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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Dec 2007 08:28:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/18/t1197990832xj2ex45xeq8fnq2.htm/, Retrieved Sat, 04 May 2024 14:11:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4541, Retrieved Sat, 04 May 2024 14:11:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKlaas Van Pelt Paper
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper (Central Te...] [2007-12-18 15:28:28] [6abd901c2e17b7d5559c695bbff3d863] [Current]
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Dataseries X:
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4541&T=0

[TABLE]
[ROW][C]Summary of compuational 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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4541&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4541&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24246.425713.55597493061333.9797098641880
Geometric Mean23348.4458371096
Harmonic Mean22357.9375796182
Quadratic Mean25062.1813396201
Winsorized Mean ( 1 / 26 )24252.35706.8534275715334.3102955351317
Winsorized Mean ( 2 / 26 )24262.575699.75678274103834.6728686286689
Winsorized Mean ( 3 / 26 )24307.3125672.48583806879236.1454637763145
Winsorized Mean ( 4 / 26 )24299.7125667.6260984561636.3971878214339
Winsorized Mean ( 5 / 26 )24382.9625646.31458163309837.726152546937
Winsorized Mean ( 6 / 26 )24496.1375620.82996121457739.4570800869152
Winsorized Mean ( 7 / 26 )24332.1625588.76741379384341.3272914396039
Winsorized Mean ( 8 / 26 )24277.7625578.3017264248841.9811343986254
Winsorized Mean ( 9 / 26 )24272.025576.35825130976342.1127396802983
Winsorized Mean ( 10 / 26 )24232.775564.78011599424142.906565429168
Winsorized Mean ( 11 / 26 )24202.1125552.72103917792143.7872105176176
Winsorized Mean ( 12 / 26 )24171.0625535.77090629562245.1145484310101
Winsorized Mean ( 13 / 26 )24129.95527.90403954540345.708970177192
Winsorized Mean ( 14 / 26 )24118.225521.76917818949846.2239358094867
Winsorized Mean ( 15 / 26 )24084.6625513.12151629855546.9375415666385
Winsorized Mean ( 16 / 26 )24049.8625505.33010915905847.5923798406203
Winsorized Mean ( 17 / 26 )24057.725489.73094200970149.1243720506503
Winsorized Mean ( 18 / 26 )24094.85481.60341210443450.0304802549346
Winsorized Mean ( 19 / 26 )24086.0625477.54595356573750.4371617436067
Winsorized Mean ( 20 / 26 )24124.0625452.10510615067853.3594117204239
Winsorized Mean ( 21 / 26 )24183.125423.05444571913157.163150617392
Winsorized Mean ( 22 / 26 )24086.05402.28517181475359.8730743451099
Winsorized Mean ( 23 / 26 )24160.225367.63372662762365.7181951765593
Winsorized Mean ( 24 / 26 )23916.625332.20925728371971.9926506430082
Winsorized Mean ( 25 / 26 )23914.75324.92623481279673.6005512567439
Winsorized Mean ( 26 / 26 )23989.825312.80240040790876.6932253995372
Trimmed Mean ( 1 / 26 )24264.6794871795684.6673477833935.4401003140231
Trimmed Mean ( 2 / 26 )24277.6578947368658.6931267909436.8573117090415
Trimmed Mean ( 3 / 26 )24285.8108108108632.67604216836838.3858549907725
Trimmed Mean ( 4 / 26 )24277.8472222222614.50039685792439.5082693947152
Trimmed Mean ( 5 / 26 )24271.6594.77981742955340.8077061271078
Trimmed Mean ( 6 / 26 )24245.3970588235578.01470005234741.9459869387885
Trimmed Mean ( 7 / 26 )24194.7424242424564.87398240281942.8321062360221
Trimmed Mean ( 8 / 26 )24170.203125557.05907860245543.3889403358042
Trimmed Mean ( 9 / 26 )24152.8548387097549.80686953206643.9297072793322
Trimmed Mean ( 10 / 26 )24135.2541.20192812447544.5955543500003
Trimmed Mean ( 11 / 26 )24121.7413793103532.90710635630345.2644393208419
Trimmed Mean ( 12 / 26 )24111.3035714286524.91364652812845.9338478450789
Trimmed Mean ( 13 / 26 )24103.9259259259518.07294170061446.5261239986843
Trimmed Mean ( 14 / 26 )24100.8461538462510.73006213506647.1890102828381
Trimmed Mean ( 15 / 26 )24098.86502.35070602607747.9721830006725
Trimmed Mean ( 16 / 26 )24100.4375493.1064460291248.8747159849067
Trimmed Mean ( 17 / 26 )24105.9347826087482.52519385770449.9578780330329
Trimmed Mean ( 18 / 26 )24111.0909090909471.79148677775451.1053963134542
Trimmed Mean ( 19 / 26 )24112.8095238095459.18976798000652.5116437804847
Trimmed Mean ( 20 / 26 )24115.625443.14064545090154.4197993290867
Trimmed Mean ( 21 / 26 )24114.7368421053427.59508219352756.3961978196725
Trimmed Mean ( 22 / 26 )24107.5413.49107685042158.3023464100552
Trimmed Mean ( 23 / 26 )24109.7941176471399.11708658569860.4078224861221
Trimmed Mean ( 24 / 26 )24104.3125388.01505945765562.1221056051062
Trimmed Mean ( 25 / 26 )24125.1666666667381.13787013840563.2977422524451
Trimmed Mean ( 26 / 26 )24149.2142857143371.94788406180064.9263386633539
Median24144.5
Midrange23534.5
Midmean - Weighted Average at Xnp23984.2682926829
Midmean - Weighted Average at X(n+1)p24115.625
Midmean - Empirical Distribution Function23984.2682926829
Midmean - Empirical Distribution Function - Averaging24115.625
Midmean - Empirical Distribution Function - Interpolation24115.625
Midmean - Closest Observation23984.2682926829
Midmean - True Basic - Statistics Graphics Toolkit24115.625
Midmean - MS Excel (old versions)24112.8095238095
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24246.425 & 713.555974930613 & 33.9797098641880 \tabularnewline
Geometric Mean & 23348.4458371096 &  &  \tabularnewline
Harmonic Mean & 22357.9375796182 &  &  \tabularnewline
Quadratic Mean & 25062.1813396201 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 24252.35 & 706.85342757153 & 34.3102955351317 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 24262.575 & 699.756782741038 & 34.6728686286689 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 24307.3125 & 672.485838068792 & 36.1454637763145 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 24299.7125 & 667.62609845616 & 36.3971878214339 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 24382.9625 & 646.314581633098 & 37.726152546937 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 24496.1375 & 620.829961214577 & 39.4570800869152 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 24332.1625 & 588.767413793843 & 41.3272914396039 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 24277.7625 & 578.30172642488 & 41.9811343986254 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 24272.025 & 576.358251309763 & 42.1127396802983 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 24232.775 & 564.780115994241 & 42.906565429168 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 24202.1125 & 552.721039177921 & 43.7872105176176 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 24171.0625 & 535.770906295622 & 45.1145484310101 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 24129.95 & 527.904039545403 & 45.708970177192 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 24118.225 & 521.769178189498 & 46.2239358094867 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 24084.6625 & 513.121516298555 & 46.9375415666385 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 24049.8625 & 505.330109159058 & 47.5923798406203 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 24057.725 & 489.730942009701 & 49.1243720506503 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 24094.85 & 481.603412104434 & 50.0304802549346 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 24086.0625 & 477.545953565737 & 50.4371617436067 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 24124.0625 & 452.105106150678 & 53.3594117204239 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 24183.125 & 423.054445719131 & 57.163150617392 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 24086.05 & 402.285171814753 & 59.8730743451099 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 24160.225 & 367.633726627623 & 65.7181951765593 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 23916.625 & 332.209257283719 & 71.9926506430082 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 23914.75 & 324.926234812796 & 73.6005512567439 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 23989.825 & 312.802400407908 & 76.6932253995372 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 24264.6794871795 & 684.66734778339 & 35.4401003140231 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 24277.6578947368 & 658.69312679094 & 36.8573117090415 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 24285.8108108108 & 632.676042168368 & 38.3858549907725 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 24277.8472222222 & 614.500396857924 & 39.5082693947152 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 24271.6 & 594.779817429553 & 40.8077061271078 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 24245.3970588235 & 578.014700052347 & 41.9459869387885 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 24194.7424242424 & 564.873982402819 & 42.8321062360221 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 24170.203125 & 557.059078602455 & 43.3889403358042 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 24152.8548387097 & 549.806869532066 & 43.9297072793322 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 24135.2 & 541.201928124475 & 44.5955543500003 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 24121.7413793103 & 532.907106356303 & 45.2644393208419 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 24111.3035714286 & 524.913646528128 & 45.9338478450789 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 24103.9259259259 & 518.072941700614 & 46.5261239986843 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 24100.8461538462 & 510.730062135066 & 47.1890102828381 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 24098.86 & 502.350706026077 & 47.9721830006725 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 24100.4375 & 493.10644602912 & 48.8747159849067 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 24105.9347826087 & 482.525193857704 & 49.9578780330329 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 24111.0909090909 & 471.791486777754 & 51.1053963134542 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 24112.8095238095 & 459.189767980006 & 52.5116437804847 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 24115.625 & 443.140645450901 & 54.4197993290867 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 24114.7368421053 & 427.595082193527 & 56.3961978196725 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 24107.5 & 413.491076850421 & 58.3023464100552 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 24109.7941176471 & 399.117086585698 & 60.4078224861221 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 24104.3125 & 388.015059457655 & 62.1221056051062 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 24125.1666666667 & 381.137870138405 & 63.2977422524451 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 24149.2142857143 & 371.947884061800 & 64.9263386633539 \tabularnewline
Median & 24144.5 &  &  \tabularnewline
Midrange & 23534.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 23984.2682926829 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 24115.625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 23984.2682926829 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 24115.625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 24115.625 &  &  \tabularnewline
Midmean - Closest Observation & 23984.2682926829 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 24115.625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 24112.8095238095 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4541&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]24246.425[/C][C]713.555974930613[/C][C]33.9797098641880[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]23348.4458371096[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]22357.9375796182[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]25062.1813396201[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]24252.35[/C][C]706.85342757153[/C][C]34.3102955351317[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]24262.575[/C][C]699.756782741038[/C][C]34.6728686286689[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]24307.3125[/C][C]672.485838068792[/C][C]36.1454637763145[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]24299.7125[/C][C]667.62609845616[/C][C]36.3971878214339[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]24382.9625[/C][C]646.314581633098[/C][C]37.726152546937[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]24496.1375[/C][C]620.829961214577[/C][C]39.4570800869152[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]24332.1625[/C][C]588.767413793843[/C][C]41.3272914396039[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]24277.7625[/C][C]578.30172642488[/C][C]41.9811343986254[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]24272.025[/C][C]576.358251309763[/C][C]42.1127396802983[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]24232.775[/C][C]564.780115994241[/C][C]42.906565429168[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]24202.1125[/C][C]552.721039177921[/C][C]43.7872105176176[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]24171.0625[/C][C]535.770906295622[/C][C]45.1145484310101[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]24129.95[/C][C]527.904039545403[/C][C]45.708970177192[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]24118.225[/C][C]521.769178189498[/C][C]46.2239358094867[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]24084.6625[/C][C]513.121516298555[/C][C]46.9375415666385[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]24049.8625[/C][C]505.330109159058[/C][C]47.5923798406203[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]24057.725[/C][C]489.730942009701[/C][C]49.1243720506503[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]24094.85[/C][C]481.603412104434[/C][C]50.0304802549346[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]24086.0625[/C][C]477.545953565737[/C][C]50.4371617436067[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]24124.0625[/C][C]452.105106150678[/C][C]53.3594117204239[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]24183.125[/C][C]423.054445719131[/C][C]57.163150617392[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]24086.05[/C][C]402.285171814753[/C][C]59.8730743451099[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]24160.225[/C][C]367.633726627623[/C][C]65.7181951765593[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]23916.625[/C][C]332.209257283719[/C][C]71.9926506430082[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]23914.75[/C][C]324.926234812796[/C][C]73.6005512567439[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]23989.825[/C][C]312.802400407908[/C][C]76.6932253995372[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]24264.6794871795[/C][C]684.66734778339[/C][C]35.4401003140231[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]24277.6578947368[/C][C]658.69312679094[/C][C]36.8573117090415[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]24285.8108108108[/C][C]632.676042168368[/C][C]38.3858549907725[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]24277.8472222222[/C][C]614.500396857924[/C][C]39.5082693947152[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]24271.6[/C][C]594.779817429553[/C][C]40.8077061271078[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]24245.3970588235[/C][C]578.014700052347[/C][C]41.9459869387885[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]24194.7424242424[/C][C]564.873982402819[/C][C]42.8321062360221[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]24170.203125[/C][C]557.059078602455[/C][C]43.3889403358042[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]24152.8548387097[/C][C]549.806869532066[/C][C]43.9297072793322[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]24135.2[/C][C]541.201928124475[/C][C]44.5955543500003[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]24121.7413793103[/C][C]532.907106356303[/C][C]45.2644393208419[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]24111.3035714286[/C][C]524.913646528128[/C][C]45.9338478450789[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]24103.9259259259[/C][C]518.072941700614[/C][C]46.5261239986843[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]24100.8461538462[/C][C]510.730062135066[/C][C]47.1890102828381[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]24098.86[/C][C]502.350706026077[/C][C]47.9721830006725[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]24100.4375[/C][C]493.10644602912[/C][C]48.8747159849067[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]24105.9347826087[/C][C]482.525193857704[/C][C]49.9578780330329[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]24111.0909090909[/C][C]471.791486777754[/C][C]51.1053963134542[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]24112.8095238095[/C][C]459.189767980006[/C][C]52.5116437804847[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]24115.625[/C][C]443.140645450901[/C][C]54.4197993290867[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]24114.7368421053[/C][C]427.595082193527[/C][C]56.3961978196725[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]24107.5[/C][C]413.491076850421[/C][C]58.3023464100552[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]24109.7941176471[/C][C]399.117086585698[/C][C]60.4078224861221[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]24104.3125[/C][C]388.015059457655[/C][C]62.1221056051062[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]24125.1666666667[/C][C]381.137870138405[/C][C]63.2977422524451[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]24149.2142857143[/C][C]371.947884061800[/C][C]64.9263386633539[/C][/ROW]
[ROW][C]Median[/C][C]24144.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]23534.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]23984.2682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]24115.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]23984.2682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]24115.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]24115.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]23984.2682926829[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]24115.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]24112.8095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4541&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4541&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 Mean24246.425713.55597493061333.9797098641880
Geometric Mean23348.4458371096
Harmonic Mean22357.9375796182
Quadratic Mean25062.1813396201
Winsorized Mean ( 1 / 26 )24252.35706.8534275715334.3102955351317
Winsorized Mean ( 2 / 26 )24262.575699.75678274103834.6728686286689
Winsorized Mean ( 3 / 26 )24307.3125672.48583806879236.1454637763145
Winsorized Mean ( 4 / 26 )24299.7125667.6260984561636.3971878214339
Winsorized Mean ( 5 / 26 )24382.9625646.31458163309837.726152546937
Winsorized Mean ( 6 / 26 )24496.1375620.82996121457739.4570800869152
Winsorized Mean ( 7 / 26 )24332.1625588.76741379384341.3272914396039
Winsorized Mean ( 8 / 26 )24277.7625578.3017264248841.9811343986254
Winsorized Mean ( 9 / 26 )24272.025576.35825130976342.1127396802983
Winsorized Mean ( 10 / 26 )24232.775564.78011599424142.906565429168
Winsorized Mean ( 11 / 26 )24202.1125552.72103917792143.7872105176176
Winsorized Mean ( 12 / 26 )24171.0625535.77090629562245.1145484310101
Winsorized Mean ( 13 / 26 )24129.95527.90403954540345.708970177192
Winsorized Mean ( 14 / 26 )24118.225521.76917818949846.2239358094867
Winsorized Mean ( 15 / 26 )24084.6625513.12151629855546.9375415666385
Winsorized Mean ( 16 / 26 )24049.8625505.33010915905847.5923798406203
Winsorized Mean ( 17 / 26 )24057.725489.73094200970149.1243720506503
Winsorized Mean ( 18 / 26 )24094.85481.60341210443450.0304802549346
Winsorized Mean ( 19 / 26 )24086.0625477.54595356573750.4371617436067
Winsorized Mean ( 20 / 26 )24124.0625452.10510615067853.3594117204239
Winsorized Mean ( 21 / 26 )24183.125423.05444571913157.163150617392
Winsorized Mean ( 22 / 26 )24086.05402.28517181475359.8730743451099
Winsorized Mean ( 23 / 26 )24160.225367.63372662762365.7181951765593
Winsorized Mean ( 24 / 26 )23916.625332.20925728371971.9926506430082
Winsorized Mean ( 25 / 26 )23914.75324.92623481279673.6005512567439
Winsorized Mean ( 26 / 26 )23989.825312.80240040790876.6932253995372
Trimmed Mean ( 1 / 26 )24264.6794871795684.6673477833935.4401003140231
Trimmed Mean ( 2 / 26 )24277.6578947368658.6931267909436.8573117090415
Trimmed Mean ( 3 / 26 )24285.8108108108632.67604216836838.3858549907725
Trimmed Mean ( 4 / 26 )24277.8472222222614.50039685792439.5082693947152
Trimmed Mean ( 5 / 26 )24271.6594.77981742955340.8077061271078
Trimmed Mean ( 6 / 26 )24245.3970588235578.01470005234741.9459869387885
Trimmed Mean ( 7 / 26 )24194.7424242424564.87398240281942.8321062360221
Trimmed Mean ( 8 / 26 )24170.203125557.05907860245543.3889403358042
Trimmed Mean ( 9 / 26 )24152.8548387097549.80686953206643.9297072793322
Trimmed Mean ( 10 / 26 )24135.2541.20192812447544.5955543500003
Trimmed Mean ( 11 / 26 )24121.7413793103532.90710635630345.2644393208419
Trimmed Mean ( 12 / 26 )24111.3035714286524.91364652812845.9338478450789
Trimmed Mean ( 13 / 26 )24103.9259259259518.07294170061446.5261239986843
Trimmed Mean ( 14 / 26 )24100.8461538462510.73006213506647.1890102828381
Trimmed Mean ( 15 / 26 )24098.86502.35070602607747.9721830006725
Trimmed Mean ( 16 / 26 )24100.4375493.1064460291248.8747159849067
Trimmed Mean ( 17 / 26 )24105.9347826087482.52519385770449.9578780330329
Trimmed Mean ( 18 / 26 )24111.0909090909471.79148677775451.1053963134542
Trimmed Mean ( 19 / 26 )24112.8095238095459.18976798000652.5116437804847
Trimmed Mean ( 20 / 26 )24115.625443.14064545090154.4197993290867
Trimmed Mean ( 21 / 26 )24114.7368421053427.59508219352756.3961978196725
Trimmed Mean ( 22 / 26 )24107.5413.49107685042158.3023464100552
Trimmed Mean ( 23 / 26 )24109.7941176471399.11708658569860.4078224861221
Trimmed Mean ( 24 / 26 )24104.3125388.01505945765562.1221056051062
Trimmed Mean ( 25 / 26 )24125.1666666667381.13787013840563.2977422524451
Trimmed Mean ( 26 / 26 )24149.2142857143371.94788406180064.9263386633539
Median24144.5
Midrange23534.5
Midmean - Weighted Average at Xnp23984.2682926829
Midmean - Weighted Average at X(n+1)p24115.625
Midmean - Empirical Distribution Function23984.2682926829
Midmean - Empirical Distribution Function - Averaging24115.625
Midmean - Empirical Distribution Function - Interpolation24115.625
Midmean - Closest Observation23984.2682926829
Midmean - True Basic - Statistics Graphics Toolkit24115.625
Midmean - MS Excel (old versions)24112.8095238095
Number of observations80



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')