:
2463:
2456:
2448:
2446:9788122404197
2442:
2438:
2437:
2429:
2427:
2411:
2407:
2400:
2392:
2390:0-7167-2426-X
2386:
2382:
2381:W. H. Freeman
2378:
2371:
2367:
2353:
2334:∴ HC =
2301:
2295:
2285:
2277:
2271:
2268:, and radius
2267:
2263:
2259:
2255:
2251:
2245:
2241:
2231:
2228:
2226:
2223:
2221:
2218:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2197:
2194:
2190:
2184:
2180:
2176:
2169:
2165:
2164:harmonic mean
2158:
2154:
2147:
2143:
2136:
2132:
2125:
2121:
2114:
2110:
2106:
2101:
2096:
2087:
2085:
2081:
2077:
2072:
2070:
2066:
2062:
2057:
2037:
2026:
2022:
2005:
2001:
1996:
1992:
1988:
1984:
1980:
1976:
1969:
1964:
1960:
1956:
1949:
1945:
1941:
1938:
1922:
1902:
1899:
1891:
1890:
1889:
1887:
1883:
1877:
1867:
1865:
1861:
1860:
1853:
1849:
1842:
1838:
1834:
1829:
1820:
1806:
1784:
1781:
1757:
1754:
1730:
1727:
1703:
1700:
1676:
1673:
1668:
1663:
1660:
1655:
1652:
1649:
1644:
1641:
1636:
1633:
1624:
1608:
1605:
1600:
1597:
1592:
1589:
1586:
1581:
1578:
1573:
1570:
1550:
1547:
1542:
1538:
1535:
1532:
1509:
1489:
1479:
1464:
1461:
1447:
1427:
1404:
1401:
1398:
1395:
1392:
1389:
1386:
1383:
1380:
1357:
1334:
1331:
1328:
1325:
1322:
1319:
1316:
1305:
1301:
1295:
1282:
1279:
1278:
1269:
1253:
1245:
1241:
1237:
1234:
1231:
1226:
1222:
1210:
1207:
1204:
1196:
1192:
1188:
1185:
1182:
1179:
1174:
1170:
1166:
1150:
1149:
1145:
1141:
1123:
1109:
1103:
1098:
1094:
1068:
1064:
1060:
1057:
1054:
1049:
1045:
1036:
1021:
1018:
1009:
1003:
994:
991:
988:
965:
957:
953:
930:
924:
919:
915:
894:
891:
879:
873:
868:
864:
857:
854:
851:
839:
833:
828:
824:
794:
769:
765:
761:
758:
755:
750:
746:
737:
736:
735:
727:
725:
709:
701:
697:
693:
689:
684:
665:
643:
635:
634:
629:
613:
606:
602:
601:
596:
577:
574:
569:
565:
562:
559:
556:
553:
550:
547:
544:
541:
538:
535:
532:
529:
526:
523:
520:
517:
514:
511:
501:
500:
499:
482:
479:
476:
473:
470:
467:
464:
461:
458:
455:
452:
449:
446:
443:
440:
437:
434:
431:
428:
405:
396:
394:
373:
367:
363:
359:
356:
353:
348:
344:
340:
335:
331:
324:
320:
313:
309:
302:
297:
294:
291:
287:
282:
276:
273:
268:
259:
249:
248:
247:
231:
227:
223:
220:
217:
212:
208:
192:
190:
186:
182:
178:
174:
170:
165:
163:
159:
155:
151:
146:
144:
140:
136:
132:
128:
124:
123:
118:
117:
112:
108:
107:
97:
55:
51:
47:
40:
33:
19:
4916:
4904:
4885:
4878:
4790:Econometrics
4740: /
4723:Chemometrics
4700:Epidemiology
4693: /
4666:Applications
4508:ARIMA model
4455:Q-statistic
4404:Stationarity
4300:Multivariate
4243: /
4239: /
4237:Multivariate
4235: /
4175: /
4171: /
3945:Bayes factor
3844:Signed rank
3756:
3730:
3722:
3710:
3405:Completeness
3241:Cohort study
3139:Opinion poll
3074:Missing data
3061:Study design
3016:Scatter plot
2938:Scatter plot
2931:Spearman's Ď
2893:Grouped data
2699:
2567:
2543:. Retrieved
2539:the original
2534:
2525:
2513:. Retrieved
2509:
2499:
2487:. Retrieved
2483:
2474:
2465:
2455:
2435:
2413:. Retrieved
2409:
2399:
2376:
2370:
2351:
2293:
2283:
2269:
2265:
2261:
2257:
2253:
2249:
2244:
2200:FrĂŠchet mean
2192:
2188:
2182:
2178:
2174:
2167:
2156:
2145:
2141:
2134:
2123:
2112:
2108:
2104:
2073:
2065:web browsers
2058:
2018:
2003:
1999:
1985:. Using the
1982:
1978:
1974:
1953:
1943:
1879:
1857:mean of the
1856:
1845:
1622:
1481:
1462:
1297:
733:
724:convex space
685:
631:
605:Greek letter
598:
592:
397:
390:
198:
166:
154:anthropology
147:
120:
114:
110:
53:
43:
4946:Mathematics
4918:WikiProject
4833:Cartography
4795:Jurimetrics
4747:Reliability
4478:Time domain
4457:(LjungâBox)
4379:Time-series
4257:Categorical
4241:Time-series
4233:Categorical
4168:(Bernoulli)
4003:Correlation
3983:Correlation
3779:JarqueâBera
3751:Chi-squared
3513:M-estimator
3466:Asymptotics
3410:Sufficiency
3177:Interaction
3089:Replication
3069:Effect size
3026:Violin plot
3006:Radar chart
2986:Forest plot
2976:Correlogram
2926:Kendall's Ď
1848:probability
738:If numbers
633:sample mean
46:mathematics
4785:Demography
4503:ARMA model
4308:Regression
3885:(Friedman)
3846:(Wilcoxon)
3784:Normality
3774:Lilliefors
3721:Student's
3597:Resampling
3471:Robustness
3459:divergence
3449:Efficiency
3387:(monotone)
3382:Likelihood
3299:Population
3132:Stratified
3084:Population
2903:Dependence
2859:Count data
2790:Percentile
2767:Dispersion
2700:Arithmetic
2635:Statistics
2545:14 October
2515:3 December
2362:References
2272:= QO = OG.
2098:Geometric
1993:GQ is the
1948:dispersion
784:have mean
195:Definition
127:experiment
50:statistics
4166:Logistic
3933:posterior
3859:Rank sum
3607:Jackknife
3602:Bootstrap
3420:Bootstrap
3355:Parameter
3304:Statistic
3099:Statistic
3011:Run chart
2996:Pie chart
2991:Histogram
2981:Fan chart
2956:Bar chart
2838:L-moments
2725:Geometric
2489:21 August
2415:21 August
2252:and BC =
2041:¯
2027:), as in
1923:τ
1903:π
1656:⋅
1637:⋅
1593:⋅
1574:⋅
1235:⋯
1211:⋅
1183:⋯
1113:¯
1104:−
1058:…
1013:¯
999:¯
952:residuals
934:¯
925:−
883:¯
874:−
855:⋯
843:¯
834:−
798:¯
759:…
669:¯
614:μ
393:summation
357:⋯
288:∑
263:¯
221:…
150:economics
139:geometric
4956:Category
4880:Category
4573:Survival
4450:Johansen
4173:Binomial
4128:Isotonic
3715:(normal)
3360:location
3167:Blocking
3122:Sampling
3001:QâQ plot
2966:Box plot
2948:Graphics
2843:Skewness
2833:Kurtosis
2805:Variance
2735:Heronian
2730:Harmonic
2339:GC²
2248:If AC =
2177: (
2107: (
2090:See also
2021:vinculum
1991:altitude
1837:skewness
1623:weighted
1144:unbiased
907:. Since
696:centroid
177:outliers
143:harmonic
102:arr-ith-
4906:Commons
4853:Kriging
4738:Process
4695:studies
4554:Wavelet
4387:General
3554:Plug-in
3348:L space
3127:Cluster
2828:Moments
2646:Outline
2348:
2336:
2332:
2320:
2316:
2304:
2256:. OC =
1965:of the
1944:average
1937:radians
813:, then
688:vectors
158:history
133:, or a
122:average
4932:Portal
4775:Census
4365:Normal
4313:Manova
4133:Robust
3883:2-way
3875:1-way
3713:-test
3384:
2961:Biplot
2752:Median
2745:Lehmer
2687:Center
2576:
2443:
2387:
2298:Using
2274:Using
2025:macron
1882:angles
1870:Angles
1300:median
1294:Median
692:scalar
189:median
135:survey
52:, the
4962:Means
4399:Trend
3928:prior
3870:anova
3759:-test
3733:-test
3725:-test
3632:Power
3577:Pivot
3370:shape
3365:scale
2815:Shape
2795:Range
2740:Heinz
2715:Cubic
2651:Index
2236:Notes
2172:>
2161:>
2150:>
2139:>
2117:>
2102:that
1841:modes
129:, an
4632:Test
3832:Sign
3684:Wald
2757:Mode
2695:Mean
2574:ISBN
2547:2018
2517:2018
2491:2020
2441:ISBN
2417:2020
2385:ISBN
2264:and
2191:and
2080:cent
2069:HTML
1981:and
1718:and
1502:and
578:2530
566:2400
560:2600
554:2450
548:2750
542:2650
536:2550
530:2300
524:2400
518:2700
512:2500
483:2400
477:2600
471:2450
465:2750
459:2650
453:2550
447:2300
441:2400
435:2700
429:2500
141:and
116:mean
48:and
39:Mean
3812:BIC
3807:AIC
2260:of
2175:min
2128:or
2124:RMS
2105:max
2076:PDF
2023:or
1977:of
1915:or
1522:is
1428:6.2
1358:2.5
1215:avg
1160:avg
683:).
395:.)
119:or
109:),
106:-ik
104:MET
44:In
4958::
2533:.
2508:.
2482:.
2464:.
2425:^
2408:.
2352:HM
2350:=
2345:OC
2329:OC
2323:GC
2318:=
2313:GC
2307:HC
2302:,
2294:GM
2292:=
2284:QM
2282:=
2258:AM
2168:HM
2157:GM
2146:AM
2135:QM
2086:.
2063:,
2056:.
1674:11
1405:16
978:,
570:10
406:10
156:,
152:,
145:.
4934::
3757:G
3731:F
3723:t
3711:Z
3430:V
3425:U
2627:e
2620:t
2613:v
2582:.
2549:.
2519:.
2493:.
2468:.
2449:.
2419:.
2393:.
2354:.
2342:/
2326:/
2310:/
2296:.
2286:.
2270:r
2266:b
2262:a
2254:b
2250:a
2193:b
2189:a
2185:)
2183:b
2181:,
2179:a
2170:)
2166:(
2159:)
2155:(
2148:)
2144:(
2137:)
2133:(
2126:)
2122:(
2115:)
2113:b
2111:,
2109:a
2038:x
2006:,
2004:b
2002::
2000:a
1983:b
1979:a
1970::
1900:2
1886:°
1807:n
1785:n
1782:1
1758:2
1755:1
1731:3
1728:1
1704:3
1701:2
1677:3
1669:=
1664:3
1661:1
1653:5
1650:+
1645:3
1642:2
1634:3
1609:4
1606:=
1601:2
1598:1
1590:5
1587:+
1582:2
1579:1
1571:3
1551:4
1548:=
1543:2
1539:5
1536:+
1533:3
1510:5
1490:3
1448:4
1408:}
1402:,
1399:8
1396:,
1393:4
1390:,
1387:2
1384:,
1381:1
1378:{
1338:}
1335:4
1332:,
1329:3
1326:,
1323:2
1320:,
1317:1
1314:{
1270:.
1254:.
1251:)
1246:n
1242:a
1238:,
1232:,
1227:1
1223:a
1219:(
1208:c
1205:=
1202:)
1197:n
1193:a
1189:c
1186:,
1180:,
1175:1
1171:a
1167:c
1164:(
1124:2
1120:)
1110:x
1099:i
1095:x
1091:(
1069:n
1065:x
1061:,
1055:,
1050:1
1046:x
1034:.
1022:a
1019:+
1010:x
1004:=
995:a
992:+
989:x
966:a
931:x
920:i
916:x
895:0
892:=
889:)
880:x
869:n
865:x
861:(
858:+
852:+
849:)
840:x
829:1
825:x
821:(
795:x
770:n
766:x
762:,
756:,
751:1
747:x
710:1
666:X
644:X
575:=
563:+
557:+
551:+
545:+
539:+
533:+
527:+
521:+
515:+
486:}
480:,
474:,
468:,
462:,
456:,
450:,
444:,
438:,
432:,
426:{
374:n
368:n
364:x
360:+
354:+
349:2
345:x
341:+
336:1
332:x
325:=
321:)
314:i
310:x
303:n
298:1
295:=
292:i
283:(
277:n
274:1
269:=
260:x
232:n
228:x
224:,
218:,
213:1
209:x
96:/
93:k
90:ÉŞ
87:t
84:É
81:m
78:Ë
75:θ
72:ÉŞ
69:r
66:ĂŚ
63:Ë
60:/
56:(
41:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.