1363:, the mean is not necessarily the same as the middle value (median), or the most likely value (mode). For example, mean income is typically skewed upwards by a small number of people with very large incomes, so that the majority have an income lower than the mean. By contrast, the median income is the level at which half the population is below and half is above. The mode income is the most likely income and favors the larger number of people with lower incomes. While the median and mode are often more intuitive measures for such skewed data, many skewed distributions are in fact best described by their mean, including the
5973:
3394:
1332:
1178:
1308:
5959:
5997:
5985:
1124:
773:
2725:. It involves discarding given parts of the data at the top or the bottom end, typically an equal amount at each end and then taking the arithmetic mean of the remaining data. The number of values removed is indicated as a percentage of the total number of values.
534:
3039:
to add and otherwise combine numbers. In all these situations, there will not be a unique mean. For example, the times an hour before and after midnight are equidistant to both midnight and noon. It is also possible that no mean exists. Consider a
2247:
2837:
2621:
1803:
872:
2916:. Intuitively, a mean of a function can be thought of as calculating the area under a section of a curve, and then dividing by the length of that section. This can be done crudely by counting squares on graph paper, or more precisely by
3019:
988:
999:
1288:
626:
is an average that is useful for sets of positive numbers, that are interpreted according to their product (as is the case with rates of growth) and not their sum (as is the case with the arithmetic mean):
612:
1607:
633:
3165:
2470:
400:
363:
3670:
under the guidance of Clark
Kimberling, an electronic encyclopedia of triangle centers (ETC) has been developed, it contains more than 7000 centers and many properties of these points
3593:
3044:âthere is no mean to the set of all colors. In these situations, you must decide which mean is most useful. You can do this by adjusting the values before averaging, or by using a
2084:
1511:
1846:
3068:. Unlike many other means, the Fréchet mean is defined on a space whose elements cannot necessarily be added together or multiplied by scalars. It is sometimes also known as the
2040:
2885:
2660:
1996:
1955:
1914:
2403:
2717:
Sometimes, a set of numbers might contain outliers (i.e., data values which are much lower or much higher than the others). Often, outliers are erroneous data caused by
2303:
392:
192:
149:
2143:
250:
2743:
2500:
1699:
784:
2347:
3024:
In this case, care must be taken to make sure that the integral converges. But the mean may be finite even if the function itself tends to infinity at some points.
2687:
2117:
1879:
2914:
1636:
1540:
1470:
221:
57:
is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers. There are several kinds of
3249:
3222:
3195:
1167:
1147:
2707:
1441:
1417:
2926:
1119:{\displaystyle {\frac {5}{{\tfrac {1}{4}}+{\tfrac {1}{36}}+{\tfrac {1}{45}}+{\tfrac {1}{50}}+{\tfrac {1}{75}}}}={\frac {5}{\;{\tfrac {1}{3}}\;}}=15.}
900:
5094:
5599:
3597:
2709:
respectively. In other applications, they represent a measure for the reliability of the influence upon the mean by the respective values.
1234:
1149:
tells us that these five different pumps working together will pump at the same rate as much as five pumps that can each empty the tank in
5749:
2737:
is a specific example of a truncated mean. It is simply the arithmetic mean after removing the lowest and the highest quarter of values.
1245:
98:, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers
5373:
4014:
1129:
If we have five pumps that can empty a tank of a certain size in respectively 4, 36, 45, 50, and 75 minutes, then the harmonic mean of
3681:
Hurst A, Brown GC, Swanson RI (2000) Swanson's 30-40-30 Rule. American
Association of Petroleum Geologists Bulletin 84(12) 1883-1891
545:
1553:
5147:
5586:
768:{\displaystyle {\bar {x}}=\left(\prod _{i=1}^{n}{x_{i}}\right)^{\frac {1}{n}}=\left(x_{1}x_{2}\cdots x_{n}\right)^{\frac {1}{n}}}
4009:
3709:
2494:(or weighted average) is used if one wants to combine average values from different sized samples of the same population:
4613:
3761:
2842:
assuming the values have been ordered, so is simply a specific example of a weighted mean for a specific set of weights.
1547:
5396:
5288:
3578:
3102:
1473:
6001:
5574:
5448:
529:{\displaystyle {\bar {x}}={\frac {1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)={\frac {x_{1}+x_{2}+\cdots +x_{n}}{n}}}
5632:
5293:
5038:
4409:
3999:
306:) of a list of numbers, is the sum of all of the numbers divided by their count. Similarly, the mean of a sample
2417:
5683:
4895:
4702:
4591:
4549:
309:
4623:
1642:. In all cases, including those in which the distribution is neither discrete nor continuous, the mean is the
89:. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.
6028:
5926:
4885:
3788:
3644:
Narboux, Julien; Braun, David (2016). "Towards a certified version of the encyclopedia of triangle centers".
5477:
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4720:
2053:
1639:
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17:
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2009:
1543:
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1968:
1927:
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5236:
5201:
5165:
4950:
4392:
4301:
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4172:
3863:
3702:
3272:
2718:
1392:
1364:
2242:{\displaystyle {\bar {x}}=f^{-1}\left({{\frac {1}{n}}\sum _{i=1}^{n}{f\left(x_{i}\right)}}\right)}
5830:
5443:
5383:
5320:
4958:
4942:
4680:
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4532:
4382:
4296:
3373:
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3093:
2361:
1659:
1650:. The mean need not exist or be finite; for some probability distributions the mean is infinite (
1335:
Geometric visualization of the mode, median and mean of an arbitrary probability density function
1324:
78:
2832:{\displaystyle {\bar {x}}={\frac {2}{n}}\;\sum _{i={\frac {n}{4}}+1}^{{\frac {3}{4}}n}\!\!x_{i}}
2616:{\displaystyle {\bar {x}}={\frac {\sum _{i=1}^{n}{w_{i}{\bar {x_{i}}}}}{\sum _{i=1}^{n}w_{i}}}.}
2266:
1798:{\displaystyle {\bar {x}}(m)=\left({\frac {1}{n}}\sum _{i=1}^{n}x_{i}^{m}\right)^{\frac {1}{m}}}
867:{\displaystyle (4\times 36\times 45\times 50\times 75)^{\frac {1}{5}}={\sqrt{24\;300\;000}}=30.}
368:
168:
125:
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5798:
5591:
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4167:
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3749:
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3378:
1340:
1205:
156:
3581:
228:
5893:
5835:
5778:
5604:
5497:
5406:
5132:
5016:
4875:
4867:
4757:
4749:
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4438:
4397:
4362:
4329:
4275:
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4205:
4144:
4104:
3906:
3729:
3342:
3061:
261:
152:
32:
3353:
2317:
256:
Outside probability and statistics, a wide range of other notions of mean are often used in
5816:
5391:
5340:
5316:
5278:
5196:
5175:
5127:
5006:
4984:
4953:
4862:
4739:
4690:
4608:
4581:
4537:
4493:
4255:
4031:
3911:
3665:
3449:
2665:
2095:
1857:
1643:
1368:
1359:). The mean of a set of observations is the arithmetic average of the values; however, for
1186:
2890:
1612:
1516:
1446:
206:
8:
5963:
5888:
5811:
5492:
5256:
5249:
5211:
5119:
5099:
5071:
4804:
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4665:
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4647:
4465:
4426:
4316:
4306:
4215:
3994:
3950:
3868:
3793:
3695:
3287:
3092:
This is an approximation to the mean for a moderately skewed distribution. It is used in
3065:
1647:
1209:
1181:
887:
3227:
3200:
3173:
1152:
1132:
886:
is an average which is useful for sets of numbers which are defined in relation to some
5977:
5788:
5642:
5538:
5487:
5363:
5260:
5244:
5221:
4998:
4732:
4715:
4675:
4586:
4481:
4443:
4414:
4374:
4334:
4280:
4197:
3883:
3878:
3454:
3444:
3399:
3357:
3036:
2851:
2734:
2692:
2131:
1426:
1402:
82:
2856:
In some circumstances, mathematicians may calculate a mean of an infinite (or even an
1355:, as any of these may incorrectly be called an "average" (more formally, a measure of
1302:
31:
This article is about quantifying the concept of "typical value". For other uses, see
5972:
5883:
5853:
5845:
5665:
5656:
5581:
5512:
5368:
5353:
5328:
5216:
5157:
5023:
5011:
4637:
4554:
4498:
4421:
4265:
4187:
3966:
3840:
3574:
3422:
3393:
1348:
1320:
278:
3620:
3084:
that can all be interpreted as the mean of a triangular set of points in the plane.
5908:
5863:
5627:
5614:
5507:
5482:
5416:
5348:
5226:
4834:
4727:
4660:
4573:
4520:
4339:
4210:
4004:
3888:
3803:
3770:
3653:
3412:
3347:
3327:
3014:{\displaystyle y_{\text{avg}}(a,b)={\frac {1}{b-a}}\int \limits _{a}^{b}\!f(x)\,dx}
1676:
1356:
62:
5825:
5569:
5431:
5358:
5033:
4907:
4880:
4857:
4826:
4453:
4448:
4402:
4132:
3783:
3661:
3459:
3439:
3081:
2351:
1960:
1396:
1386:
1331:
1312:
1193:
394:, is the sum of the sampled values divided by the number of items in the sample.
295:
289:
195:
94:
5315:
3057:
1177:
6023:
5774:
5769:
4232:
4162:
3808:
3368:
3363:
3332:
3260:
2722:
2407:
2001:
1919:
1680:
1420:
1380:
1213:
983:{\displaystyle {\bar {x}}=n\left(\sum _{i=1}^{n}{\frac {1}{x_{i}}}\right)^{-1}}
623:
199:
3657:
3547:
3277:
1307:
6017:
5931:
5898:
5761:
5722:
5533:
5502:
4966:
4920:
4525:
4227:
4054:
3818:
3813:
3317:
3312:
2491:
2474:
2045:
1513:, where the sum is taken over all possible values of the random variable and
883:
5873:
5806:
5783:
5698:
5028:
4324:
4222:
4157:
4099:
4084:
4021:
3976:
3282:
119:
3523:
3251:
are the 10th, 50th and 90th percentiles of the distribution, respctively.
5916:
5878:
5561:
5462:
5324:
5137:
5104:
4596:
4513:
4508:
4152:
4109:
4089:
4069:
4059:
3828:
3492:
3322:
3041:
2857:
161:
66:
3060:
gives a manner for determining the "center" of a mass distribution on a
1683:, arithmetic, geometric, and harmonic means. It is defined for a set of
1679:, also known as the power mean or Hölder mean, is an abstraction of the
993:
For example, the harmonic mean of the five values: 4, 36, 45, 50, 75 is
4762:
4242:
3942:
3873:
3823:
3798:
3718:
3307:
3302:
2307:
539:
For example, the arithmetic mean of five values: 4, 36, 45, 50, 75 is:
70:
778:
For example, the geometric mean of five values: 4, 36, 45, 50, 75 is:
4915:
4767:
4387:
4182:
4094:
4079:
4074:
4039:
1352:
3594:"AP Statistics Review - Density Curves and the Normal Distributions"
4431:
4049:
3926:
3921:
3916:
3434:
2917:
1360:
1283:{\displaystyle \mathrm {AM} \geq \mathrm {GM} \geq \mathrm {HM} \,}
1192:
PR is the diameter of a circle centered on O; its radius AO is the
257:
86:
46:
27:
Numeric quantity representing the center of a collection of numbers
1293:
Equality holds if all the elements of the given sample are equal.
5936:
5637:
2860:) set of values. This can happen when calculating the mean value
2089:
1851:
39:
5858:
4839:
4813:
4793:
4044:
3835:
3417:
1399:
having that distribution. If the random variable is denoted by
1344:
1316:
607:{\displaystyle {\frac {4+36+45+50+75}{5}}={\frac {210}{5}}=42.}
3549:
Why Few Math
Students Actually Understand the Meaning of Means
3080:
In geometry, there are thousands of different definitions for
1602:{\displaystyle \textstyle \int _{-\infty }^{\infty }xf(x)\,dx}
3687:
3032:
891:
74:
3027:
2049:
2005:
1964:
1923:
1882:
1814:
3046:
specialized approach for the mean of circular quantities
73:. Each attempts to summarize or typify a given group of
3230:
3203:
3176:
3035:, times of day, and other cyclical quantities require
1557:
1483:
1172:
1095:
1070:
1055:
1040:
1025:
1010:
3105:
2929:
2893:
2866:
2746:
2695:
2668:
2632:
2503:
2420:
2364:
2320:
2269:
2146:
2098:
2056:
2012:
1971:
1930:
1889:
1860:
1821:
1702:
1615:
1556:
1519:
1482:
1449:
1429:
1405:
1374:
1248:
1155:
1135:
1002:
903:
787:
636:
548:
403:
371:
312:
231:
209:
171:
128:
5600:
Autoregressive conditional heteroskedasticity (ARCH)
3389:
5062:
3243:
3216:
3189:
3159:
3013:
2908:
2879:
2831:
2701:
2681:
2654:
2615:
2464:
2397:
2341:
2297:
2241:
2111:
2078:
2034:
1990:
1949:
1908:
1873:
1840:
1797:
1630:
1601:
1534:
1505:
1464:
1435:
1411:
1282:
1161:
1141:
1118:
982:
866:
767:
606:
528:
386:
357:
244:
215:
186:
143:
2991:
2818:
2817:
6015:
2058:
2014:
1973:
1932:
1891:
1823:
5148:Multivariate adaptive regression splines (MARS)
3160:{\displaystyle m=0.3P_{10}+0.4P_{50}+0.3P_{90}}
1807:By choosing different values for the parameter
1395:is the long-run arithmetic average value of a
3703:
2252:and again a suitable choice of an invertible
1811:, the following types of means are obtained:
3643:
1235:Inequality of arithmetic and geometric means
3552:(YouTube video). Math The World. 2024-08-27
2485:
1646:of the random variable with respect to its
1239:AM, GM, and HM satisfy these inequalities:
3748:
3710:
3696:
2772:
2465:{\displaystyle f(x)=x^{-1}={\frac {1}{x}}}
1106:
1093:
846:
842:
202:) of the underlying distribution, denoted
45:For the state of being mean or cruel, see
4361:
3004:
2920:. The integration formula is written as:
1591:
1279:
358:{\displaystyle x_{1},x_{2},\ldots ,x_{n}}
3675:
1330:
1306:
1176:
38:For broader coverage of this topic, see
2130:This can be generalized further as the
1296:
283:
14:
6016:
5674:KaplanâMeier estimator (product limit)
3028:Mean of angles and cyclical quantities
617:
151:. If the numbers are from observing a
5747:
5314:
5061:
4360:
4130:
3747:
3691:
3618:
3569:Underhill, L.G.; Bradfield d. (1998)
2845:
2728:
2079:{\displaystyle \lim _{m\to -\infty }}
1506:{\displaystyle \textstyle \sum xP(x)}
1419:, then the mean is also known as the
877:
5984:
5684:Accelerated failure time (AFT) model
3518:
3516:
3514:
3512:
1841:{\displaystyle \lim _{m\to \infty }}
1665:
1343:, the mean may be confused with the
272:
159:, the arithmetic mean is termed the
5996:
5279:Analysis of variance (ANOVA, anova)
4131:
1303:Average § Statistical location
1173:Relationship between AM, GM, and HM
894:(i.e., distance per unit of time):
24:
5374:CochranâMantelâHaenszel statistics
4000:Pearson product-moment correlation
3075:
2071:
1833:
1571:
1566:
1375:Mean of a probability distribution
1275:
1272:
1264:
1261:
1253:
1250:
25:
6040:
3612:
3509:
3087:
2712:
1474:discrete probability distribution
267:
5995:
5983:
5971:
5958:
5957:
5748:
3392:
2689:are the mean and size of sample
1658:), while for others the mean is
5633:Least-squares spectral analysis
3646:Mathematics in Computer Science
3072:(named after Hermann Karcher).
3051:
2035:{\displaystyle \lim _{m\to -1}}
4614:Mean-unbiased minimum-variance
3717:
3637:
3586:
3563:
3540:
3485:
3472:
3254:
3001:
2995:
2952:
2940:
2903:
2897:
2880:{\displaystyle y_{\text{avg}}}
2753:
2721:. In this case, one can use a
2655:{\displaystyle {\bar {x_{i}}}}
2646:
2567:
2510:
2430:
2424:
2392:
2386:
2374:
2368:
2330:
2324:
2279:
2273:
2153:
2065:
2021:
1991:{\displaystyle \lim _{m\to 0}}
1980:
1950:{\displaystyle \lim _{m\to 1}}
1939:
1909:{\displaystyle \lim _{m\to 2}}
1898:
1830:
1721:
1715:
1709:
1625:
1619:
1588:
1582:
1529:
1523:
1499:
1493:
1459:
1453:
910:
819:
788:
643:
410:
378:
178:
135:
118:is typically denoted using an
13:
1:
5927:Geographic information system
5143:Simultaneous equations models
3502:
1670:
194:) to distinguish it from the
5110:Coefficient of determination
4721:Uniformly most powerful test
1640:probability density function
264:; examples are given below.
7:
5679:Proportional hazards models
5623:Spectral density estimation
5605:Vector autoregression (VAR)
5039:Maximum posterior estimator
4271:Randomized controlled trial
3385:
2398:{\displaystyle f(x)=\ln(x)}
10:
6045:
5439:Multivariate distributions
3859:Average absolute deviation
3258:
2849:
2298:{\displaystyle f(x)=x^{m}}
1384:
1378:
1300:
1232:
387:{\displaystyle {\bar {x}}}
287:
276:
187:{\displaystyle {\bar {x}}}
144:{\displaystyle {\bar {x}}}
29:
5953:
5907:
5844:
5797:
5760:
5756:
5743:
5715:
5697:
5664:
5655:
5613:
5560:
5521:
5470:
5461:
5427:Structural equation model
5382:
5339:
5335:
5310:
5269:
5235:
5189:
5156:
5118:
5085:
5081:
5057:
4997:
4906:
4825:
4789:
4780:
4763:Score/Lagrange multiplier
4748:
4701:
4646:
4572:
4563:
4373:
4369:
4356:
4315:
4289:
4241:
4196:
4178:Sample size determination
4143:
4139:
4126:
4030:
3985:
3959:
3941:
3897:
3849:
3769:
3760:
3756:
3743:
3725:
3658:10.1007/s11786-016-0254-4
3293:Elementary symmetric mean
3268:Arithmetic-geometric mean
2122:
1544:probability mass function
5922:Environmental statistics
5444:Elliptical distributions
5237:Generalized linear model
5166:Simple linear regression
4936:HodgesâLehmann estimator
4393:Probability distribution
4302:Stochastic approximation
3864:Coefficient of variation
3573:, Juta and Company Ltd.
3465:
3273:Arithmetic-harmonic mean
3082:the center of a triangle
2492:weighted arithmetic mean
2486:Weighted arithmetic mean
1393:probability distribution
245:{\displaystyle \mu _{x}}
5582:Cross-correlation (XCF)
5190:Non-standard predictors
4624:LehmannâScheffĂ© theorem
4297:Adaptive clinical trial
3528:Encyclopedia Britannica
3374:Weighted geometric mean
3298:Geometric-harmonic mean
3094:hydrocarbon exploration
1548:continuous distribution
1476:, the mean is given by
5978:Mathematics portal
5799:Engineering statistics
5707:NelsonâAalen estimator
5284:Analysis of covariance
5171:Ordinary least squares
5095:Pearson product-moment
4499:Statistical functional
4410:Empirical distribution
4243:Controlled experiments
3972:Frequency distribution
3750:Descriptive statistics
3430:Descriptive statistics
3408:Statistical dispersion
3379:Weighted harmonic mean
3245:
3218:
3191:
3161:
3015:
2990:
2910:
2881:
2833:
2816:
2703:
2683:
2656:
2617:
2596:
2542:
2466:
2399:
2343:
2342:{\displaystyle f(x)=x}
2299:
2243:
2210:
2113:
2080:
2036:
1992:
1951:
1910:
1875:
1842:
1799:
1763:
1632:
1603:
1536:
1507:
1466:
1437:
1413:
1341:descriptive statistics
1336:
1328:
1284:
1230:
1206:geometric mean theorem
1163:
1143:
1120:
984:
948:
868:
769:
678:
608:
530:
454:
388:
359:
246:
217:
188:
145:
5894:Population statistics
5836:System identification
5570:Autocorrelation (ACF)
5498:Exponential smoothing
5412:Discriminant analysis
5407:Canonical correlation
5271:Partition of variance
5133:Regression validation
4977:(JonckheereâTerpstra)
4876:Likelihood-ratio test
4565:Frequentist inference
4477:Locationâscale family
4398:Sampling distribution
4363:Statistical inference
4330:Cross-sectional study
4317:Observational studies
4276:Randomized experiment
4105:Stem-and-leaf display
3907:Central limit theorem
3625:mathworld.wolfram.com
3495:, pronounced /'mjuË/.
3343:Quasi-arithmetic mean
3246:
3219:
3192:
3162:
3016:
2976:
2911:
2882:
2834:
2773:
2704:
2684:
2682:{\displaystyle w_{i}}
2657:
2618:
2576:
2522:
2467:
2400:
2344:
2300:
2244:
2190:
2114:
2112:{\displaystyle x_{i}}
2081:
2037:
1993:
1952:
1911:
1876:
1874:{\displaystyle x_{i}}
1843:
1800:
1743:
1633:
1604:
1537:
1508:
1467:
1438:
1414:
1334:
1310:
1285:
1180:
1164:
1144:
1121:
985:
928:
869:
770:
658:
609:
531:
434:
389:
365:, usually denoted by
360:
262:mathematical analysis
247:
218:
189:
146:
33:Mean (disambiguation)
6029:Moment (mathematics)
5817:Probabilistic design
5402:Principal components
5245:Exponential families
5197:Nonlinear regression
5176:General linear model
5138:Mixed effects models
5128:Errors and residuals
5105:Confounding variable
5007:Bayesian probability
4985:Van der Waerden test
4975:Ordered alternative
4740:Multiple comparisons
4619:RaoâBlackwellization
4582:Estimating equations
4538:Statistical distance
4256:Factorial experiment
3789:Arithmetic-Geometric
3524:"Mean | mathematics"
3450:Moment (mathematics)
3228:
3201:
3174:
3103:
3064:or, more generally,
2927:
2909:{\displaystyle f(x)}
2891:
2864:
2744:
2693:
2666:
2630:
2501:
2418:
2362:
2318:
2267:
2144:
2096:
2054:
2010:
1969:
1928:
1887:
1858:
1819:
1700:
1631:{\displaystyle f(x)}
1613:
1554:
1535:{\displaystyle P(x)}
1517:
1480:
1465:{\displaystyle E(X)}
1447:
1427:
1403:
1361:skewed distributions
1297:Statistical location
1246:
1153:
1133:
1000:
901:
890:, as in the case of
785:
634:
546:
401:
369:
310:
284:Arithmetic mean (AM)
229:
216:{\displaystyle \mu }
207:
169:
126:
5889:Official statistics
5812:Methods engineering
5493:Seasonal adjustment
5261:Poisson regressions
5181:Bayesian regression
5120:Regression analysis
5100:Partial correlation
5072:Regression analysis
4671:Prediction interval
4666:Likelihood interval
4656:Confidence interval
4648:Interval estimation
4609:Unbiased estimators
4427:Model specification
4307:Up-and-down designs
3995:Partial correlation
3951:Index of dispersion
3869:Interquartile range
3619:Weisstein, Eric W.
3288:Contraharmonic mean
3244:{\textstyle P_{90}}
3217:{\textstyle P_{50}}
3190:{\textstyle P_{10}}
3096:and is defined as:
3066:Riemannian manifold
1778:
1648:probability measure
1575:
1182:Proof without words
618:Geometric mean (GM)
77:, illustrating the
5909:Spatial statistics
5789:Medical statistics
5689:First hitting time
5643:Whittle likelihood
5294:Degrees of freedom
5289:Multivariate ANOVA
5222:Heteroscedasticity
5034:Bayesian estimator
4999:Bayesian inference
4848:KolmogorovâSmirnov
4733:Randomization test
4703:Testing hypotheses
4676:Tolerance interval
4587:Maximum likelihood
4482:Exponential family
4415:Density estimation
4375:Statistical theory
4335:Natural experiment
4281:Scientific control
4198:Survey methodology
3884:Standard deviation
3455:Summary statistics
3445:Mean value theorem
3400:Mathematics portal
3358:generalized f-mean
3338:NeumanâSĂĄndor mean
3241:
3214:
3187:
3157:
3037:modular arithmetic
3011:
2906:
2877:
2852:Mean of a function
2846:Mean of a function
2829:
2735:interquartile mean
2729:Interquartile mean
2699:
2679:
2652:
2613:
2462:
2395:
2339:
2295:
2239:
2109:
2076:
2075:
2032:
2031:
1988:
1987:
1947:
1946:
1906:
1905:
1871:
1838:
1837:
1795:
1764:
1628:
1599:
1598:
1558:
1532:
1503:
1502:
1462:
1433:
1409:
1337:
1329:
1311:Comparison of the
1280:
1231:
1162:{\displaystyle 15}
1159:
1142:{\displaystyle 15}
1139:
1116:
1104:
1079:
1064:
1049:
1034:
1019:
980:
878:Harmonic mean (HM)
864:
765:
604:
526:
384:
355:
242:
213:
184:
141:
6011:
6010:
5949:
5948:
5945:
5944:
5884:National accounts
5854:Actuarial science
5846:Social statistics
5739:
5738:
5735:
5734:
5731:
5730:
5666:Survival function
5651:
5650:
5513:Granger causality
5354:Contingency table
5329:Survival analysis
5306:
5305:
5302:
5301:
5158:Linear regression
5053:
5052:
5049:
5048:
5024:Credible interval
4993:
4992:
4776:
4775:
4592:Method of moments
4461:Parametric family
4422:Statistical model
4352:
4351:
4348:
4347:
4266:Random assignment
4188:Statistical power
4122:
4121:
4118:
4117:
3967:Contingency table
3937:
3936:
3804:Generalized/power
3621:"Population Mean"
2974:
2937:
2874:
2810:
2792:
2770:
2756:
2702:{\displaystyle i}
2649:
2608:
2570:
2513:
2481:
2480:
2460:
2188:
2156:
2057:
2013:
1972:
1931:
1890:
1822:
1792:
1741:
1712:
1687:positive numbers
1666:Generalized means
1644:Lebesgue integral
1436:{\displaystyle X}
1412:{\displaystyle X}
1208:, triangle PGR's
1108:
1103:
1082:
1078:
1063:
1048:
1033:
1018:
964:
913:
856:
830:
762:
704:
646:
596:
583:
524:
427:
413:
381:
279:Pythagorean means
273:Pythagorean means
181:
138:
61:(or "measures of
16:(Redirected from
6036:
5999:
5998:
5987:
5986:
5976:
5975:
5961:
5960:
5864:Crime statistics
5758:
5757:
5745:
5744:
5662:
5661:
5628:Fourier analysis
5615:Frequency domain
5595:
5542:
5508:Structural break
5468:
5467:
5417:Cluster analysis
5364:Log-linear model
5337:
5336:
5312:
5311:
5253:
5227:Homoscedasticity
5083:
5082:
5059:
5058:
4978:
4970:
4962:
4961:(KruskalâWallis)
4946:
4931:
4886:Cross validation
4871:
4853:AndersonâDarling
4800:
4787:
4786:
4758:Likelihood-ratio
4750:Parametric tests
4728:Permutation test
4711:1- & 2-tails
4602:Minimum distance
4574:Point estimation
4570:
4569:
4521:Optimal decision
4472:
4371:
4370:
4358:
4357:
4340:Quasi-experiment
4290:Adaptive designs
4141:
4140:
4128:
4127:
4005:Rank correlation
3767:
3766:
3758:
3757:
3745:
3744:
3712:
3705:
3698:
3689:
3688:
3682:
3679:
3673:
3672:
3641:
3635:
3634:
3632:
3631:
3616:
3610:
3609:
3607:
3605:
3596:. Archived from
3590:
3584:
3567:
3561:
3560:
3558:
3557:
3544:
3538:
3537:
3535:
3534:
3520:
3496:
3489:
3483:
3476:
3413:Central tendency
3402:
3397:
3396:
3350:(quadratic mean)
3348:Root mean square
3328:Logarithmic mean
3250:
3248:
3247:
3242:
3240:
3239:
3223:
3221:
3220:
3215:
3213:
3212:
3196:
3194:
3193:
3188:
3186:
3185:
3166:
3164:
3163:
3158:
3156:
3155:
3140:
3139:
3124:
3123:
3020:
3018:
3017:
3012:
2989:
2984:
2975:
2973:
2959:
2939:
2938:
2935:
2915:
2913:
2912:
2907:
2886:
2884:
2883:
2878:
2876:
2875:
2872:
2838:
2836:
2835:
2830:
2828:
2827:
2815:
2811:
2803:
2800:
2793:
2785:
2771:
2763:
2758:
2757:
2749:
2708:
2706:
2705:
2700:
2688:
2686:
2685:
2680:
2678:
2677:
2661:
2659:
2658:
2653:
2651:
2650:
2645:
2644:
2635:
2622:
2620:
2619:
2614:
2609:
2607:
2606:
2605:
2595:
2590:
2574:
2573:
2572:
2571:
2566:
2565:
2556:
2553:
2552:
2541:
2536:
2520:
2515:
2514:
2506:
2471:
2469:
2468:
2463:
2461:
2453:
2448:
2447:
2404:
2402:
2401:
2396:
2348:
2346:
2345:
2340:
2304:
2302:
2301:
2296:
2294:
2293:
2261:
2260:
2255:
2248:
2246:
2245:
2240:
2238:
2234:
2233:
2232:
2228:
2227:
2209:
2204:
2189:
2181:
2174:
2173:
2158:
2157:
2149:
2135:
2118:
2116:
2115:
2110:
2108:
2107:
2085:
2083:
2082:
2077:
2074:
2041:
2039:
2038:
2033:
2030:
1997:
1995:
1994:
1989:
1986:
1956:
1954:
1953:
1948:
1945:
1915:
1913:
1912:
1907:
1904:
1880:
1878:
1877:
1872:
1870:
1869:
1847:
1845:
1844:
1839:
1836:
1804:
1802:
1801:
1796:
1794:
1793:
1785:
1783:
1779:
1777:
1772:
1762:
1757:
1742:
1734:
1714:
1713:
1705:
1677:generalized mean
1657:
1653:
1637:
1635:
1634:
1629:
1608:
1606:
1605:
1600:
1574:
1569:
1541:
1539:
1538:
1533:
1512:
1510:
1509:
1504:
1471:
1469:
1468:
1463:
1442:
1440:
1439:
1434:
1418:
1416:
1415:
1410:
1357:central tendency
1289:
1287:
1286:
1281:
1278:
1267:
1256:
1229:
1226:
1216:. For any ratio
1190:
1187:AMâGM inequality
1168:
1166:
1165:
1160:
1148:
1146:
1145:
1140:
1125:
1123:
1122:
1117:
1109:
1107:
1105:
1096:
1088:
1083:
1081:
1080:
1071:
1065:
1056:
1050:
1041:
1035:
1026:
1020:
1011:
1004:
989:
987:
986:
981:
979:
978:
970:
966:
965:
963:
962:
950:
947:
942:
915:
914:
906:
873:
871:
870:
865:
857:
855:
850:
837:
832:
831:
823:
774:
772:
771:
766:
764:
763:
755:
753:
749:
748:
747:
735:
734:
725:
724:
706:
705:
697:
695:
691:
690:
689:
688:
677:
672:
648:
647:
639:
613:
611:
610:
605:
597:
589:
584:
579:
550:
535:
533:
532:
527:
525:
520:
519:
518:
500:
499:
487:
486:
476:
471:
467:
466:
465:
464:
453:
448:
428:
420:
415:
414:
406:
393:
391:
390:
385:
383:
382:
374:
364:
362:
361:
356:
354:
353:
335:
334:
322:
321:
251:
249:
248:
243:
241:
240:
222:
220:
219:
214:
193:
191:
190:
185:
183:
182:
174:
150:
148:
147:
142:
140:
139:
131:
69:, especially in
63:central tendency
50:
43:
36:
21:
6044:
6043:
6039:
6038:
6037:
6035:
6034:
6033:
6014:
6013:
6012:
6007:
5970:
5941:
5903:
5840:
5826:quality control
5793:
5775:Clinical trials
5752:
5727:
5711:
5699:Hazard function
5693:
5647:
5609:
5593:
5556:
5552:BreuschâGodfrey
5540:
5517:
5457:
5432:Factor analysis
5378:
5359:Graphical model
5331:
5298:
5265:
5251:
5231:
5185:
5152:
5114:
5077:
5076:
5045:
4989:
4976:
4968:
4960:
4944:
4929:
4908:Rank statistics
4902:
4881:Model selection
4869:
4827:Goodness of fit
4821:
4798:
4772:
4744:
4697:
4642:
4631:Median unbiased
4559:
4470:
4403:Order statistic
4365:
4344:
4311:
4285:
4237:
4192:
4135:
4133:Data collection
4114:
4026:
3981:
3955:
3933:
3893:
3845:
3762:Continuous data
3752:
3739:
3721:
3716:
3686:
3685:
3680:
3676:
3642:
3638:
3629:
3627:
3617:
3613:
3603:
3601:
3600:on 2 April 2015
3592:
3591:
3587:
3568:
3564:
3555:
3553:
3546:
3545:
3541:
3532:
3530:
3522:
3521:
3510:
3505:
3500:
3499:
3490:
3486:
3477:
3473:
3468:
3440:Law of averages
3398:
3391:
3388:
3383:
3354:RĂ©nyi's entropy
3263:
3259:Main category:
3257:
3235:
3231:
3229:
3226:
3225:
3208:
3204:
3202:
3199:
3198:
3181:
3177:
3175:
3172:
3171:
3151:
3147:
3135:
3131:
3119:
3115:
3104:
3101:
3100:
3090:
3078:
3076:Triangular sets
3054:
3030:
2985:
2980:
2963:
2958:
2934:
2930:
2928:
2925:
2924:
2892:
2889:
2888:
2871:
2867:
2865:
2862:
2861:
2854:
2848:
2823:
2819:
2802:
2801:
2784:
2777:
2762:
2748:
2747:
2745:
2742:
2741:
2731:
2715:
2694:
2691:
2690:
2673:
2669:
2667:
2664:
2663:
2640:
2636:
2634:
2633:
2631:
2628:
2627:
2601:
2597:
2591:
2580:
2575:
2561:
2557:
2555:
2554:
2548:
2544:
2543:
2537:
2526:
2521:
2519:
2505:
2504:
2502:
2499:
2498:
2488:
2452:
2440:
2436:
2419:
2416:
2415:
2363:
2360:
2359:
2352:arithmetic mean
2319:
2316:
2315:
2289:
2285:
2268:
2265:
2264:
2253:
2223:
2219:
2215:
2211:
2205:
2194:
2180:
2179:
2175:
2166:
2162:
2148:
2147:
2145:
2142:
2141:
2133:
2128:
2103:
2099:
2097:
2094:
2093:
2086:
2061:
2055:
2052:
2051:
2042:
2017:
2011:
2008:
2007:
1998:
1976:
1970:
1967:
1966:
1961:arithmetic mean
1957:
1935:
1929:
1926:
1925:
1916:
1894:
1888:
1885:
1884:
1865:
1861:
1859:
1856:
1855:
1848:
1826:
1820:
1817:
1816:
1784:
1773:
1768:
1758:
1747:
1733:
1732:
1728:
1727:
1704:
1703:
1701:
1698:
1697:
1693:
1673:
1668:
1655:
1651:
1614:
1611:
1610:
1570:
1562:
1555:
1552:
1551:
1518:
1515:
1514:
1481:
1478:
1477:
1448:
1445:
1444:
1428:
1425:
1424:
1404:
1401:
1400:
1397:random variable
1389:
1387:Population mean
1383:
1377:
1371:distributions.
1327:) distributions
1323:of two skewed (
1313:arithmetic mean
1305:
1299:
1271:
1260:
1249:
1247:
1244:
1243:
1237:
1227:
1217:
1194:arithmetic mean
1185:
1175:
1154:
1151:
1150:
1134:
1131:
1130:
1094:
1092:
1087:
1069:
1054:
1039:
1024:
1009:
1008:
1003:
1001:
998:
997:
971:
958:
954:
949:
943:
932:
927:
923:
922:
905:
904:
902:
899:
898:
880:
851:
838:
836:
822:
818:
786:
783:
782:
754:
743:
739:
730:
726:
720:
716:
715:
711:
710:
696:
684:
680:
679:
673:
662:
657:
653:
652:
638:
637:
635:
632:
631:
620:
588:
551:
549:
547:
544:
543:
514:
510:
495:
491:
482:
478:
477:
475:
460:
456:
455:
449:
438:
433:
429:
419:
405:
404:
402:
399:
398:
373:
372:
370:
367:
366:
349:
345:
330:
326:
317:
313:
311:
308:
307:
296:arithmetic mean
292:
290:Arithmetic mean
286:
281:
275:
270:
236:
232:
230:
227:
226:
208:
205:
204:
173:
172:
170:
167:
166:
130:
129:
127:
124:
123:
116:
111:
104:
95:arithmetic mean
51:
44:
37:
30:
28:
23:
22:
15:
12:
11:
5:
6042:
6032:
6031:
6026:
6009:
6008:
6006:
6005:
5993:
5981:
5967:
5954:
5951:
5950:
5947:
5946:
5943:
5942:
5940:
5939:
5934:
5929:
5924:
5919:
5913:
5911:
5905:
5904:
5902:
5901:
5896:
5891:
5886:
5881:
5876:
5871:
5866:
5861:
5856:
5850:
5848:
5842:
5841:
5839:
5838:
5833:
5828:
5819:
5814:
5809:
5803:
5801:
5795:
5794:
5792:
5791:
5786:
5781:
5772:
5770:Bioinformatics
5766:
5764:
5754:
5753:
5741:
5740:
5737:
5736:
5733:
5732:
5729:
5728:
5726:
5725:
5719:
5717:
5713:
5712:
5710:
5709:
5703:
5701:
5695:
5694:
5692:
5691:
5686:
5681:
5676:
5670:
5668:
5659:
5653:
5652:
5649:
5648:
5646:
5645:
5640:
5635:
5630:
5625:
5619:
5617:
5611:
5610:
5608:
5607:
5602:
5597:
5589:
5584:
5579:
5578:
5577:
5575:partial (PACF)
5566:
5564:
5558:
5557:
5555:
5554:
5549:
5544:
5536:
5531:
5525:
5523:
5522:Specific tests
5519:
5518:
5516:
5515:
5510:
5505:
5500:
5495:
5490:
5485:
5480:
5474:
5472:
5465:
5459:
5458:
5456:
5455:
5454:
5453:
5452:
5451:
5436:
5435:
5434:
5424:
5422:Classification
5419:
5414:
5409:
5404:
5399:
5394:
5388:
5386:
5380:
5379:
5377:
5376:
5371:
5369:McNemar's test
5366:
5361:
5356:
5351:
5345:
5343:
5333:
5332:
5308:
5307:
5304:
5303:
5300:
5299:
5297:
5296:
5291:
5286:
5281:
5275:
5273:
5267:
5266:
5264:
5263:
5247:
5241:
5239:
5233:
5232:
5230:
5229:
5224:
5219:
5214:
5209:
5207:Semiparametric
5204:
5199:
5193:
5191:
5187:
5186:
5184:
5183:
5178:
5173:
5168:
5162:
5160:
5154:
5153:
5151:
5150:
5145:
5140:
5135:
5130:
5124:
5122:
5116:
5115:
5113:
5112:
5107:
5102:
5097:
5091:
5089:
5079:
5078:
5075:
5074:
5069:
5063:
5055:
5054:
5051:
5050:
5047:
5046:
5044:
5043:
5042:
5041:
5031:
5026:
5021:
5020:
5019:
5014:
5003:
5001:
4995:
4994:
4991:
4990:
4988:
4987:
4982:
4981:
4980:
4972:
4964:
4948:
4945:(MannâWhitney)
4940:
4939:
4938:
4925:
4924:
4923:
4912:
4910:
4904:
4903:
4901:
4900:
4899:
4898:
4893:
4888:
4878:
4873:
4870:(ShapiroâWilk)
4865:
4860:
4855:
4850:
4845:
4837:
4831:
4829:
4823:
4822:
4820:
4819:
4811:
4802:
4790:
4784:
4782:Specific tests
4778:
4777:
4774:
4773:
4771:
4770:
4765:
4760:
4754:
4752:
4746:
4745:
4743:
4742:
4737:
4736:
4735:
4725:
4724:
4723:
4713:
4707:
4705:
4699:
4698:
4696:
4695:
4694:
4693:
4688:
4678:
4673:
4668:
4663:
4658:
4652:
4650:
4644:
4643:
4641:
4640:
4635:
4634:
4633:
4628:
4627:
4626:
4621:
4606:
4605:
4604:
4599:
4594:
4589:
4578:
4576:
4567:
4561:
4560:
4558:
4557:
4552:
4547:
4546:
4545:
4535:
4530:
4529:
4528:
4518:
4517:
4516:
4511:
4506:
4496:
4491:
4486:
4485:
4484:
4479:
4474:
4458:
4457:
4456:
4451:
4446:
4436:
4435:
4434:
4429:
4419:
4418:
4417:
4407:
4406:
4405:
4395:
4390:
4385:
4379:
4377:
4367:
4366:
4354:
4353:
4350:
4349:
4346:
4345:
4343:
4342:
4337:
4332:
4327:
4321:
4319:
4313:
4312:
4310:
4309:
4304:
4299:
4293:
4291:
4287:
4286:
4284:
4283:
4278:
4273:
4268:
4263:
4258:
4253:
4247:
4245:
4239:
4238:
4236:
4235:
4233:Standard error
4230:
4225:
4220:
4219:
4218:
4213:
4202:
4200:
4194:
4193:
4191:
4190:
4185:
4180:
4175:
4170:
4165:
4163:Optimal design
4160:
4155:
4149:
4147:
4137:
4136:
4124:
4123:
4120:
4119:
4116:
4115:
4113:
4112:
4107:
4102:
4097:
4092:
4087:
4082:
4077:
4072:
4067:
4062:
4057:
4052:
4047:
4042:
4036:
4034:
4028:
4027:
4025:
4024:
4019:
4018:
4017:
4012:
4002:
3997:
3991:
3989:
3983:
3982:
3980:
3979:
3974:
3969:
3963:
3961:
3960:Summary tables
3957:
3956:
3954:
3953:
3947:
3945:
3939:
3938:
3935:
3934:
3932:
3931:
3930:
3929:
3924:
3919:
3909:
3903:
3901:
3895:
3894:
3892:
3891:
3886:
3881:
3876:
3871:
3866:
3861:
3855:
3853:
3847:
3846:
3844:
3843:
3838:
3833:
3832:
3831:
3826:
3821:
3816:
3811:
3806:
3801:
3796:
3794:Contraharmonic
3791:
3786:
3775:
3773:
3764:
3754:
3753:
3741:
3740:
3738:
3737:
3732:
3726:
3723:
3722:
3715:
3714:
3707:
3700:
3692:
3684:
3683:
3674:
3636:
3611:
3585:
3562:
3539:
3507:
3506:
3504:
3501:
3498:
3497:
3484:
3470:
3469:
3467:
3464:
3463:
3462:
3457:
3452:
3447:
3442:
3437:
3432:
3427:
3426:
3425:
3420:
3410:
3404:
3403:
3387:
3384:
3382:
3381:
3376:
3371:
3369:Stolarsky mean
3366:
3364:Spherical mean
3361:
3351:
3345:
3340:
3335:
3333:Moving average
3330:
3325:
3320:
3315:
3310:
3305:
3300:
3295:
3290:
3285:
3280:
3275:
3270:
3264:
3256:
3253:
3238:
3234:
3211:
3207:
3184:
3180:
3168:
3167:
3154:
3150:
3146:
3143:
3138:
3134:
3130:
3127:
3122:
3118:
3114:
3111:
3108:
3089:
3088:Swanson's rule
3086:
3077:
3074:
3053:
3050:
3029:
3026:
3022:
3021:
3010:
3007:
3003:
3000:
2997:
2994:
2988:
2983:
2979:
2972:
2969:
2966:
2962:
2957:
2954:
2951:
2948:
2945:
2942:
2933:
2905:
2902:
2899:
2896:
2887:of a function
2870:
2850:Main article:
2847:
2844:
2840:
2839:
2826:
2822:
2814:
2809:
2806:
2799:
2796:
2791:
2788:
2783:
2780:
2776:
2769:
2766:
2761:
2755:
2752:
2730:
2727:
2723:truncated mean
2714:
2713:Truncated mean
2711:
2698:
2676:
2672:
2648:
2643:
2639:
2624:
2623:
2612:
2604:
2600:
2594:
2589:
2586:
2583:
2579:
2569:
2564:
2560:
2551:
2547:
2540:
2535:
2532:
2529:
2525:
2518:
2512:
2509:
2487:
2484:
2483:
2482:
2479:
2478:
2472:
2459:
2456:
2451:
2446:
2443:
2439:
2435:
2432:
2429:
2426:
2423:
2412:
2411:
2408:geometric mean
2405:
2394:
2391:
2388:
2385:
2382:
2379:
2376:
2373:
2370:
2367:
2356:
2355:
2349:
2338:
2335:
2332:
2329:
2326:
2323:
2312:
2311:
2305:
2292:
2288:
2284:
2281:
2278:
2275:
2272:
2250:
2249:
2237:
2231:
2226:
2222:
2218:
2214:
2208:
2203:
2200:
2197:
2193:
2187:
2184:
2178:
2172:
2169:
2165:
2161:
2155:
2152:
2127:
2121:
2120:
2119:
2106:
2102:
2087:
2073:
2070:
2067:
2064:
2060:
2050:
2048:
2043:
2029:
2026:
2023:
2020:
2016:
2006:
2004:
2002:geometric mean
1999:
1985:
1982:
1979:
1975:
1965:
1963:
1958:
1944:
1941:
1938:
1934:
1924:
1922:
1920:quadratic mean
1917:
1903:
1900:
1897:
1893:
1883:
1881:
1868:
1864:
1849:
1835:
1832:
1829:
1825:
1815:
1791:
1788:
1782:
1776:
1771:
1767:
1761:
1756:
1753:
1750:
1746:
1740:
1737:
1731:
1726:
1723:
1720:
1717:
1711:
1708:
1691:
1672:
1669:
1667:
1664:
1627:
1624:
1621:
1618:
1597:
1594:
1590:
1587:
1584:
1581:
1578:
1573:
1568:
1565:
1561:
1550:, the mean is
1531:
1528:
1525:
1522:
1501:
1498:
1495:
1492:
1489:
1486:
1461:
1458:
1455:
1452:
1432:
1421:expected value
1408:
1391:The mean of a
1381:Expected value
1379:Main article:
1376:
1373:
1298:
1295:
1291:
1290:
1277:
1274:
1270:
1266:
1263:
1259:
1255:
1252:
1233:Main article:
1228:AO ≥ GQ.
1214:geometric mean
1191:
1174:
1171:
1158:
1138:
1127:
1126:
1115:
1112:
1102:
1099:
1091:
1086:
1077:
1074:
1068:
1062:
1059:
1053:
1047:
1044:
1038:
1032:
1029:
1023:
1017:
1014:
1007:
991:
990:
977:
974:
969:
961:
957:
953:
946:
941:
938:
935:
931:
926:
921:
918:
912:
909:
879:
876:
875:
874:
863:
860:
854:
849:
845:
841:
835:
829:
826:
821:
817:
814:
811:
808:
805:
802:
799:
796:
793:
790:
776:
775:
761:
758:
752:
746:
742:
738:
733:
729:
723:
719:
714:
709:
703:
700:
694:
687:
683:
676:
671:
668:
665:
661:
656:
651:
645:
642:
624:geometric mean
619:
616:
615:
614:
603:
600:
595:
592:
587:
582:
578:
575:
572:
569:
566:
563:
560:
557:
554:
537:
536:
523:
517:
513:
509:
506:
503:
498:
494:
490:
485:
481:
474:
470:
463:
459:
452:
447:
444:
441:
437:
432:
426:
423:
418:
412:
409:
380:
377:
352:
348:
344:
341:
338:
333:
329:
325:
320:
316:
288:Main article:
285:
282:
277:Main article:
274:
271:
269:
268:Types of means
266:
239:
235:
212:
200:expected value
180:
177:
137:
134:
114:
109:
102:
26:
9:
6:
4:
3:
2:
6041:
6030:
6027:
6025:
6022:
6021:
6019:
6004:
6003:
5994:
5992:
5991:
5982:
5980:
5979:
5974:
5968:
5966:
5965:
5956:
5955:
5952:
5938:
5935:
5933:
5932:Geostatistics
5930:
5928:
5925:
5923:
5920:
5918:
5915:
5914:
5912:
5910:
5906:
5900:
5899:Psychometrics
5897:
5895:
5892:
5890:
5887:
5885:
5882:
5880:
5877:
5875:
5872:
5870:
5867:
5865:
5862:
5860:
5857:
5855:
5852:
5851:
5849:
5847:
5843:
5837:
5834:
5832:
5829:
5827:
5823:
5820:
5818:
5815:
5813:
5810:
5808:
5805:
5804:
5802:
5800:
5796:
5790:
5787:
5785:
5782:
5780:
5776:
5773:
5771:
5768:
5767:
5765:
5763:
5762:Biostatistics
5759:
5755:
5751:
5746:
5742:
5724:
5723:Log-rank test
5721:
5720:
5718:
5714:
5708:
5705:
5704:
5702:
5700:
5696:
5690:
5687:
5685:
5682:
5680:
5677:
5675:
5672:
5671:
5669:
5667:
5663:
5660:
5658:
5654:
5644:
5641:
5639:
5636:
5634:
5631:
5629:
5626:
5624:
5621:
5620:
5618:
5616:
5612:
5606:
5603:
5601:
5598:
5596:
5594:(BoxâJenkins)
5590:
5588:
5585:
5583:
5580:
5576:
5573:
5572:
5571:
5568:
5567:
5565:
5563:
5559:
5553:
5550:
5548:
5547:DurbinâWatson
5545:
5543:
5537:
5535:
5532:
5530:
5529:DickeyâFuller
5527:
5526:
5524:
5520:
5514:
5511:
5509:
5506:
5504:
5503:Cointegration
5501:
5499:
5496:
5494:
5491:
5489:
5486:
5484:
5481:
5479:
5478:Decomposition
5476:
5475:
5473:
5469:
5466:
5464:
5460:
5450:
5447:
5446:
5445:
5442:
5441:
5440:
5437:
5433:
5430:
5429:
5428:
5425:
5423:
5420:
5418:
5415:
5413:
5410:
5408:
5405:
5403:
5400:
5398:
5395:
5393:
5390:
5389:
5387:
5385:
5381:
5375:
5372:
5370:
5367:
5365:
5362:
5360:
5357:
5355:
5352:
5350:
5349:Cohen's kappa
5347:
5346:
5344:
5342:
5338:
5334:
5330:
5326:
5322:
5318:
5313:
5309:
5295:
5292:
5290:
5287:
5285:
5282:
5280:
5277:
5276:
5274:
5272:
5268:
5262:
5258:
5254:
5248:
5246:
5243:
5242:
5240:
5238:
5234:
5228:
5225:
5223:
5220:
5218:
5215:
5213:
5210:
5208:
5205:
5203:
5202:Nonparametric
5200:
5198:
5195:
5194:
5192:
5188:
5182:
5179:
5177:
5174:
5172:
5169:
5167:
5164:
5163:
5161:
5159:
5155:
5149:
5146:
5144:
5141:
5139:
5136:
5134:
5131:
5129:
5126:
5125:
5123:
5121:
5117:
5111:
5108:
5106:
5103:
5101:
5098:
5096:
5093:
5092:
5090:
5088:
5084:
5080:
5073:
5070:
5068:
5065:
5064:
5060:
5056:
5040:
5037:
5036:
5035:
5032:
5030:
5027:
5025:
5022:
5018:
5015:
5013:
5010:
5009:
5008:
5005:
5004:
5002:
5000:
4996:
4986:
4983:
4979:
4973:
4971:
4965:
4963:
4957:
4956:
4955:
4952:
4951:Nonparametric
4949:
4947:
4941:
4937:
4934:
4933:
4932:
4926:
4922:
4921:Sample median
4919:
4918:
4917:
4914:
4913:
4911:
4909:
4905:
4897:
4894:
4892:
4889:
4887:
4884:
4883:
4882:
4879:
4877:
4874:
4872:
4866:
4864:
4861:
4859:
4856:
4854:
4851:
4849:
4846:
4844:
4842:
4838:
4836:
4833:
4832:
4830:
4828:
4824:
4818:
4816:
4812:
4810:
4808:
4803:
4801:
4796:
4792:
4791:
4788:
4785:
4783:
4779:
4769:
4766:
4764:
4761:
4759:
4756:
4755:
4753:
4751:
4747:
4741:
4738:
4734:
4731:
4730:
4729:
4726:
4722:
4719:
4718:
4717:
4714:
4712:
4709:
4708:
4706:
4704:
4700:
4692:
4689:
4687:
4684:
4683:
4682:
4679:
4677:
4674:
4672:
4669:
4667:
4664:
4662:
4659:
4657:
4654:
4653:
4651:
4649:
4645:
4639:
4636:
4632:
4629:
4625:
4622:
4620:
4617:
4616:
4615:
4612:
4611:
4610:
4607:
4603:
4600:
4598:
4595:
4593:
4590:
4588:
4585:
4584:
4583:
4580:
4579:
4577:
4575:
4571:
4568:
4566:
4562:
4556:
4553:
4551:
4548:
4544:
4541:
4540:
4539:
4536:
4534:
4531:
4527:
4526:loss function
4524:
4523:
4522:
4519:
4515:
4512:
4510:
4507:
4505:
4502:
4501:
4500:
4497:
4495:
4492:
4490:
4487:
4483:
4480:
4478:
4475:
4473:
4467:
4464:
4463:
4462:
4459:
4455:
4452:
4450:
4447:
4445:
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4441:
4440:
4437:
4433:
4430:
4428:
4425:
4424:
4423:
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4416:
4413:
4412:
4411:
4408:
4404:
4401:
4400:
4399:
4396:
4394:
4391:
4389:
4386:
4384:
4381:
4380:
4378:
4376:
4372:
4368:
4364:
4359:
4355:
4341:
4338:
4336:
4333:
4331:
4328:
4326:
4323:
4322:
4320:
4318:
4314:
4308:
4305:
4303:
4300:
4298:
4295:
4294:
4292:
4288:
4282:
4279:
4277:
4274:
4272:
4269:
4267:
4264:
4262:
4259:
4257:
4254:
4252:
4249:
4248:
4246:
4244:
4240:
4234:
4231:
4229:
4228:Questionnaire
4226:
4224:
4221:
4217:
4214:
4212:
4209:
4208:
4207:
4204:
4203:
4201:
4199:
4195:
4189:
4186:
4184:
4181:
4179:
4176:
4174:
4171:
4169:
4166:
4164:
4161:
4159:
4156:
4154:
4151:
4150:
4148:
4146:
4142:
4138:
4134:
4129:
4125:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4091:
4088:
4086:
4083:
4081:
4078:
4076:
4073:
4071:
4068:
4066:
4063:
4061:
4058:
4056:
4055:Control chart
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4037:
4035:
4033:
4029:
4023:
4020:
4016:
4013:
4011:
4008:
4007:
4006:
4003:
4001:
3998:
3996:
3993:
3992:
3990:
3988:
3984:
3978:
3975:
3973:
3970:
3968:
3965:
3964:
3962:
3958:
3952:
3949:
3948:
3946:
3944:
3940:
3928:
3925:
3923:
3920:
3918:
3915:
3914:
3913:
3910:
3908:
3905:
3904:
3902:
3900:
3896:
3890:
3887:
3885:
3882:
3880:
3877:
3875:
3872:
3870:
3867:
3865:
3862:
3860:
3857:
3856:
3854:
3852:
3848:
3842:
3839:
3837:
3834:
3830:
3827:
3825:
3822:
3820:
3817:
3815:
3812:
3810:
3807:
3805:
3802:
3800:
3797:
3795:
3792:
3790:
3787:
3785:
3782:
3781:
3780:
3777:
3776:
3774:
3772:
3768:
3765:
3763:
3759:
3755:
3751:
3746:
3742:
3736:
3733:
3731:
3728:
3727:
3724:
3720:
3713:
3708:
3706:
3701:
3699:
3694:
3693:
3690:
3678:
3671:
3667:
3663:
3659:
3655:
3651:
3647:
3640:
3626:
3622:
3615:
3599:
3595:
3589:
3583:
3580:
3579:0-7021-3838-X
3576:
3572:
3566:
3551:
3550:
3543:
3529:
3525:
3519:
3517:
3515:
3513:
3508:
3494:
3491:Greek letter
3488:
3481:
3475:
3471:
3461:
3458:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3436:
3433:
3431:
3428:
3424:
3421:
3419:
3416:
3415:
3414:
3411:
3409:
3406:
3405:
3401:
3395:
3390:
3380:
3377:
3375:
3372:
3370:
3367:
3365:
3362:
3359:
3355:
3352:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3318:Identric mean
3316:
3314:
3313:Heronian mean
3311:
3309:
3306:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3265:
3262:
3252:
3236:
3232:
3209:
3205:
3182:
3178:
3152:
3148:
3144:
3141:
3136:
3132:
3128:
3125:
3120:
3116:
3112:
3109:
3106:
3099:
3098:
3097:
3095:
3085:
3083:
3073:
3071:
3067:
3063:
3059:
3049:
3047:
3043:
3038:
3034:
3025:
3008:
3005:
2998:
2992:
2986:
2981:
2977:
2970:
2967:
2964:
2960:
2955:
2949:
2946:
2943:
2931:
2923:
2922:
2921:
2919:
2900:
2894:
2868:
2859:
2853:
2843:
2824:
2820:
2812:
2807:
2804:
2797:
2794:
2789:
2786:
2781:
2778:
2774:
2767:
2764:
2759:
2750:
2740:
2739:
2738:
2736:
2726:
2724:
2720:
2710:
2696:
2674:
2670:
2641:
2637:
2610:
2602:
2598:
2592:
2587:
2584:
2581:
2577:
2562:
2558:
2549:
2545:
2538:
2533:
2530:
2527:
2523:
2516:
2507:
2497:
2496:
2495:
2493:
2476:
2475:harmonic mean
2473:
2457:
2454:
2449:
2444:
2441:
2437:
2433:
2427:
2421:
2414:
2413:
2409:
2406:
2389:
2383:
2380:
2377:
2371:
2365:
2358:
2357:
2353:
2350:
2336:
2333:
2327:
2321:
2314:
2313:
2309:
2306:
2290:
2286:
2282:
2276:
2270:
2263:
2262:
2259:
2258:
2257:
2235:
2229:
2224:
2220:
2216:
2212:
2206:
2201:
2198:
2195:
2191:
2185:
2182:
2176:
2170:
2167:
2163:
2159:
2150:
2140:
2139:
2138:
2137:
2125:
2104:
2100:
2091:
2088:
2068:
2062:
2047:
2046:harmonic mean
2044:
2027:
2024:
2018:
2003:
2000:
1983:
1977:
1962:
1959:
1942:
1936:
1921:
1918:
1901:
1895:
1866:
1862:
1853:
1850:
1827:
1813:
1812:
1810:
1805:
1789:
1786:
1780:
1774:
1769:
1765:
1759:
1754:
1751:
1748:
1744:
1738:
1735:
1729:
1724:
1718:
1706:
1695:
1690:
1686:
1682:
1678:
1663:
1661:
1649:
1645:
1641:
1622:
1616:
1595:
1592:
1585:
1579:
1576:
1563:
1559:
1549:
1545:
1526:
1520:
1496:
1490:
1487:
1484:
1475:
1456:
1450:
1430:
1422:
1406:
1398:
1394:
1388:
1382:
1372:
1370:
1366:
1362:
1358:
1354:
1350:
1346:
1342:
1333:
1326:
1322:
1318:
1314:
1309:
1304:
1294:
1268:
1257:
1242:
1241:
1240:
1236:
1224:
1220:
1215:
1211:
1207:
1203:
1199:
1195:
1188:
1183:
1179:
1170:
1156:
1136:
1113:
1110:
1100:
1097:
1089:
1084:
1075:
1072:
1066:
1060:
1057:
1051:
1045:
1042:
1036:
1030:
1027:
1021:
1015:
1012:
1005:
996:
995:
994:
975:
972:
967:
959:
955:
951:
944:
939:
936:
933:
929:
924:
919:
916:
907:
897:
896:
895:
893:
889:
885:
884:harmonic mean
861:
858:
852:
847:
843:
839:
833:
827:
824:
815:
812:
809:
806:
803:
800:
797:
794:
791:
781:
780:
779:
759:
756:
750:
744:
740:
736:
731:
727:
721:
717:
712:
707:
701:
698:
692:
685:
681:
674:
669:
666:
663:
659:
654:
649:
640:
630:
629:
628:
625:
601:
598:
593:
590:
585:
580:
576:
573:
570:
567:
564:
561:
558:
555:
552:
542:
541:
540:
521:
515:
511:
507:
504:
501:
496:
492:
488:
483:
479:
472:
468:
461:
457:
450:
445:
442:
439:
435:
430:
424:
421:
416:
407:
397:
396:
395:
375:
350:
346:
342:
339:
336:
331:
327:
323:
318:
314:
305:
301:
297:
291:
280:
265:
263:
259:
254:
252:
237:
233:
223:
210:
201:
197:
175:
164:
163:
158:
154:
132:
121:
117:
108:
101:
97:
96:
90:
88:
84:
80:
76:
72:
68:
64:
60:
56:
48:
41:
34:
19:
6000:
5988:
5969:
5962:
5874:Econometrics
5824: /
5807:Chemometrics
5784:Epidemiology
5777: /
5750:Applications
5592:ARIMA model
5539:Q-statistic
5488:Stationarity
5384:Multivariate
5327: /
5323: /
5321:Multivariate
5319: /
5259: /
5255: /
5029:Bayes factor
4928:Signed rank
4840:
4814:
4806:
4794:
4489:Completeness
4325:Cohort study
4223:Opinion poll
4158:Missing data
4145:Study design
4100:Scatter plot
4022:Scatter plot
4015:Spearman's Ï
3977:Grouped data
3778:
3677:
3669:
3652:(1): 57â73.
3649:
3645:
3639:
3628:. Retrieved
3624:
3614:
3602:. Retrieved
3598:the original
3588:
3570:
3565:
3554:. Retrieved
3548:
3542:
3531:. Retrieved
3527:
3487:
3479:
3478:Pronounced "
3474:
3460:Taylor's law
3283:Chisini mean
3169:
3091:
3079:
3070:Karcher mean
3069:
3058:Fréchet mean
3055:
3052:Fréchet mean
3031:
3023:
2855:
2841:
2732:
2716:
2625:
2489:
2251:
2132:generalized
2129:
2123:
1808:
1806:
1696:
1688:
1684:
1674:
1390:
1338:
1292:
1238:
1222:
1218:
1204:. Using the
1201:
1197:
1128:
992:
881:
777:
621:
538:
303:
299:
293:
255:
225:
203:
160:
157:larger group
120:overhead bar
113:
106:
99:
93:
91:
58:
54:
52:
6002:WikiProject
5917:Cartography
5879:Jurimetrics
5831:Reliability
5562:Time domain
5541:(LjungâBox)
5463:Time-series
5341:Categorical
5325:Time-series
5317:Categorical
5252:(Bernoulli)
5087:Correlation
5067:Correlation
4863:JarqueâBera
4835:Chi-squared
4597:M-estimator
4550:Asymptotics
4494:Sufficiency
4261:Interaction
4173:Replication
4153:Effect size
4110:Violin plot
4090:Radar chart
4070:Forest plot
4060:Correlogram
4010:Kendall's Ï
3323:Lehmer mean
3278:CesĂ ro mean
3255:Other means
3042:color wheel
2918:integration
2858:uncountable
1365:exponential
298:(or simply
162:sample mean
67:mathematics
18:Mean values
6018:Categories
5869:Demography
5587:ARMA model
5392:Regression
4969:(Friedman)
4930:(Wilcoxon)
4868:Normality
4858:Lilliefors
4805:Student's
4681:Resampling
4555:Robustness
4543:divergence
4533:Efficiency
4471:(monotone)
4466:Likelihood
4383:Population
4216:Stratified
4168:Population
3987:Dependence
3943:Count data
3874:Percentile
3851:Dispersion
3784:Arithmetic
3719:Statistics
3630:2020-08-21
3556:2024-09-10
3533:2020-08-21
3503:References
3308:Heinz mean
3303:Grand mean
2308:power mean
2256:will give
1671:Power mean
1385:See also:
1325:log-normal
1301:See also:
1212:GQ is the
196:group mean
71:statistics
5250:Logistic
5017:posterior
4943:Rank sum
4691:Jackknife
4686:Bootstrap
4504:Bootstrap
4439:Parameter
4388:Statistic
4183:Statistic
4095:Run chart
4080:Pie chart
4075:Histogram
4065:Fan chart
4040:Bar chart
3922:L-moments
3809:Geometric
3571:Introstat
2978:∫
2968:−
2775:∑
2754:¯
2719:artifacts
2647:¯
2578:∑
2568:¯
2524:∑
2511:¯
2442:−
2384:
2192:∑
2168:−
2154:¯
2072:∞
2069:−
2066:→
2025:−
2022:→
1981:→
1940:→
1899:→
1834:∞
1831:→
1745:∑
1710:¯
1681:quadratic
1660:undefined
1572:∞
1567:∞
1564:−
1560:∫
1485:∑
1472:). For a
1443:(denoted
1353:mid-range
1269:≥
1258:≥
1169:minutes.
973:−
930:∑
911:¯
813:×
807:×
801:×
795:×
737:⋯
660:∏
644:¯
505:⋯
436:∑
411:¯
379:¯
340:…
234:μ
211:μ
179:¯
136:¯
79:magnitude
5964:Category
5657:Survival
5534:Johansen
5257:Binomial
5212:Isotonic
4799:(normal)
4444:location
4251:Blocking
4206:Sampling
4085:QâQ plot
4050:Box plot
4032:Graphics
3927:Skewness
3917:Kurtosis
3889:Variance
3819:Heronian
3814:Harmonic
3604:16 March
3435:Kurtosis
3386:See also
1656:â∞
1652:+∞
1609:, where
1546:. For a
1210:altitude
258:geometry
112:, ..., x
87:data set
47:Meanness
5990:Commons
5937:Kriging
5822:Process
5779:studies
5638:Wavelet
5471:General
4638:Plug-in
4432:L space
4211:Cluster
3912:Moments
3730:Outline
3666:3483261
3062:surface
2090:minimum
1852:maximum
1638:is the
1542:is the
1369:Poisson
1184:of the
304:average
85:of the
40:Average
5859:Census
5449:Normal
5397:Manova
5217:Robust
4967:2-way
4959:1-way
4797:-test
4468:
4045:Biplot
3836:Median
3829:Lehmer
3771:Center
3664:
3582:p. 181
3577:
3418:Median
3170:where
3033:Angles
2626:Where
1345:median
1319:, and
1317:median
153:sample
65:") in
6024:Means
5483:Trend
5012:prior
4954:anova
4843:-test
4817:-test
4809:-test
4716:Power
4661:Pivot
4454:shape
4449:scale
3899:Shape
3879:Range
3824:Heinz
3799:Cubic
3735:Index
3482:bar".
3466:Notes
3261:Means
2136:-mean
2126:-mean
892:speed
155:of a
59:means
5716:Test
4916:Sign
4768:Wald
3841:Mode
3779:Mean
3606:2015
3575:ISBN
3423:Mode
3224:and
3056:The
2733:The
2662:and
2490:The
1675:The
1367:and
1349:mode
1321:mode
1200:and
888:unit
882:The
622:The
300:mean
294:The
260:and
198:(or
92:The
83:sign
81:and
75:data
55:mean
4896:BIC
4891:AIC
3654:doi
3356:(a
3145:0.3
3129:0.4
3113:0.3
2936:avg
2873:avg
2092:of
2059:lim
2015:lim
1974:lim
1933:lim
1892:lim
1854:of
1824:lim
1694:by
1654:or
1423:of
1351:or
1339:In
1196:of
1114:15.
862:30.
848:000
844:300
602:42.
591:210
302:or
224:or
6020::
3668:.
3662:MR
3660:.
3650:10
3648:.
3623:.
3526:.
3511:^
3237:90
3210:50
3197:,
3183:10
3153:90
3137:50
3121:10
3048:.
2477:,
2410:.
2381:ln
2354:,
2310:,
1662:.
1347:,
1315:,
1157:15
1137:15
1076:75
1061:50
1046:45
1031:36
840:24
816:75
810:50
804:45
798:36
577:75
571:50
565:45
559:36
253:.
122:,
105:,
53:A
4841:G
4815:F
4807:t
4795:Z
4514:V
4509:U
3711:e
3704:t
3697:v
3656::
3633:.
3608:.
3559:.
3536:.
3493:Ό
3480:x
3360:)
3233:P
3206:P
3179:P
3149:P
3142:+
3133:P
3126:+
3117:P
3110:=
3107:m
3009:x
3006:d
3002:)
2999:x
2996:(
2993:f
2987:b
2982:a
2971:a
2965:b
2961:1
2956:=
2953:)
2950:b
2947:,
2944:a
2941:(
2932:y
2904:)
2901:x
2898:(
2895:f
2869:y
2825:i
2821:x
2813:n
2808:4
2805:3
2798:1
2795:+
2790:4
2787:n
2782:=
2779:i
2768:n
2765:2
2760:=
2751:x
2697:i
2675:i
2671:w
2642:i
2638:x
2611:.
2603:i
2599:w
2593:n
2588:1
2585:=
2582:i
2563:i
2559:x
2550:i
2546:w
2539:n
2534:1
2531:=
2528:i
2517:=
2508:x
2458:x
2455:1
2450:=
2445:1
2438:x
2434:=
2431:)
2428:x
2425:(
2422:f
2393:)
2390:x
2387:(
2378:=
2375:)
2372:x
2369:(
2366:f
2337:x
2334:=
2331:)
2328:x
2325:(
2322:f
2291:m
2287:x
2283:=
2280:)
2277:x
2274:(
2271:f
2254:f
2236:)
2230:)
2225:i
2221:x
2217:(
2213:f
2207:n
2202:1
2199:=
2196:i
2186:n
2183:1
2177:(
2171:1
2164:f
2160:=
2151:x
2134:f
2124:f
2105:i
2101:x
2063:m
2028:1
2019:m
1984:0
1978:m
1943:1
1937:m
1902:2
1896:m
1867:i
1863:x
1828:m
1809:m
1790:m
1787:1
1781:)
1775:m
1770:i
1766:x
1760:n
1755:1
1752:=
1749:i
1739:n
1736:1
1730:(
1725:=
1722:)
1719:m
1716:(
1707:x
1692:i
1689:x
1685:n
1626:)
1623:x
1620:(
1617:f
1596:x
1593:d
1589:)
1586:x
1583:(
1580:f
1577:x
1530:)
1527:x
1524:(
1521:P
1500:)
1497:x
1494:(
1491:P
1488:x
1460:)
1457:X
1454:(
1451:E
1431:X
1407:X
1276:M
1273:H
1265:M
1262:G
1254:M
1251:A
1225:,
1223:b
1221::
1219:a
1202:b
1198:a
1189::
1111:=
1101:3
1098:1
1090:5
1085:=
1073:1
1067:+
1058:1
1052:+
1043:1
1037:+
1028:1
1022:+
1016:4
1013:1
1006:5
976:1
968:)
960:i
956:x
952:1
945:n
940:1
937:=
934:i
925:(
920:n
917:=
908:x
859:=
853:5
834:=
828:5
825:1
820:)
792:4
789:(
760:n
757:1
751:)
745:n
741:x
732:2
728:x
722:1
718:x
713:(
708:=
702:n
699:1
693:)
686:i
682:x
675:n
670:1
667:=
664:i
655:(
650:=
641:x
599:=
594:5
586:=
581:5
574:+
568:+
562:+
556:+
553:4
522:n
516:n
512:x
508:+
502:+
497:2
493:x
489:+
484:1
480:x
473:=
469:)
462:i
458:x
451:n
446:1
443:=
440:i
431:(
425:n
422:1
417:=
408:x
376:x
351:n
347:x
343:,
337:,
332:2
328:x
324:,
319:1
315:x
238:x
176:x
165:(
133:x
115:n
110:2
107:x
103:1
100:x
49:.
42:.
35:.
20:)
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