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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 computationWed, 17 Mar 2010 09:18:17 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/17/t1268839640vgslvbx2vu05qpc.htm/, Retrieved Fri, 21 Jan 2022 11:30:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74513, Retrieved Fri, 21 Jan 2022 11:30:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendancy ...] [2010-03-17 15:18:17] [2aa5bad7942f7e33426bcac9d4e6ffec] [Current]
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Dataseries X:
3592,21
5955,74
4652,25
4211,65
4787,85
3599,73
4174,27
5106,33
5325,75
6604,61
5711,90
6919,30
7048,76
8655,98
6658,53
7247,03
8779,57
6602,49
9832,48
9369,49
8582,76
8206,94
6515,83
8618,10
8505,39
9881,64
9375,29
15642,50
12232,73
6288,93
12473,94
11142,82
10236,32
10581,51
8763,71
10819,04
11636,25
14650,13
10671,38
17468,63
13873,19
13077,58
16866,81
14186,64
19919,87
17681,78
9984,28
17423,09
13514,45
12334,57
12274,56
11752,23
13054,00
12460,98
8626,68
13722,62
12066,22
6798,83
6593,82
6606,19
6315,28
7232,95
6747,44
7803,61
6700,31
5369,53
8081,19
10718,39
9447,21
6815,10
5497,80
6805,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74513&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74513&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74513&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9409.47597222222441.85143496977121.2955650418244
Geometric Mean8703.53701065494
Harmonic Mean8035.31974130394
Quadratic Mean10119.2766096867
Winsorized Mean ( 1 / 24 )9378.49583333333432.41044896859321.6888742066788
Winsorized Mean ( 2 / 24 )9388.53444444445427.95038257243421.9383714252326
Winsorized Mean ( 3 / 24 )9388.19444444445427.18018669993821.977129878074
Winsorized Mean ( 4 / 24 )9381.76777777778415.10516741392322.6009419160584
Winsorized Mean ( 5 / 24 )9306.16291666667393.10921640106823.6732249675167
Winsorized Mean ( 6 / 24 )9250.00541666667370.98099052198824.933906731047
Winsorized Mean ( 7 / 24 )9226.27638888889358.65647589407225.7245498380847
Winsorized Mean ( 8 / 24 )9196.31305555556351.25157443978226.1815568235472
Winsorized Mean ( 9 / 24 )9193.52555555556345.30926239396826.6240340378317
Winsorized Mean ( 10 / 24 )9194.34916666667335.60181796595827.3966011936184
Winsorized Mean ( 11 / 24 )9164.85847222222318.39948049254328.7841502066674
Winsorized Mean ( 12 / 24 )9216.46013888889310.07989473072329.7228562557807
Winsorized Mean ( 13 / 24 )9116.48472222222291.80855053861631.2413214259662
Winsorized Mean ( 14 / 24 )9152.96055555556286.23192924043531.9774267666241
Winsorized Mean ( 15 / 24 )9142.87305555556279.87677145078832.6674950842185
Winsorized Mean ( 16 / 24 )9131.46416666666277.49482584277732.9067907444169
Winsorized Mean ( 17 / 24 )9122.08819444444275.8584200290333.0680071084453
Winsorized Mean ( 18 / 24 )9080.85569444444269.25079229455433.7263843016298
Winsorized Mean ( 19 / 24 )9011.80916666667254.70507979071635.3813483974148
Winsorized Mean ( 20 / 24 )8991.19805555556248.33819490976936.2054578790122
Winsorized Mean ( 21 / 24 )8861.02722222222225.46040069151339.301922621642
Winsorized Mean ( 22 / 24 )8777.79694444444209.53155588261341.8924820534531
Winsorized Mean ( 23 / 24 )8747.71486111111204.87157808157242.6985282342489
Winsorized Mean ( 24 / 24 )8735.30819444444202.31804868010843.1761192411269
Trimmed Mean ( 1 / 24 )9342.43128571428420.34342140342822.2257107165425
Trimmed Mean ( 2 / 24 )9304.24529411765405.94338591150522.9200563847737
Trimmed Mean ( 3 / 24 )9258.2693939394391.53932498729923.6458225345302
Trimmed Mean ( 4 / 24 )9209.5475374.46571297251524.593833776915
Trimmed Mean ( 5 / 24 )9159.54806451613358.41026312756325.5560429117961
Trimmed Mean ( 6 / 24 )9124.3605346.33396465873626.3455549587543
Trimmed Mean ( 7 / 24 )9098.365338.09153054045226.9109521479462
Trimmed Mean ( 8 / 24 )9074.87107142857331.14381308978327.4046221391069
Trimmed Mean ( 9 / 24 )9054.63074074074324.28259453976727.9220374241528
Trimmed Mean ( 10 / 24 )9033.2623076923317.00231551695128.4958874605106
Trimmed Mean ( 11 / 24 )9010.0658309.94491060161729.0698943322253
Trimmed Mean ( 12 / 24 )8988.95770833333304.71062477682529.4999812196145
Trimmed Mean ( 13 / 24 )8959.28347826087299.44484712333429.9196448505616
Trimmed Mean ( 14 / 24 )8939.49590909091296.42901556805630.1572904122084
Trimmed Mean ( 15 / 24 )8913.35738095238293.11360996318730.4092238571652
Trimmed Mean ( 16 / 24 )8885.8155289.59670396351530.6834137902325
Trimmed Mean ( 17 / 24 )8856.72552631579284.87479498998031.0898881967684
Trimmed Mean ( 18 / 24 )8825.5063888889278.31339085675231.7106782455588
Trimmed Mean ( 19 / 24 )8795.46529411765270.56954357268832.5072259722194
Trimmed Mean ( 20 / 24 )8769.845625263.37083906451033.2984686389366
Trimmed Mean ( 21 / 24 )8743.28333333333254.36164605127834.3734343171011
Trimmed Mean ( 22 / 24 )8728.86571428571248.11959415748535.1800741248406
Trimmed Mean ( 23 / 24 )8722.70653846154243.20623419068235.8654726408971
Trimmed Mean ( 24 / 24 )8719.44458333333236.16658367158636.9207380984035
Median8641.33
Midrange11756.04
Midmean - Weighted Average at Xnp8765.48216216216
Midmean - Weighted Average at X(n+1)p8825.5063888889
Midmean - Empirical Distribution Function8765.48216216216
Midmean - Empirical Distribution Function - Averaging8825.5063888889
Midmean - Empirical Distribution Function - Interpolation8825.5063888889
Midmean - Closest Observation8765.48216216216
Midmean - True Basic - Statistics Graphics Toolkit8825.5063888889
Midmean - MS Excel (old versions)8856.72552631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9409.47597222222 & 441.851434969771 & 21.2955650418244 \tabularnewline
Geometric Mean & 8703.53701065494 &  &  \tabularnewline
Harmonic Mean & 8035.31974130394 &  &  \tabularnewline
Quadratic Mean & 10119.2766096867 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 9378.49583333333 & 432.410448968593 & 21.6888742066788 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 9388.53444444445 & 427.950382572434 & 21.9383714252326 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 9388.19444444445 & 427.180186699938 & 21.977129878074 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 9381.76777777778 & 415.105167413923 & 22.6009419160584 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 9306.16291666667 & 393.109216401068 & 23.6732249675167 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 9250.00541666667 & 370.980990521988 & 24.933906731047 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 9226.27638888889 & 358.656475894072 & 25.7245498380847 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 9196.31305555556 & 351.251574439782 & 26.1815568235472 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 9193.52555555556 & 345.309262393968 & 26.6240340378317 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 9194.34916666667 & 335.601817965958 & 27.3966011936184 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 9164.85847222222 & 318.399480492543 & 28.7841502066674 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 9216.46013888889 & 310.079894730723 & 29.7228562557807 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9116.48472222222 & 291.808550538616 & 31.2413214259662 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9152.96055555556 & 286.231929240435 & 31.9774267666241 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9142.87305555556 & 279.876771450788 & 32.6674950842185 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 9131.46416666666 & 277.494825842777 & 32.9067907444169 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 9122.08819444444 & 275.85842002903 & 33.0680071084453 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9080.85569444444 & 269.250792294554 & 33.7263843016298 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 9011.80916666667 & 254.705079790716 & 35.3813483974148 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8991.19805555556 & 248.338194909769 & 36.2054578790122 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8861.02722222222 & 225.460400691513 & 39.301922621642 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8777.79694444444 & 209.531555882613 & 41.8924820534531 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8747.71486111111 & 204.871578081572 & 42.6985282342489 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8735.30819444444 & 202.318048680108 & 43.1761192411269 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 9342.43128571428 & 420.343421403428 & 22.2257107165425 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 9304.24529411765 & 405.943385911505 & 22.9200563847737 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 9258.2693939394 & 391.539324987299 & 23.6458225345302 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 9209.5475 & 374.465712972515 & 24.593833776915 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 9159.54806451613 & 358.410263127563 & 25.5560429117961 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 9124.3605 & 346.333964658736 & 26.3455549587543 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 9098.365 & 338.091530540452 & 26.9109521479462 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 9074.87107142857 & 331.143813089783 & 27.4046221391069 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9054.63074074074 & 324.282594539767 & 27.9220374241528 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9033.2623076923 & 317.002315516951 & 28.4958874605106 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 9010.0658 & 309.944910601617 & 29.0698943322253 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8988.95770833333 & 304.710624776825 & 29.4999812196145 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8959.28347826087 & 299.444847123334 & 29.9196448505616 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8939.49590909091 & 296.429015568056 & 30.1572904122084 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8913.35738095238 & 293.113609963187 & 30.4092238571652 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8885.8155 & 289.596703963515 & 30.6834137902325 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8856.72552631579 & 284.874794989980 & 31.0898881967684 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8825.5063888889 & 278.313390856752 & 31.7106782455588 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8795.46529411765 & 270.569543572688 & 32.5072259722194 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8769.845625 & 263.370839064510 & 33.2984686389366 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8743.28333333333 & 254.361646051278 & 34.3734343171011 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8728.86571428571 & 248.119594157485 & 35.1800741248406 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8722.70653846154 & 243.206234190682 & 35.8654726408971 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8719.44458333333 & 236.166583671586 & 36.9207380984035 \tabularnewline
Median & 8641.33 &  &  \tabularnewline
Midrange & 11756.04 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8765.48216216216 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8825.5063888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8765.48216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8825.5063888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8825.5063888889 &  &  \tabularnewline
Midmean - Closest Observation & 8765.48216216216 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8825.5063888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8856.72552631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74513&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]9409.47597222222[/C][C]441.851434969771[/C][C]21.2955650418244[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8703.53701065494[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8035.31974130394[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10119.2766096867[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]9378.49583333333[/C][C]432.410448968593[/C][C]21.6888742066788[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]9388.53444444445[/C][C]427.950382572434[/C][C]21.9383714252326[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]9388.19444444445[/C][C]427.180186699938[/C][C]21.977129878074[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]9381.76777777778[/C][C]415.105167413923[/C][C]22.6009419160584[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]9306.16291666667[/C][C]393.109216401068[/C][C]23.6732249675167[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]9250.00541666667[/C][C]370.980990521988[/C][C]24.933906731047[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]9226.27638888889[/C][C]358.656475894072[/C][C]25.7245498380847[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]9196.31305555556[/C][C]351.251574439782[/C][C]26.1815568235472[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]9193.52555555556[/C][C]345.309262393968[/C][C]26.6240340378317[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]9194.34916666667[/C][C]335.601817965958[/C][C]27.3966011936184[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]9164.85847222222[/C][C]318.399480492543[/C][C]28.7841502066674[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]9216.46013888889[/C][C]310.079894730723[/C][C]29.7228562557807[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9116.48472222222[/C][C]291.808550538616[/C][C]31.2413214259662[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9152.96055555556[/C][C]286.231929240435[/C][C]31.9774267666241[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9142.87305555556[/C][C]279.876771450788[/C][C]32.6674950842185[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]9131.46416666666[/C][C]277.494825842777[/C][C]32.9067907444169[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]9122.08819444444[/C][C]275.85842002903[/C][C]33.0680071084453[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9080.85569444444[/C][C]269.250792294554[/C][C]33.7263843016298[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]9011.80916666667[/C][C]254.705079790716[/C][C]35.3813483974148[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8991.19805555556[/C][C]248.338194909769[/C][C]36.2054578790122[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8861.02722222222[/C][C]225.460400691513[/C][C]39.301922621642[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8777.79694444444[/C][C]209.531555882613[/C][C]41.8924820534531[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8747.71486111111[/C][C]204.871578081572[/C][C]42.6985282342489[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8735.30819444444[/C][C]202.318048680108[/C][C]43.1761192411269[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]9342.43128571428[/C][C]420.343421403428[/C][C]22.2257107165425[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]9304.24529411765[/C][C]405.943385911505[/C][C]22.9200563847737[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]9258.2693939394[/C][C]391.539324987299[/C][C]23.6458225345302[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]9209.5475[/C][C]374.465712972515[/C][C]24.593833776915[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]9159.54806451613[/C][C]358.410263127563[/C][C]25.5560429117961[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]9124.3605[/C][C]346.333964658736[/C][C]26.3455549587543[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]9098.365[/C][C]338.091530540452[/C][C]26.9109521479462[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]9074.87107142857[/C][C]331.143813089783[/C][C]27.4046221391069[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9054.63074074074[/C][C]324.282594539767[/C][C]27.9220374241528[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9033.2623076923[/C][C]317.002315516951[/C][C]28.4958874605106[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]9010.0658[/C][C]309.944910601617[/C][C]29.0698943322253[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8988.95770833333[/C][C]304.710624776825[/C][C]29.4999812196145[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8959.28347826087[/C][C]299.444847123334[/C][C]29.9196448505616[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8939.49590909091[/C][C]296.429015568056[/C][C]30.1572904122084[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8913.35738095238[/C][C]293.113609963187[/C][C]30.4092238571652[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8885.8155[/C][C]289.596703963515[/C][C]30.6834137902325[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8856.72552631579[/C][C]284.874794989980[/C][C]31.0898881967684[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8825.5063888889[/C][C]278.313390856752[/C][C]31.7106782455588[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8795.46529411765[/C][C]270.569543572688[/C][C]32.5072259722194[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8769.845625[/C][C]263.370839064510[/C][C]33.2984686389366[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8743.28333333333[/C][C]254.361646051278[/C][C]34.3734343171011[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8728.86571428571[/C][C]248.119594157485[/C][C]35.1800741248406[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8722.70653846154[/C][C]243.206234190682[/C][C]35.8654726408971[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8719.44458333333[/C][C]236.166583671586[/C][C]36.9207380984035[/C][/ROW]
[ROW][C]Median[/C][C]8641.33[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11756.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8765.48216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8825.5063888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8765.48216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8825.5063888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8825.5063888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8765.48216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8825.5063888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8856.72552631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74513&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74513&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 Mean9409.47597222222441.85143496977121.2955650418244
Geometric Mean8703.53701065494
Harmonic Mean8035.31974130394
Quadratic Mean10119.2766096867
Winsorized Mean ( 1 / 24 )9378.49583333333432.41044896859321.6888742066788
Winsorized Mean ( 2 / 24 )9388.53444444445427.95038257243421.9383714252326
Winsorized Mean ( 3 / 24 )9388.19444444445427.18018669993821.977129878074
Winsorized Mean ( 4 / 24 )9381.76777777778415.10516741392322.6009419160584
Winsorized Mean ( 5 / 24 )9306.16291666667393.10921640106823.6732249675167
Winsorized Mean ( 6 / 24 )9250.00541666667370.98099052198824.933906731047
Winsorized Mean ( 7 / 24 )9226.27638888889358.65647589407225.7245498380847
Winsorized Mean ( 8 / 24 )9196.31305555556351.25157443978226.1815568235472
Winsorized Mean ( 9 / 24 )9193.52555555556345.30926239396826.6240340378317
Winsorized Mean ( 10 / 24 )9194.34916666667335.60181796595827.3966011936184
Winsorized Mean ( 11 / 24 )9164.85847222222318.39948049254328.7841502066674
Winsorized Mean ( 12 / 24 )9216.46013888889310.07989473072329.7228562557807
Winsorized Mean ( 13 / 24 )9116.48472222222291.80855053861631.2413214259662
Winsorized Mean ( 14 / 24 )9152.96055555556286.23192924043531.9774267666241
Winsorized Mean ( 15 / 24 )9142.87305555556279.87677145078832.6674950842185
Winsorized Mean ( 16 / 24 )9131.46416666666277.49482584277732.9067907444169
Winsorized Mean ( 17 / 24 )9122.08819444444275.8584200290333.0680071084453
Winsorized Mean ( 18 / 24 )9080.85569444444269.25079229455433.7263843016298
Winsorized Mean ( 19 / 24 )9011.80916666667254.70507979071635.3813483974148
Winsorized Mean ( 20 / 24 )8991.19805555556248.33819490976936.2054578790122
Winsorized Mean ( 21 / 24 )8861.02722222222225.46040069151339.301922621642
Winsorized Mean ( 22 / 24 )8777.79694444444209.53155588261341.8924820534531
Winsorized Mean ( 23 / 24 )8747.71486111111204.87157808157242.6985282342489
Winsorized Mean ( 24 / 24 )8735.30819444444202.31804868010843.1761192411269
Trimmed Mean ( 1 / 24 )9342.43128571428420.34342140342822.2257107165425
Trimmed Mean ( 2 / 24 )9304.24529411765405.94338591150522.9200563847737
Trimmed Mean ( 3 / 24 )9258.2693939394391.53932498729923.6458225345302
Trimmed Mean ( 4 / 24 )9209.5475374.46571297251524.593833776915
Trimmed Mean ( 5 / 24 )9159.54806451613358.41026312756325.5560429117961
Trimmed Mean ( 6 / 24 )9124.3605346.33396465873626.3455549587543
Trimmed Mean ( 7 / 24 )9098.365338.09153054045226.9109521479462
Trimmed Mean ( 8 / 24 )9074.87107142857331.14381308978327.4046221391069
Trimmed Mean ( 9 / 24 )9054.63074074074324.28259453976727.9220374241528
Trimmed Mean ( 10 / 24 )9033.2623076923317.00231551695128.4958874605106
Trimmed Mean ( 11 / 24 )9010.0658309.94491060161729.0698943322253
Trimmed Mean ( 12 / 24 )8988.95770833333304.71062477682529.4999812196145
Trimmed Mean ( 13 / 24 )8959.28347826087299.44484712333429.9196448505616
Trimmed Mean ( 14 / 24 )8939.49590909091296.42901556805630.1572904122084
Trimmed Mean ( 15 / 24 )8913.35738095238293.11360996318730.4092238571652
Trimmed Mean ( 16 / 24 )8885.8155289.59670396351530.6834137902325
Trimmed Mean ( 17 / 24 )8856.72552631579284.87479498998031.0898881967684
Trimmed Mean ( 18 / 24 )8825.5063888889278.31339085675231.7106782455588
Trimmed Mean ( 19 / 24 )8795.46529411765270.56954357268832.5072259722194
Trimmed Mean ( 20 / 24 )8769.845625263.37083906451033.2984686389366
Trimmed Mean ( 21 / 24 )8743.28333333333254.36164605127834.3734343171011
Trimmed Mean ( 22 / 24 )8728.86571428571248.11959415748535.1800741248406
Trimmed Mean ( 23 / 24 )8722.70653846154243.20623419068235.8654726408971
Trimmed Mean ( 24 / 24 )8719.44458333333236.16658367158636.9207380984035
Median8641.33
Midrange11756.04
Midmean - Weighted Average at Xnp8765.48216216216
Midmean - Weighted Average at X(n+1)p8825.5063888889
Midmean - Empirical Distribution Function8765.48216216216
Midmean - Empirical Distribution Function - Averaging8825.5063888889
Midmean - Empirical Distribution Function - Interpolation8825.5063888889
Midmean - Closest Observation8765.48216216216
Midmean - True Basic - Statistics Graphics Toolkit8825.5063888889
Midmean - MS Excel (old versions)8856.72552631579
Number of observations72



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')