Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Dec 2014 16:41:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/16/t14187481180ev96izeefsqop6.htm/, Retrieved Thu, 16 May 2024 12:28:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269827, Retrieved Thu, 16 May 2024 12:28:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2014-11-04 10:08:09] [32b17a345b130fdf5cc88718ed94a974]
- R  D  [Central Tendency] [paper46] [2014-12-16 16:38:46] [55a850ac261e4a7d4f206113c00d6f60]
-    D      [Central Tendency] [paper47] [2014-12-16 16:41:40] [0015a2406d94cac8c1a56a29b9122359] [Current]
-    D        [Central Tendency] [paper48] [2014-12-16 16:43:24] [55a850ac261e4a7d4f206113c00d6f60]
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Dataseries X:
12.9125
9.03172
-6.83478
12.7765
19.3125
-7.965
84.9546
15.7396
-27.3773
10.8209
24.0976
24.9843
14.0722
-21.5432
45.7921
-82.2624
27.035
-14.9593
-18.721
20.2607
8.5992
80.5859
47.5644
10.8185
105.568
5.53519
20.8731
-34.1851
21.4911
29.1569
-11.4097
16.8836
-30.1656
-36.6248
17.9889
23.5605
25.9281
-23.8669
11.5461
28.5892
22.6128
42.0292
-23.213
-36.9967
11.7214
-13.5166
-19.0365
-1.9081
31.1746
24.5385
-34.0124
69.0306
41.2633
37.9861
76.8951
54.1895
34.3102
-17.5955
20.4859
11.5791
-63.8904
29.0091
26.5958
-29.9296
-91.359
-83.6207
24.0273
12.9507
59.0914
20.0109
22.2518
-69.9555
6.84157
-102.997
-38.1397
-25.5773
2.18437
-40.7195
-39.2863
-28.7544
21.6333
-14.6038
-27.7736
-60.0311
-64.4902
-18.8018
-95.2984
13.8224
-11.3319
41.1387
14.7634
3.77925
2.01476
17.8218
10.1762
-14.9355
-3.78408
-20.7449
-8.30779
33.2115
43.0501
-20.1523
21.2556
36.8828
23.9482
-15.7747
31.6007
-135.632
32.3455
28.4442
-15.4754
20.9853
-90.2097
33.0362
18.4518
70.0487
4.48722
-15.5691
-87.4918
25.6719
-33.9632
18.0363
-38.8271
19.4977
37.9166
3.4916
-25.1226
0.855368
27.9331
-0.989068
-16.6109
15.9243
31.3379
5.7265
33.9971
-29.397
-88.5084
8.31634
-65.4513
-26.2922
-6.50895
22.3222
-23.9401
-15.4907
-0.782324
6.34989
-40.4616
31.4898
-40.902
-18.9435




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269827&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269827&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.73333333475645e-073.18908356682851.79779965454407e-07
Geometric MeanNaN
Harmonic Mean109.271530006499
Quadratic Mean38.9277259217145
Winsorized Mean ( 1 / 50 )0.08014457333333353.105809216420120.0258047316331012
Winsorized Mean ( 2 / 50 )0.124543243.073217543717960.0405253576189496
Winsorized Mean ( 3 / 50 )0.129515243.044329088953480.0425431141692117
Winsorized Mean ( 4 / 50 )-0.02240742666666663.00842990972101-0.00744821296792138
Winsorized Mean ( 5 / 50 )0.0003659066666671152.99181482755850.000122302578119688
Winsorized Mean ( 6 / 50 )-0.3565380933333332.92578359800457-0.121860719151101
Winsorized Mean ( 7 / 50 )-0.4046420933333342.85982272009343-0.141492019938954
Winsorized Mean ( 8 / 50 )-0.6855380933333332.80260243852708-0.244607684596757
Winsorized Mean ( 9 / 50 )-0.05346209333333382.65268309935082-0.0201539691440781
Winsorized Mean ( 10 / 50 )0.06401790666666632.579697276931660.0248160538987002
Winsorized Mean ( 11 / 50 )0.05963257333333372.559419370864870.0232992584225003
Winsorized Mean ( 12 / 50 )0.04634457333333372.544610300106380.0182128372786183
Winsorized Mean ( 13 / 50 )0.3700185733333332.487968691285320.148723163048397
Winsorized Mean ( 14 / 50 )1.861158573333332.191342247856230.849323548228984
Winsorized Mean ( 15 / 50 )1.872458573333332.188186464063260.855712529112509
Winsorized Mean ( 16 / 50 )1.789695906666672.172521209600420.823787541754696
Winsorized Mean ( 17 / 50 )1.631335242.124354730047490.767920355732461
Winsorized Mean ( 18 / 50 )1.648867242.113382191258750.780203054052387
Winsorized Mean ( 19 / 50 )1.636428573333332.092079486015410.7822019116731
Winsorized Mean ( 20 / 50 )1.765455242.070412433593630.852707031388761
Winsorized Mean ( 21 / 50 )1.720823242.054140820517940.837733821757215
Winsorized Mean ( 22 / 50 )1.969408573333331.999101551473750.985146838529276
Winsorized Mean ( 23 / 50 )1.978884573333331.994200454976120.992319788311869
Winsorized Mean ( 24 / 50 )1.962452573333331.990836690398030.985742619069865
Winsorized Mean ( 25 / 50 )2.568169241.913421806244261.34218666873088
Winsorized Mean ( 26 / 50 )2.259341241.874321044558031.20541848823596
Winsorized Mean ( 27 / 50 )2.328605241.860749789437931.25143383232809
Winsorized Mean ( 28 / 50 )2.370175906666671.839555565864911.28845029236845
Winsorized Mean ( 29 / 50 )2.531763906666671.81548316938781.39454000420197
Winsorized Mean ( 30 / 50 )2.508803906666671.796869901712231.3962078747471
Winsorized Mean ( 31 / 50 )2.547450573333331.754474596231341.45197347331521
Winsorized Mean ( 32 / 50 )2.606266573333331.728967864444241.50741180731609
Winsorized Mean ( 33 / 50 )2.559406573333331.704445540435591.50160654160839
Winsorized Mean ( 34 / 50 )2.769367906666671.670106825800281.65819806486908
Winsorized Mean ( 35 / 50 )2.626007906666671.653608868924981.58804657861677
Winsorized Mean ( 36 / 50 )2.675951906666671.627113072659711.64460107390846
Winsorized Mean ( 37 / 50 )2.979080573333331.573776387004931.89295035681839
Winsorized Mean ( 38 / 50 )3.163507241.551134981199892.03947901268583
Winsorized Mean ( 39 / 50 )3.297017241.533400953208632.15013381405628
Winsorized Mean ( 40 / 50 )3.491177241.493736801587922.33721043512398
Winsorized Mean ( 41 / 50 )3.257559241.468018640647252.2190176267542
Winsorized Mean ( 42 / 50 )3.215867241.456811741689392.20746933043711
Winsorized Mean ( 43 / 50 )3.218848573333331.452687609351962.2157885512421
Winsorized Mean ( 44 / 50 )3.367568573333331.403503912138822.39940091666823
Winsorized Mean ( 45 / 50 )3.620288573333331.370333121903422.64190401258394
Winsorized Mean ( 46 / 50 )3.804503241.338722229909162.84189143572985
Winsorized Mean ( 47 / 50 )3.784230573333331.325008516669542.85600471674336
Winsorized Mean ( 48 / 50 )3.773414573333331.319424114390612.85989511043318
Winsorized Mean ( 49 / 50 )3.651927241.307970220497512.7920568700799
Winsorized Mean ( 50 / 50 )3.748893906666671.284640814373952.91824287747982
Trimmed Mean ( 1 / 50 )0.2031357162162163.014935150550210.0673764794506924
Trimmed Mean ( 2 / 50 )0.3294964794520552.915297863584290.113023263786482
Trimmed Mean ( 3 / 50 )0.4362429583333342.824987640465680.15442296174486
Trimmed Mean ( 4 / 50 )0.5442456760563382.737669865195060.198798870154331
Trimmed Mean ( 5 / 50 )0.6960277571428572.653230487406850.262332187288834
Trimmed Mean ( 6 / 50 )0.8472585942028992.564734090707780.330349488187715
Trimmed Mean ( 7 / 50 )1.068544752.482599689465290.430413632344467
Trimmed Mean ( 8 / 50 )1.3041292.405860467541390.542063439503091
Trimmed Mean ( 9 / 50 )1.586752166666672.331813741183960.680479807903099
Trimmed Mean ( 10 / 50 )1.797036046153852.276956629388720.789227174096982
Trimmed Mean ( 11 / 50 )2.0001241093752.228284863520880.897607008026179
Trimmed Mean ( 12 / 50 )2.210134015873022.177610639992671.01493534945277
Trimmed Mean ( 13 / 50 )2.42825795161292.123667761166791.14342647942198
Trimmed Mean ( 14 / 50 )2.622921196721312.072093298546691.26583161026628
Trimmed Mean ( 15 / 50 )2.690935716666672.05383022413681.31020358208899
Trimmed Mean ( 16 / 50 )2.760298186440682.033870099460351.35716542918502
Trimmed Mean ( 17 / 50 )2.838741258620692.013393850451051.40992844394788
Trimmed Mean ( 18 / 50 )2.932193736842111.995786618607841.46919200154145
Trimmed Mean ( 19 / 50 )3.027679339285711.977211577146791.53128748297883
Trimmed Mean ( 20 / 50 )3.127529872727271.958585397250481.59683099706441
Trimmed Mean ( 21 / 50 )3.222118388888891.939926628550641.66094858509994
Trimmed Mean ( 22 / 50 )3.323283830188681.920519517659021.73040877722479
Trimmed Mean ( 23 / 50 )3.412043134615381.904274904590151.7917807593803
Trimmed Mean ( 24 / 50 )3.503677313725491.886271465434231.85746186481113
Trimmed Mean ( 25 / 50 )3.600003861.866106077539821.92915285113163
Trimmed Mean ( 26 / 50 )3.663177408163271.851140699292341.9788757329811
Trimmed Mean ( 27 / 50 )3.74754256251.837574751111562.03939598116109
Trimmed Mean ( 28 / 50 )3.831404106382981.823170047275952.10150672018092
Trimmed Mean ( 29 / 50 )3.916491152173911.808514699273222.16558436254227
Trimmed Mean ( 30 / 50 )3.996073177777781.793874750141542.22762106298808
Trimmed Mean ( 31 / 50 )4.080577113636361.778564996245532.29430868270222
Trimmed Mean ( 32 / 50 )4.166837046511631.764838346871582.36103043312603
Trimmed Mean ( 33 / 50 )4.253922452380951.751145616432052.42922256862241
Trimmed Mean ( 34 / 50 )4.347853487804881.737268869226252.5026946403186
Trimmed Mean ( 35 / 50 )4.4349023251.724300971798672.57200013079725
Trimmed Mean ( 36 / 50 )4.534292128205131.710220360343412.65129116302571
Trimmed Mean ( 37 / 50 )4.636174815789471.696011925253112.7335744205322
Trimmed Mean ( 38 / 50 )4.726957918918921.684647950843982.80590251307449
Trimmed Mean ( 39 / 50 )4.812673416666671.673065031150682.87656087902133
Trimmed Mean ( 40 / 50 )4.895951228571431.660610134600152.94828456514888
Trimmed Mean ( 41 / 50 )4.973420382352941.64960673006623.01491276175465
Trimmed Mean ( 42 / 50 )5.068534636363641.638268607662563.09383614668372
Trimmed Mean ( 43 / 50 )5.171920093751.624913625668913.18288923918705
Trimmed Mean ( 44 / 50 )5.281807838709681.608291378734613.2841112677389
Trimmed Mean ( 45 / 50 )5.390571433333331.593691066439953.38244440647773
Trimmed Mean ( 46 / 50 )5.492311827586211.579433491788573.47739354404006
Trimmed Mean ( 47 / 50 )5.590592607142861.565234434957743.57172860645235
Trimmed Mean ( 48 / 50 )5.697351592592591.54826023787873.6798410585023
Trimmed Mean ( 49 / 50 )5.812972807692311.526611124478833.80776264137128
Trimmed Mean ( 50 / 50 )5.945281721.499827368802293.96397735077183
Median8.45777
Midrange-15.032
Midmean - Weighted Average at Xnp4.37668914666667
Midmean - Weighted Average at X(n+1)p4.63617481578947
Midmean - Empirical Distribution Function4.63617481578947
Midmean - Empirical Distribution Function - Averaging4.63617481578947
Midmean - Empirical Distribution Function - Interpolation4.72695791891892
Midmean - Closest Observation4.63617481578947
Midmean - True Basic - Statistics Graphics Toolkit4.63617481578947
Midmean - MS Excel (old versions)4.63617481578947
Number of observations150

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.73333333475645e-07 & 3.1890835668285 & 1.79779965454407e-07 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 109.271530006499 &  &  \tabularnewline
Quadratic Mean & 38.9277259217145 &  &  \tabularnewline
Winsorized Mean ( 1 / 50 ) & 0.0801445733333335 & 3.10580921642012 & 0.0258047316331012 \tabularnewline
Winsorized Mean ( 2 / 50 ) & 0.12454324 & 3.07321754371796 & 0.0405253576189496 \tabularnewline
Winsorized Mean ( 3 / 50 ) & 0.12951524 & 3.04432908895348 & 0.0425431141692117 \tabularnewline
Winsorized Mean ( 4 / 50 ) & -0.0224074266666666 & 3.00842990972101 & -0.00744821296792138 \tabularnewline
Winsorized Mean ( 5 / 50 ) & 0.000365906666667115 & 2.9918148275585 & 0.000122302578119688 \tabularnewline
Winsorized Mean ( 6 / 50 ) & -0.356538093333333 & 2.92578359800457 & -0.121860719151101 \tabularnewline
Winsorized Mean ( 7 / 50 ) & -0.404642093333334 & 2.85982272009343 & -0.141492019938954 \tabularnewline
Winsorized Mean ( 8 / 50 ) & -0.685538093333333 & 2.80260243852708 & -0.244607684596757 \tabularnewline
Winsorized Mean ( 9 / 50 ) & -0.0534620933333338 & 2.65268309935082 & -0.0201539691440781 \tabularnewline
Winsorized Mean ( 10 / 50 ) & 0.0640179066666663 & 2.57969727693166 & 0.0248160538987002 \tabularnewline
Winsorized Mean ( 11 / 50 ) & 0.0596325733333337 & 2.55941937086487 & 0.0232992584225003 \tabularnewline
Winsorized Mean ( 12 / 50 ) & 0.0463445733333337 & 2.54461030010638 & 0.0182128372786183 \tabularnewline
Winsorized Mean ( 13 / 50 ) & 0.370018573333333 & 2.48796869128532 & 0.148723163048397 \tabularnewline
Winsorized Mean ( 14 / 50 ) & 1.86115857333333 & 2.19134224785623 & 0.849323548228984 \tabularnewline
Winsorized Mean ( 15 / 50 ) & 1.87245857333333 & 2.18818646406326 & 0.855712529112509 \tabularnewline
Winsorized Mean ( 16 / 50 ) & 1.78969590666667 & 2.17252120960042 & 0.823787541754696 \tabularnewline
Winsorized Mean ( 17 / 50 ) & 1.63133524 & 2.12435473004749 & 0.767920355732461 \tabularnewline
Winsorized Mean ( 18 / 50 ) & 1.64886724 & 2.11338219125875 & 0.780203054052387 \tabularnewline
Winsorized Mean ( 19 / 50 ) & 1.63642857333333 & 2.09207948601541 & 0.7822019116731 \tabularnewline
Winsorized Mean ( 20 / 50 ) & 1.76545524 & 2.07041243359363 & 0.852707031388761 \tabularnewline
Winsorized Mean ( 21 / 50 ) & 1.72082324 & 2.05414082051794 & 0.837733821757215 \tabularnewline
Winsorized Mean ( 22 / 50 ) & 1.96940857333333 & 1.99910155147375 & 0.985146838529276 \tabularnewline
Winsorized Mean ( 23 / 50 ) & 1.97888457333333 & 1.99420045497612 & 0.992319788311869 \tabularnewline
Winsorized Mean ( 24 / 50 ) & 1.96245257333333 & 1.99083669039803 & 0.985742619069865 \tabularnewline
Winsorized Mean ( 25 / 50 ) & 2.56816924 & 1.91342180624426 & 1.34218666873088 \tabularnewline
Winsorized Mean ( 26 / 50 ) & 2.25934124 & 1.87432104455803 & 1.20541848823596 \tabularnewline
Winsorized Mean ( 27 / 50 ) & 2.32860524 & 1.86074978943793 & 1.25143383232809 \tabularnewline
Winsorized Mean ( 28 / 50 ) & 2.37017590666667 & 1.83955556586491 & 1.28845029236845 \tabularnewline
Winsorized Mean ( 29 / 50 ) & 2.53176390666667 & 1.8154831693878 & 1.39454000420197 \tabularnewline
Winsorized Mean ( 30 / 50 ) & 2.50880390666667 & 1.79686990171223 & 1.3962078747471 \tabularnewline
Winsorized Mean ( 31 / 50 ) & 2.54745057333333 & 1.75447459623134 & 1.45197347331521 \tabularnewline
Winsorized Mean ( 32 / 50 ) & 2.60626657333333 & 1.72896786444424 & 1.50741180731609 \tabularnewline
Winsorized Mean ( 33 / 50 ) & 2.55940657333333 & 1.70444554043559 & 1.50160654160839 \tabularnewline
Winsorized Mean ( 34 / 50 ) & 2.76936790666667 & 1.67010682580028 & 1.65819806486908 \tabularnewline
Winsorized Mean ( 35 / 50 ) & 2.62600790666667 & 1.65360886892498 & 1.58804657861677 \tabularnewline
Winsorized Mean ( 36 / 50 ) & 2.67595190666667 & 1.62711307265971 & 1.64460107390846 \tabularnewline
Winsorized Mean ( 37 / 50 ) & 2.97908057333333 & 1.57377638700493 & 1.89295035681839 \tabularnewline
Winsorized Mean ( 38 / 50 ) & 3.16350724 & 1.55113498119989 & 2.03947901268583 \tabularnewline
Winsorized Mean ( 39 / 50 ) & 3.29701724 & 1.53340095320863 & 2.15013381405628 \tabularnewline
Winsorized Mean ( 40 / 50 ) & 3.49117724 & 1.49373680158792 & 2.33721043512398 \tabularnewline
Winsorized Mean ( 41 / 50 ) & 3.25755924 & 1.46801864064725 & 2.2190176267542 \tabularnewline
Winsorized Mean ( 42 / 50 ) & 3.21586724 & 1.45681174168939 & 2.20746933043711 \tabularnewline
Winsorized Mean ( 43 / 50 ) & 3.21884857333333 & 1.45268760935196 & 2.2157885512421 \tabularnewline
Winsorized Mean ( 44 / 50 ) & 3.36756857333333 & 1.40350391213882 & 2.39940091666823 \tabularnewline
Winsorized Mean ( 45 / 50 ) & 3.62028857333333 & 1.37033312190342 & 2.64190401258394 \tabularnewline
Winsorized Mean ( 46 / 50 ) & 3.80450324 & 1.33872222990916 & 2.84189143572985 \tabularnewline
Winsorized Mean ( 47 / 50 ) & 3.78423057333333 & 1.32500851666954 & 2.85600471674336 \tabularnewline
Winsorized Mean ( 48 / 50 ) & 3.77341457333333 & 1.31942411439061 & 2.85989511043318 \tabularnewline
Winsorized Mean ( 49 / 50 ) & 3.65192724 & 1.30797022049751 & 2.7920568700799 \tabularnewline
Winsorized Mean ( 50 / 50 ) & 3.74889390666667 & 1.28464081437395 & 2.91824287747982 \tabularnewline
Trimmed Mean ( 1 / 50 ) & 0.203135716216216 & 3.01493515055021 & 0.0673764794506924 \tabularnewline
Trimmed Mean ( 2 / 50 ) & 0.329496479452055 & 2.91529786358429 & 0.113023263786482 \tabularnewline
Trimmed Mean ( 3 / 50 ) & 0.436242958333334 & 2.82498764046568 & 0.15442296174486 \tabularnewline
Trimmed Mean ( 4 / 50 ) & 0.544245676056338 & 2.73766986519506 & 0.198798870154331 \tabularnewline
Trimmed Mean ( 5 / 50 ) & 0.696027757142857 & 2.65323048740685 & 0.262332187288834 \tabularnewline
Trimmed Mean ( 6 / 50 ) & 0.847258594202899 & 2.56473409070778 & 0.330349488187715 \tabularnewline
Trimmed Mean ( 7 / 50 ) & 1.06854475 & 2.48259968946529 & 0.430413632344467 \tabularnewline
Trimmed Mean ( 8 / 50 ) & 1.304129 & 2.40586046754139 & 0.542063439503091 \tabularnewline
Trimmed Mean ( 9 / 50 ) & 1.58675216666667 & 2.33181374118396 & 0.680479807903099 \tabularnewline
Trimmed Mean ( 10 / 50 ) & 1.79703604615385 & 2.27695662938872 & 0.789227174096982 \tabularnewline
Trimmed Mean ( 11 / 50 ) & 2.000124109375 & 2.22828486352088 & 0.897607008026179 \tabularnewline
Trimmed Mean ( 12 / 50 ) & 2.21013401587302 & 2.17761063999267 & 1.01493534945277 \tabularnewline
Trimmed Mean ( 13 / 50 ) & 2.4282579516129 & 2.12366776116679 & 1.14342647942198 \tabularnewline
Trimmed Mean ( 14 / 50 ) & 2.62292119672131 & 2.07209329854669 & 1.26583161026628 \tabularnewline
Trimmed Mean ( 15 / 50 ) & 2.69093571666667 & 2.0538302241368 & 1.31020358208899 \tabularnewline
Trimmed Mean ( 16 / 50 ) & 2.76029818644068 & 2.03387009946035 & 1.35716542918502 \tabularnewline
Trimmed Mean ( 17 / 50 ) & 2.83874125862069 & 2.01339385045105 & 1.40992844394788 \tabularnewline
Trimmed Mean ( 18 / 50 ) & 2.93219373684211 & 1.99578661860784 & 1.46919200154145 \tabularnewline
Trimmed Mean ( 19 / 50 ) & 3.02767933928571 & 1.97721157714679 & 1.53128748297883 \tabularnewline
Trimmed Mean ( 20 / 50 ) & 3.12752987272727 & 1.95858539725048 & 1.59683099706441 \tabularnewline
Trimmed Mean ( 21 / 50 ) & 3.22211838888889 & 1.93992662855064 & 1.66094858509994 \tabularnewline
Trimmed Mean ( 22 / 50 ) & 3.32328383018868 & 1.92051951765902 & 1.73040877722479 \tabularnewline
Trimmed Mean ( 23 / 50 ) & 3.41204313461538 & 1.90427490459015 & 1.7917807593803 \tabularnewline
Trimmed Mean ( 24 / 50 ) & 3.50367731372549 & 1.88627146543423 & 1.85746186481113 \tabularnewline
Trimmed Mean ( 25 / 50 ) & 3.60000386 & 1.86610607753982 & 1.92915285113163 \tabularnewline
Trimmed Mean ( 26 / 50 ) & 3.66317740816327 & 1.85114069929234 & 1.9788757329811 \tabularnewline
Trimmed Mean ( 27 / 50 ) & 3.7475425625 & 1.83757475111156 & 2.03939598116109 \tabularnewline
Trimmed Mean ( 28 / 50 ) & 3.83140410638298 & 1.82317004727595 & 2.10150672018092 \tabularnewline
Trimmed Mean ( 29 / 50 ) & 3.91649115217391 & 1.80851469927322 & 2.16558436254227 \tabularnewline
Trimmed Mean ( 30 / 50 ) & 3.99607317777778 & 1.79387475014154 & 2.22762106298808 \tabularnewline
Trimmed Mean ( 31 / 50 ) & 4.08057711363636 & 1.77856499624553 & 2.29430868270222 \tabularnewline
Trimmed Mean ( 32 / 50 ) & 4.16683704651163 & 1.76483834687158 & 2.36103043312603 \tabularnewline
Trimmed Mean ( 33 / 50 ) & 4.25392245238095 & 1.75114561643205 & 2.42922256862241 \tabularnewline
Trimmed Mean ( 34 / 50 ) & 4.34785348780488 & 1.73726886922625 & 2.5026946403186 \tabularnewline
Trimmed Mean ( 35 / 50 ) & 4.434902325 & 1.72430097179867 & 2.57200013079725 \tabularnewline
Trimmed Mean ( 36 / 50 ) & 4.53429212820513 & 1.71022036034341 & 2.65129116302571 \tabularnewline
Trimmed Mean ( 37 / 50 ) & 4.63617481578947 & 1.69601192525311 & 2.7335744205322 \tabularnewline
Trimmed Mean ( 38 / 50 ) & 4.72695791891892 & 1.68464795084398 & 2.80590251307449 \tabularnewline
Trimmed Mean ( 39 / 50 ) & 4.81267341666667 & 1.67306503115068 & 2.87656087902133 \tabularnewline
Trimmed Mean ( 40 / 50 ) & 4.89595122857143 & 1.66061013460015 & 2.94828456514888 \tabularnewline
Trimmed Mean ( 41 / 50 ) & 4.97342038235294 & 1.6496067300662 & 3.01491276175465 \tabularnewline
Trimmed Mean ( 42 / 50 ) & 5.06853463636364 & 1.63826860766256 & 3.09383614668372 \tabularnewline
Trimmed Mean ( 43 / 50 ) & 5.17192009375 & 1.62491362566891 & 3.18288923918705 \tabularnewline
Trimmed Mean ( 44 / 50 ) & 5.28180783870968 & 1.60829137873461 & 3.2841112677389 \tabularnewline
Trimmed Mean ( 45 / 50 ) & 5.39057143333333 & 1.59369106643995 & 3.38244440647773 \tabularnewline
Trimmed Mean ( 46 / 50 ) & 5.49231182758621 & 1.57943349178857 & 3.47739354404006 \tabularnewline
Trimmed Mean ( 47 / 50 ) & 5.59059260714286 & 1.56523443495774 & 3.57172860645235 \tabularnewline
Trimmed Mean ( 48 / 50 ) & 5.69735159259259 & 1.5482602378787 & 3.6798410585023 \tabularnewline
Trimmed Mean ( 49 / 50 ) & 5.81297280769231 & 1.52661112447883 & 3.80776264137128 \tabularnewline
Trimmed Mean ( 50 / 50 ) & 5.94528172 & 1.49982736880229 & 3.96397735077183 \tabularnewline
Median & 8.45777 &  &  \tabularnewline
Midrange & -15.032 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.37668914666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.63617481578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.63617481578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.63617481578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.72695791891892 &  &  \tabularnewline
Midmean - Closest Observation & 4.63617481578947 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.63617481578947 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.63617481578947 &  &  \tabularnewline
Number of observations & 150 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269827&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]5.73333333475645e-07[/C][C]3.1890835668285[/C][C]1.79779965454407e-07[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]109.271530006499[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]38.9277259217145[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 50 )[/C][C]0.0801445733333335[/C][C]3.10580921642012[/C][C]0.0258047316331012[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 50 )[/C][C]0.12454324[/C][C]3.07321754371796[/C][C]0.0405253576189496[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 50 )[/C][C]0.12951524[/C][C]3.04432908895348[/C][C]0.0425431141692117[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 50 )[/C][C]-0.0224074266666666[/C][C]3.00842990972101[/C][C]-0.00744821296792138[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 50 )[/C][C]0.000365906666667115[/C][C]2.9918148275585[/C][C]0.000122302578119688[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 50 )[/C][C]-0.356538093333333[/C][C]2.92578359800457[/C][C]-0.121860719151101[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 50 )[/C][C]-0.404642093333334[/C][C]2.85982272009343[/C][C]-0.141492019938954[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 50 )[/C][C]-0.685538093333333[/C][C]2.80260243852708[/C][C]-0.244607684596757[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 50 )[/C][C]-0.0534620933333338[/C][C]2.65268309935082[/C][C]-0.0201539691440781[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 50 )[/C][C]0.0640179066666663[/C][C]2.57969727693166[/C][C]0.0248160538987002[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 50 )[/C][C]0.0596325733333337[/C][C]2.55941937086487[/C][C]0.0232992584225003[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 50 )[/C][C]0.0463445733333337[/C][C]2.54461030010638[/C][C]0.0182128372786183[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 50 )[/C][C]0.370018573333333[/C][C]2.48796869128532[/C][C]0.148723163048397[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 50 )[/C][C]1.86115857333333[/C][C]2.19134224785623[/C][C]0.849323548228984[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 50 )[/C][C]1.87245857333333[/C][C]2.18818646406326[/C][C]0.855712529112509[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 50 )[/C][C]1.78969590666667[/C][C]2.17252120960042[/C][C]0.823787541754696[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 50 )[/C][C]1.63133524[/C][C]2.12435473004749[/C][C]0.767920355732461[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 50 )[/C][C]1.64886724[/C][C]2.11338219125875[/C][C]0.780203054052387[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 50 )[/C][C]1.63642857333333[/C][C]2.09207948601541[/C][C]0.7822019116731[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 50 )[/C][C]1.76545524[/C][C]2.07041243359363[/C][C]0.852707031388761[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 50 )[/C][C]1.72082324[/C][C]2.05414082051794[/C][C]0.837733821757215[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 50 )[/C][C]1.96940857333333[/C][C]1.99910155147375[/C][C]0.985146838529276[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 50 )[/C][C]1.97888457333333[/C][C]1.99420045497612[/C][C]0.992319788311869[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 50 )[/C][C]1.96245257333333[/C][C]1.99083669039803[/C][C]0.985742619069865[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 50 )[/C][C]2.56816924[/C][C]1.91342180624426[/C][C]1.34218666873088[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 50 )[/C][C]2.25934124[/C][C]1.87432104455803[/C][C]1.20541848823596[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 50 )[/C][C]2.32860524[/C][C]1.86074978943793[/C][C]1.25143383232809[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 50 )[/C][C]2.37017590666667[/C][C]1.83955556586491[/C][C]1.28845029236845[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 50 )[/C][C]2.53176390666667[/C][C]1.8154831693878[/C][C]1.39454000420197[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 50 )[/C][C]2.50880390666667[/C][C]1.79686990171223[/C][C]1.3962078747471[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 50 )[/C][C]2.54745057333333[/C][C]1.75447459623134[/C][C]1.45197347331521[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 50 )[/C][C]2.60626657333333[/C][C]1.72896786444424[/C][C]1.50741180731609[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 50 )[/C][C]2.55940657333333[/C][C]1.70444554043559[/C][C]1.50160654160839[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 50 )[/C][C]2.76936790666667[/C][C]1.67010682580028[/C][C]1.65819806486908[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 50 )[/C][C]2.62600790666667[/C][C]1.65360886892498[/C][C]1.58804657861677[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 50 )[/C][C]2.67595190666667[/C][C]1.62711307265971[/C][C]1.64460107390846[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 50 )[/C][C]2.97908057333333[/C][C]1.57377638700493[/C][C]1.89295035681839[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 50 )[/C][C]3.16350724[/C][C]1.55113498119989[/C][C]2.03947901268583[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 50 )[/C][C]3.29701724[/C][C]1.53340095320863[/C][C]2.15013381405628[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 50 )[/C][C]3.49117724[/C][C]1.49373680158792[/C][C]2.33721043512398[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 50 )[/C][C]3.25755924[/C][C]1.46801864064725[/C][C]2.2190176267542[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 50 )[/C][C]3.21586724[/C][C]1.45681174168939[/C][C]2.20746933043711[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 50 )[/C][C]3.21884857333333[/C][C]1.45268760935196[/C][C]2.2157885512421[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 50 )[/C][C]3.36756857333333[/C][C]1.40350391213882[/C][C]2.39940091666823[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 50 )[/C][C]3.62028857333333[/C][C]1.37033312190342[/C][C]2.64190401258394[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 50 )[/C][C]3.80450324[/C][C]1.33872222990916[/C][C]2.84189143572985[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 50 )[/C][C]3.78423057333333[/C][C]1.32500851666954[/C][C]2.85600471674336[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 50 )[/C][C]3.77341457333333[/C][C]1.31942411439061[/C][C]2.85989511043318[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 50 )[/C][C]3.65192724[/C][C]1.30797022049751[/C][C]2.7920568700799[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 50 )[/C][C]3.74889390666667[/C][C]1.28464081437395[/C][C]2.91824287747982[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 50 )[/C][C]0.203135716216216[/C][C]3.01493515055021[/C][C]0.0673764794506924[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 50 )[/C][C]0.329496479452055[/C][C]2.91529786358429[/C][C]0.113023263786482[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 50 )[/C][C]0.436242958333334[/C][C]2.82498764046568[/C][C]0.15442296174486[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 50 )[/C][C]0.544245676056338[/C][C]2.73766986519506[/C][C]0.198798870154331[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 50 )[/C][C]0.696027757142857[/C][C]2.65323048740685[/C][C]0.262332187288834[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 50 )[/C][C]0.847258594202899[/C][C]2.56473409070778[/C][C]0.330349488187715[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 50 )[/C][C]1.06854475[/C][C]2.48259968946529[/C][C]0.430413632344467[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 50 )[/C][C]1.304129[/C][C]2.40586046754139[/C][C]0.542063439503091[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 50 )[/C][C]1.58675216666667[/C][C]2.33181374118396[/C][C]0.680479807903099[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 50 )[/C][C]1.79703604615385[/C][C]2.27695662938872[/C][C]0.789227174096982[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 50 )[/C][C]2.000124109375[/C][C]2.22828486352088[/C][C]0.897607008026179[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 50 )[/C][C]2.21013401587302[/C][C]2.17761063999267[/C][C]1.01493534945277[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 50 )[/C][C]2.4282579516129[/C][C]2.12366776116679[/C][C]1.14342647942198[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 50 )[/C][C]2.62292119672131[/C][C]2.07209329854669[/C][C]1.26583161026628[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 50 )[/C][C]2.69093571666667[/C][C]2.0538302241368[/C][C]1.31020358208899[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 50 )[/C][C]2.76029818644068[/C][C]2.03387009946035[/C][C]1.35716542918502[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 50 )[/C][C]2.83874125862069[/C][C]2.01339385045105[/C][C]1.40992844394788[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 50 )[/C][C]2.93219373684211[/C][C]1.99578661860784[/C][C]1.46919200154145[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 50 )[/C][C]3.02767933928571[/C][C]1.97721157714679[/C][C]1.53128748297883[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 50 )[/C][C]3.12752987272727[/C][C]1.95858539725048[/C][C]1.59683099706441[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 50 )[/C][C]3.22211838888889[/C][C]1.93992662855064[/C][C]1.66094858509994[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 50 )[/C][C]3.32328383018868[/C][C]1.92051951765902[/C][C]1.73040877722479[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 50 )[/C][C]3.41204313461538[/C][C]1.90427490459015[/C][C]1.7917807593803[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 50 )[/C][C]3.50367731372549[/C][C]1.88627146543423[/C][C]1.85746186481113[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 50 )[/C][C]3.60000386[/C][C]1.86610607753982[/C][C]1.92915285113163[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 50 )[/C][C]3.66317740816327[/C][C]1.85114069929234[/C][C]1.9788757329811[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 50 )[/C][C]3.7475425625[/C][C]1.83757475111156[/C][C]2.03939598116109[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 50 )[/C][C]3.83140410638298[/C][C]1.82317004727595[/C][C]2.10150672018092[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 50 )[/C][C]3.91649115217391[/C][C]1.80851469927322[/C][C]2.16558436254227[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 50 )[/C][C]3.99607317777778[/C][C]1.79387475014154[/C][C]2.22762106298808[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 50 )[/C][C]4.08057711363636[/C][C]1.77856499624553[/C][C]2.29430868270222[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 50 )[/C][C]4.16683704651163[/C][C]1.76483834687158[/C][C]2.36103043312603[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 50 )[/C][C]4.25392245238095[/C][C]1.75114561643205[/C][C]2.42922256862241[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 50 )[/C][C]4.34785348780488[/C][C]1.73726886922625[/C][C]2.5026946403186[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 50 )[/C][C]4.434902325[/C][C]1.72430097179867[/C][C]2.57200013079725[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 50 )[/C][C]4.53429212820513[/C][C]1.71022036034341[/C][C]2.65129116302571[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 50 )[/C][C]4.63617481578947[/C][C]1.69601192525311[/C][C]2.7335744205322[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 50 )[/C][C]4.72695791891892[/C][C]1.68464795084398[/C][C]2.80590251307449[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 50 )[/C][C]4.81267341666667[/C][C]1.67306503115068[/C][C]2.87656087902133[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 50 )[/C][C]4.89595122857143[/C][C]1.66061013460015[/C][C]2.94828456514888[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 50 )[/C][C]4.97342038235294[/C][C]1.6496067300662[/C][C]3.01491276175465[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 50 )[/C][C]5.06853463636364[/C][C]1.63826860766256[/C][C]3.09383614668372[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 50 )[/C][C]5.17192009375[/C][C]1.62491362566891[/C][C]3.18288923918705[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 50 )[/C][C]5.28180783870968[/C][C]1.60829137873461[/C][C]3.2841112677389[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 50 )[/C][C]5.39057143333333[/C][C]1.59369106643995[/C][C]3.38244440647773[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 50 )[/C][C]5.49231182758621[/C][C]1.57943349178857[/C][C]3.47739354404006[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 50 )[/C][C]5.59059260714286[/C][C]1.56523443495774[/C][C]3.57172860645235[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 50 )[/C][C]5.69735159259259[/C][C]1.5482602378787[/C][C]3.6798410585023[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 50 )[/C][C]5.81297280769231[/C][C]1.52661112447883[/C][C]3.80776264137128[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 50 )[/C][C]5.94528172[/C][C]1.49982736880229[/C][C]3.96397735077183[/C][/ROW]
[ROW][C]Median[/C][C]8.45777[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-15.032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.37668914666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.63617481578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.63617481578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.63617481578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.72695791891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.63617481578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.63617481578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.63617481578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]150[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269827&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.73333333475645e-073.18908356682851.79779965454407e-07
Geometric MeanNaN
Harmonic Mean109.271530006499
Quadratic Mean38.9277259217145
Winsorized Mean ( 1 / 50 )0.08014457333333353.105809216420120.0258047316331012
Winsorized Mean ( 2 / 50 )0.124543243.073217543717960.0405253576189496
Winsorized Mean ( 3 / 50 )0.129515243.044329088953480.0425431141692117
Winsorized Mean ( 4 / 50 )-0.02240742666666663.00842990972101-0.00744821296792138
Winsorized Mean ( 5 / 50 )0.0003659066666671152.99181482755850.000122302578119688
Winsorized Mean ( 6 / 50 )-0.3565380933333332.92578359800457-0.121860719151101
Winsorized Mean ( 7 / 50 )-0.4046420933333342.85982272009343-0.141492019938954
Winsorized Mean ( 8 / 50 )-0.6855380933333332.80260243852708-0.244607684596757
Winsorized Mean ( 9 / 50 )-0.05346209333333382.65268309935082-0.0201539691440781
Winsorized Mean ( 10 / 50 )0.06401790666666632.579697276931660.0248160538987002
Winsorized Mean ( 11 / 50 )0.05963257333333372.559419370864870.0232992584225003
Winsorized Mean ( 12 / 50 )0.04634457333333372.544610300106380.0182128372786183
Winsorized Mean ( 13 / 50 )0.3700185733333332.487968691285320.148723163048397
Winsorized Mean ( 14 / 50 )1.861158573333332.191342247856230.849323548228984
Winsorized Mean ( 15 / 50 )1.872458573333332.188186464063260.855712529112509
Winsorized Mean ( 16 / 50 )1.789695906666672.172521209600420.823787541754696
Winsorized Mean ( 17 / 50 )1.631335242.124354730047490.767920355732461
Winsorized Mean ( 18 / 50 )1.648867242.113382191258750.780203054052387
Winsorized Mean ( 19 / 50 )1.636428573333332.092079486015410.7822019116731
Winsorized Mean ( 20 / 50 )1.765455242.070412433593630.852707031388761
Winsorized Mean ( 21 / 50 )1.720823242.054140820517940.837733821757215
Winsorized Mean ( 22 / 50 )1.969408573333331.999101551473750.985146838529276
Winsorized Mean ( 23 / 50 )1.978884573333331.994200454976120.992319788311869
Winsorized Mean ( 24 / 50 )1.962452573333331.990836690398030.985742619069865
Winsorized Mean ( 25 / 50 )2.568169241.913421806244261.34218666873088
Winsorized Mean ( 26 / 50 )2.259341241.874321044558031.20541848823596
Winsorized Mean ( 27 / 50 )2.328605241.860749789437931.25143383232809
Winsorized Mean ( 28 / 50 )2.370175906666671.839555565864911.28845029236845
Winsorized Mean ( 29 / 50 )2.531763906666671.81548316938781.39454000420197
Winsorized Mean ( 30 / 50 )2.508803906666671.796869901712231.3962078747471
Winsorized Mean ( 31 / 50 )2.547450573333331.754474596231341.45197347331521
Winsorized Mean ( 32 / 50 )2.606266573333331.728967864444241.50741180731609
Winsorized Mean ( 33 / 50 )2.559406573333331.704445540435591.50160654160839
Winsorized Mean ( 34 / 50 )2.769367906666671.670106825800281.65819806486908
Winsorized Mean ( 35 / 50 )2.626007906666671.653608868924981.58804657861677
Winsorized Mean ( 36 / 50 )2.675951906666671.627113072659711.64460107390846
Winsorized Mean ( 37 / 50 )2.979080573333331.573776387004931.89295035681839
Winsorized Mean ( 38 / 50 )3.163507241.551134981199892.03947901268583
Winsorized Mean ( 39 / 50 )3.297017241.533400953208632.15013381405628
Winsorized Mean ( 40 / 50 )3.491177241.493736801587922.33721043512398
Winsorized Mean ( 41 / 50 )3.257559241.468018640647252.2190176267542
Winsorized Mean ( 42 / 50 )3.215867241.456811741689392.20746933043711
Winsorized Mean ( 43 / 50 )3.218848573333331.452687609351962.2157885512421
Winsorized Mean ( 44 / 50 )3.367568573333331.403503912138822.39940091666823
Winsorized Mean ( 45 / 50 )3.620288573333331.370333121903422.64190401258394
Winsorized Mean ( 46 / 50 )3.804503241.338722229909162.84189143572985
Winsorized Mean ( 47 / 50 )3.784230573333331.325008516669542.85600471674336
Winsorized Mean ( 48 / 50 )3.773414573333331.319424114390612.85989511043318
Winsorized Mean ( 49 / 50 )3.651927241.307970220497512.7920568700799
Winsorized Mean ( 50 / 50 )3.748893906666671.284640814373952.91824287747982
Trimmed Mean ( 1 / 50 )0.2031357162162163.014935150550210.0673764794506924
Trimmed Mean ( 2 / 50 )0.3294964794520552.915297863584290.113023263786482
Trimmed Mean ( 3 / 50 )0.4362429583333342.824987640465680.15442296174486
Trimmed Mean ( 4 / 50 )0.5442456760563382.737669865195060.198798870154331
Trimmed Mean ( 5 / 50 )0.6960277571428572.653230487406850.262332187288834
Trimmed Mean ( 6 / 50 )0.8472585942028992.564734090707780.330349488187715
Trimmed Mean ( 7 / 50 )1.068544752.482599689465290.430413632344467
Trimmed Mean ( 8 / 50 )1.3041292.405860467541390.542063439503091
Trimmed Mean ( 9 / 50 )1.586752166666672.331813741183960.680479807903099
Trimmed Mean ( 10 / 50 )1.797036046153852.276956629388720.789227174096982
Trimmed Mean ( 11 / 50 )2.0001241093752.228284863520880.897607008026179
Trimmed Mean ( 12 / 50 )2.210134015873022.177610639992671.01493534945277
Trimmed Mean ( 13 / 50 )2.42825795161292.123667761166791.14342647942198
Trimmed Mean ( 14 / 50 )2.622921196721312.072093298546691.26583161026628
Trimmed Mean ( 15 / 50 )2.690935716666672.05383022413681.31020358208899
Trimmed Mean ( 16 / 50 )2.760298186440682.033870099460351.35716542918502
Trimmed Mean ( 17 / 50 )2.838741258620692.013393850451051.40992844394788
Trimmed Mean ( 18 / 50 )2.932193736842111.995786618607841.46919200154145
Trimmed Mean ( 19 / 50 )3.027679339285711.977211577146791.53128748297883
Trimmed Mean ( 20 / 50 )3.127529872727271.958585397250481.59683099706441
Trimmed Mean ( 21 / 50 )3.222118388888891.939926628550641.66094858509994
Trimmed Mean ( 22 / 50 )3.323283830188681.920519517659021.73040877722479
Trimmed Mean ( 23 / 50 )3.412043134615381.904274904590151.7917807593803
Trimmed Mean ( 24 / 50 )3.503677313725491.886271465434231.85746186481113
Trimmed Mean ( 25 / 50 )3.600003861.866106077539821.92915285113163
Trimmed Mean ( 26 / 50 )3.663177408163271.851140699292341.9788757329811
Trimmed Mean ( 27 / 50 )3.74754256251.837574751111562.03939598116109
Trimmed Mean ( 28 / 50 )3.831404106382981.823170047275952.10150672018092
Trimmed Mean ( 29 / 50 )3.916491152173911.808514699273222.16558436254227
Trimmed Mean ( 30 / 50 )3.996073177777781.793874750141542.22762106298808
Trimmed Mean ( 31 / 50 )4.080577113636361.778564996245532.29430868270222
Trimmed Mean ( 32 / 50 )4.166837046511631.764838346871582.36103043312603
Trimmed Mean ( 33 / 50 )4.253922452380951.751145616432052.42922256862241
Trimmed Mean ( 34 / 50 )4.347853487804881.737268869226252.5026946403186
Trimmed Mean ( 35 / 50 )4.4349023251.724300971798672.57200013079725
Trimmed Mean ( 36 / 50 )4.534292128205131.710220360343412.65129116302571
Trimmed Mean ( 37 / 50 )4.636174815789471.696011925253112.7335744205322
Trimmed Mean ( 38 / 50 )4.726957918918921.684647950843982.80590251307449
Trimmed Mean ( 39 / 50 )4.812673416666671.673065031150682.87656087902133
Trimmed Mean ( 40 / 50 )4.895951228571431.660610134600152.94828456514888
Trimmed Mean ( 41 / 50 )4.973420382352941.64960673006623.01491276175465
Trimmed Mean ( 42 / 50 )5.068534636363641.638268607662563.09383614668372
Trimmed Mean ( 43 / 50 )5.171920093751.624913625668913.18288923918705
Trimmed Mean ( 44 / 50 )5.281807838709681.608291378734613.2841112677389
Trimmed Mean ( 45 / 50 )5.390571433333331.593691066439953.38244440647773
Trimmed Mean ( 46 / 50 )5.492311827586211.579433491788573.47739354404006
Trimmed Mean ( 47 / 50 )5.590592607142861.565234434957743.57172860645235
Trimmed Mean ( 48 / 50 )5.697351592592591.54826023787873.6798410585023
Trimmed Mean ( 49 / 50 )5.812972807692311.526611124478833.80776264137128
Trimmed Mean ( 50 / 50 )5.945281721.499827368802293.96397735077183
Median8.45777
Midrange-15.032
Midmean - Weighted Average at Xnp4.37668914666667
Midmean - Weighted Average at X(n+1)p4.63617481578947
Midmean - Empirical Distribution Function4.63617481578947
Midmean - Empirical Distribution Function - Averaging4.63617481578947
Midmean - Empirical Distribution Function - Interpolation4.72695791891892
Midmean - Closest Observation4.63617481578947
Midmean - True Basic - Statistics Graphics Toolkit4.63617481578947
Midmean - MS Excel (old versions)4.63617481578947
Number of observations150



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')