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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 27 Oct 2009 05:47:31 -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/2009/Oct/27/t1256644198retfe9lfrjafdzb.htm/, Retrieved Tue, 07 May 2024 13:36:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50904, Retrieved Tue, 07 May 2024 13:36:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-27 11:47:31] [ab2b68d5442f7c9b7e2e9d790849a234] [Current]
- RM D    [Univariate Data Series] [] [2009-12-02 08:39:03] [e5e09c53da17fb7444fa9ceb236a5291]
- RMPD    [Univariate Data Series] [] [2009-12-02 08:47:51] [e5e09c53da17fb7444fa9ceb236a5291]
- RMPD    [Mean Plot] [] [2009-12-02 08:52:16] [e5e09c53da17fb7444fa9ceb236a5291]
-   P       [Mean Plot] [] [2010-01-06 09:08:16] [74be16979710d4c4e7c6647856088456]
- RMP     [Mean Plot] [] [2009-12-02 08:56:02] [e5e09c53da17fb7444fa9ceb236a5291]
- RMPD      [(Partial) Autocorrelation Function] [] [2009-12-13 10:04:21] [e5e09c53da17fb7444fa9ceb236a5291]
- RMPD      [(Partial) Autocorrelation Function] [] [2009-12-13 10:07:50] [e5e09c53da17fb7444fa9ceb236a5291]
- RMP       [(Partial) Autocorrelation Function] [] [2009-12-13 10:12:58] [e5e09c53da17fb7444fa9ceb236a5291]
-   PD        [(Partial) Autocorrelation Function] [] [2010-01-06 09:56:35] [74be16979710d4c4e7c6647856088456]
- RMPD      [Bootstrap Plot - Central Tendency] [] [2009-12-13 10:21:52] [e5e09c53da17fb7444fa9ceb236a5291]
- RMP       [Blocked Bootstrap Plot - Central Tendency] [] [2009-12-13 10:46:34] [e5e09c53da17fb7444fa9ceb236a5291]
-   PD      [Mean Plot] [] [2010-01-06 09:23:38] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
2,14
2,45
2,52
2,3
2,25
2,06
1,99
2,25
2,26
2,36
2,3
2,19
2,31
2,21
2,21
2,26
2,18
2,21
2,33
2,12
2,08
1,97
2,09
2,11
2,24
2,45
2,68
2,73
2,76
2,83
3,16
3,22
3,22
3,34
3,35
3,42
3,58
3,71
3,68
3,83
3,94
3,88
4,03
4,15
4,32
4,4
4,37
4,14
4,11
4,16
3,98
4,13
3,76
3,66
3,85
4,03
4,31
4,58
4,46
4,41
3,84
2,84
2,66
2,17
1,43
1,47
1,29
1,23
1,09
0,94
0,76
0,67




Summary of computational 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 computational 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=50904&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]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=50904&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50904&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.866805555555560.12129305075856423.6353652383761
Geometric Mean2.65112009545915
Harmonic Mean2.3875895524265
Quadratic Mean3.04353846515678
Winsorized Mean ( 1 / 24 )2.866388888888890.12065910306806823.7560931252062
Winsorized Mean ( 2 / 24 )2.870.11921856941200424.073430960924
Winsorized Mean ( 3 / 24 )2.875833333333330.11776241798299624.4206376073951
Winsorized Mean ( 4 / 24 )2.881944444444440.1158476683953924.8770172448212
Winsorized Mean ( 5 / 24 )2.882638888888890.11439932823700525.1980403496498
Winsorized Mean ( 6 / 24 )2.893472222222220.11203362026869225.8268206925989
Winsorized Mean ( 7 / 24 )2.882777777777780.10881496804226926.4924746075188
Winsorized Mean ( 8 / 24 )2.937222222222220.099696766817477429.4615594465528
Winsorized Mean ( 9 / 24 )2.938472222222220.099143763821156629.6384977629342
Winsorized Mean ( 10 / 24 )2.946805555555560.097629538839561230.1835447609577
Winsorized Mean ( 11 / 24 )2.946805555555560.096721658793108530.4668632892131
Winsorized Mean ( 12 / 24 )2.935138888888890.094291276366006731.1284246221854
Winsorized Mean ( 13 / 24 )2.938750.093838742557918731.3170223715025
Winsorized Mean ( 14 / 24 )2.930972222222220.092020265450649931.8513776054481
Winsorized Mean ( 15 / 24 )2.926805555555560.090177148382126832.4561777353302
Winsorized Mean ( 16 / 24 )2.920138888888890.087275868331955633.4587205455474
Winsorized Mean ( 17 / 24 )2.915416666666670.085899215223751333.9399685907788
Winsorized Mean ( 18 / 24 )2.915416666666670.085216041726928634.2120639211218
Winsorized Mean ( 19 / 24 )2.918055555555560.084184070363746234.6627995409
Winsorized Mean ( 20 / 24 )2.898611111111110.08124840327203335.6759147795937
Winsorized Mean ( 21 / 24 )2.884027777777780.079086791858118336.4666173708465
Winsorized Mean ( 22 / 24 )2.884027777777780.076649482591995337.6261871607071
Winsorized Mean ( 23 / 24 )2.880833333333330.075339541789955838.2379991288638
Winsorized Mean ( 24 / 24 )2.854166666666670.071489777878785339.9241227397021
Trimmed Mean ( 1 / 24 )2.873714285714290.11816701718962724.3190896585189
Trimmed Mean ( 2 / 24 )2.881470588235290.1151927545769225.0143387821427
Trimmed Mean ( 3 / 24 )2.887727272727270.11255349320380825.6564873335230
Trimmed Mean ( 4 / 24 )2.89218750.11004473944746126.2819241930309
Trimmed Mean ( 5 / 24 )2.895161290322580.10771354325282626.8783404843255
Trimmed Mean ( 6 / 24 )2.898166666666670.10532743985157627.5157800355792
Trimmed Mean ( 7 / 24 )2.899137931034480.10307354239145328.1268874996468
Trimmed Mean ( 8 / 24 )2.902142857142860.10111511836224128.7013742766541
Trimmed Mean ( 9 / 24 )2.896296296296300.10077071839911328.741447340141
Trimmed Mean ( 10 / 24 )2.889807692307690.10032469548285028.8045498508558
Trimmed Mean ( 11 / 24 )2.88160.099923382893993328.8380949137504
Trimmed Mean ( 12 / 24 )2.872708333333330.09943802178154728.8894356692284
Trimmed Mean ( 13 / 24 )2.864565217391300.09915620162622728.8894206354272
Trimmed Mean ( 14 / 24 )2.855227272727270.098671668499729328.9366473288643
Trimmed Mean ( 15 / 24 )2.845952380952380.098217008021962528.9761665343745
Trimmed Mean ( 16 / 24 )2.836250.097771113858481829.0090793494008
Trimmed Mean ( 17 / 24 )2.826315789473680.097534631886112928.9775614550312
Trimmed Mean ( 18 / 24 )2.815833333333330.097205701544191428.9677795499805
Trimmed Mean ( 19 / 24 )2.804117647058820.09655576431970129.0414318276664
Trimmed Mean ( 20 / 24 )2.7906250.09551002470185229.2181371401728
Trimmed Mean ( 21 / 24 )2.777666666666670.094487952565798729.3970457739824
Trimmed Mean ( 22 / 24 )2.764642857142860.093230501944478229.6538450344212
Trimmed Mean ( 23 / 24 )2.749615384615380.091585152927133330.0225014288399
Trimmed Mean ( 24 / 24 )2.73250.088941541621938230.7224267779726
Median2.67
Midrange2.625
Midmean - Weighted Average at Xnp2.79864864864865
Midmean - Weighted Average at X(n+1)p2.81583333333333
Midmean - Empirical Distribution Function2.79864864864865
Midmean - Empirical Distribution Function - Averaging2.81583333333333
Midmean - Empirical Distribution Function - Interpolation2.81583333333333
Midmean - Closest Observation2.79864864864865
Midmean - True Basic - Statistics Graphics Toolkit2.81583333333333
Midmean - MS Excel (old versions)2.82631578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.86680555555556 & 0.121293050758564 & 23.6353652383761 \tabularnewline
Geometric Mean & 2.65112009545915 &  &  \tabularnewline
Harmonic Mean & 2.3875895524265 &  &  \tabularnewline
Quadratic Mean & 3.04353846515678 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.86638888888889 & 0.120659103068068 & 23.7560931252062 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.87 & 0.119218569412004 & 24.073430960924 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.87583333333333 & 0.117762417982996 & 24.4206376073951 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.88194444444444 & 0.11584766839539 & 24.8770172448212 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.88263888888889 & 0.114399328237005 & 25.1980403496498 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.89347222222222 & 0.112033620268692 & 25.8268206925989 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.88277777777778 & 0.108814968042269 & 26.4924746075188 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.93722222222222 & 0.0996967668174774 & 29.4615594465528 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.93847222222222 & 0.0991437638211566 & 29.6384977629342 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.94680555555556 & 0.0976295388395612 & 30.1835447609577 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.94680555555556 & 0.0967216587931085 & 30.4668632892131 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.93513888888889 & 0.0942912763660067 & 31.1284246221854 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.93875 & 0.0938387425579187 & 31.3170223715025 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.93097222222222 & 0.0920202654506499 & 31.8513776054481 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.92680555555556 & 0.0901771483821268 & 32.4561777353302 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.92013888888889 & 0.0872758683319556 & 33.4587205455474 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.91541666666667 & 0.0858992152237513 & 33.9399685907788 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.91541666666667 & 0.0852160417269286 & 34.2120639211218 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.91805555555556 & 0.0841840703637462 & 34.6627995409 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.89861111111111 & 0.081248403272033 & 35.6759147795937 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.88402777777778 & 0.0790867918581183 & 36.4666173708465 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.88402777777778 & 0.0766494825919953 & 37.6261871607071 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.88083333333333 & 0.0753395417899558 & 38.2379991288638 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.85416666666667 & 0.0714897778787853 & 39.9241227397021 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.87371428571429 & 0.118167017189627 & 24.3190896585189 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.88147058823529 & 0.11519275457692 & 25.0143387821427 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.88772727272727 & 0.112553493203808 & 25.6564873335230 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.8921875 & 0.110044739447461 & 26.2819241930309 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.89516129032258 & 0.107713543252826 & 26.8783404843255 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.89816666666667 & 0.105327439851576 & 27.5157800355792 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.89913793103448 & 0.103073542391453 & 28.1268874996468 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.90214285714286 & 0.101115118362241 & 28.7013742766541 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.89629629629630 & 0.100770718399113 & 28.741447340141 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.88980769230769 & 0.100324695482850 & 28.8045498508558 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.8816 & 0.0999233828939933 & 28.8380949137504 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.87270833333333 & 0.099438021781547 & 28.8894356692284 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.86456521739130 & 0.099156201626227 & 28.8894206354272 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.85522727272727 & 0.0986716684997293 & 28.9366473288643 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.84595238095238 & 0.0982170080219625 & 28.9761665343745 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.83625 & 0.0977711138584818 & 29.0090793494008 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.82631578947368 & 0.0975346318861129 & 28.9775614550312 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.81583333333333 & 0.0972057015441914 & 28.9677795499805 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.80411764705882 & 0.096555764319701 & 29.0414318276664 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.790625 & 0.095510024701852 & 29.2181371401728 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.77766666666667 & 0.0944879525657987 & 29.3970457739824 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.76464285714286 & 0.0932305019444782 & 29.6538450344212 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.74961538461538 & 0.0915851529271333 & 30.0225014288399 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.7325 & 0.0889415416219382 & 30.7224267779726 \tabularnewline
Median & 2.67 &  &  \tabularnewline
Midrange & 2.625 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.79864864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.81583333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.79864864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.81583333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.81583333333333 &  &  \tabularnewline
Midmean - Closest Observation & 2.79864864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.81583333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.82631578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50904&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]2.86680555555556[/C][C]0.121293050758564[/C][C]23.6353652383761[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.65112009545915[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.3875895524265[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.04353846515678[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.86638888888889[/C][C]0.120659103068068[/C][C]23.7560931252062[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.87[/C][C]0.119218569412004[/C][C]24.073430960924[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.87583333333333[/C][C]0.117762417982996[/C][C]24.4206376073951[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.88194444444444[/C][C]0.11584766839539[/C][C]24.8770172448212[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.88263888888889[/C][C]0.114399328237005[/C][C]25.1980403496498[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.89347222222222[/C][C]0.112033620268692[/C][C]25.8268206925989[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.88277777777778[/C][C]0.108814968042269[/C][C]26.4924746075188[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.93722222222222[/C][C]0.0996967668174774[/C][C]29.4615594465528[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.93847222222222[/C][C]0.0991437638211566[/C][C]29.6384977629342[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.94680555555556[/C][C]0.0976295388395612[/C][C]30.1835447609577[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.94680555555556[/C][C]0.0967216587931085[/C][C]30.4668632892131[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.93513888888889[/C][C]0.0942912763660067[/C][C]31.1284246221854[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.93875[/C][C]0.0938387425579187[/C][C]31.3170223715025[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.93097222222222[/C][C]0.0920202654506499[/C][C]31.8513776054481[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.92680555555556[/C][C]0.0901771483821268[/C][C]32.4561777353302[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.92013888888889[/C][C]0.0872758683319556[/C][C]33.4587205455474[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.91541666666667[/C][C]0.0858992152237513[/C][C]33.9399685907788[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.91541666666667[/C][C]0.0852160417269286[/C][C]34.2120639211218[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.91805555555556[/C][C]0.0841840703637462[/C][C]34.6627995409[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.89861111111111[/C][C]0.081248403272033[/C][C]35.6759147795937[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.88402777777778[/C][C]0.0790867918581183[/C][C]36.4666173708465[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.88402777777778[/C][C]0.0766494825919953[/C][C]37.6261871607071[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.88083333333333[/C][C]0.0753395417899558[/C][C]38.2379991288638[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.85416666666667[/C][C]0.0714897778787853[/C][C]39.9241227397021[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.87371428571429[/C][C]0.118167017189627[/C][C]24.3190896585189[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.88147058823529[/C][C]0.11519275457692[/C][C]25.0143387821427[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.88772727272727[/C][C]0.112553493203808[/C][C]25.6564873335230[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.8921875[/C][C]0.110044739447461[/C][C]26.2819241930309[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.89516129032258[/C][C]0.107713543252826[/C][C]26.8783404843255[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.89816666666667[/C][C]0.105327439851576[/C][C]27.5157800355792[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.89913793103448[/C][C]0.103073542391453[/C][C]28.1268874996468[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.90214285714286[/C][C]0.101115118362241[/C][C]28.7013742766541[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.89629629629630[/C][C]0.100770718399113[/C][C]28.741447340141[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.88980769230769[/C][C]0.100324695482850[/C][C]28.8045498508558[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.8816[/C][C]0.0999233828939933[/C][C]28.8380949137504[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.87270833333333[/C][C]0.099438021781547[/C][C]28.8894356692284[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.86456521739130[/C][C]0.099156201626227[/C][C]28.8894206354272[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.85522727272727[/C][C]0.0986716684997293[/C][C]28.9366473288643[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.84595238095238[/C][C]0.0982170080219625[/C][C]28.9761665343745[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.83625[/C][C]0.0977711138584818[/C][C]29.0090793494008[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.82631578947368[/C][C]0.0975346318861129[/C][C]28.9775614550312[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.81583333333333[/C][C]0.0972057015441914[/C][C]28.9677795499805[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.80411764705882[/C][C]0.096555764319701[/C][C]29.0414318276664[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.790625[/C][C]0.095510024701852[/C][C]29.2181371401728[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.77766666666667[/C][C]0.0944879525657987[/C][C]29.3970457739824[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.76464285714286[/C][C]0.0932305019444782[/C][C]29.6538450344212[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.74961538461538[/C][C]0.0915851529271333[/C][C]30.0225014288399[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.7325[/C][C]0.0889415416219382[/C][C]30.7224267779726[/C][/ROW]
[ROW][C]Median[/C][C]2.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.79864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.81583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.79864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.81583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.81583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.79864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.81583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.82631578947368[/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=50904&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50904&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 Mean2.866805555555560.12129305075856423.6353652383761
Geometric Mean2.65112009545915
Harmonic Mean2.3875895524265
Quadratic Mean3.04353846515678
Winsorized Mean ( 1 / 24 )2.866388888888890.12065910306806823.7560931252062
Winsorized Mean ( 2 / 24 )2.870.11921856941200424.073430960924
Winsorized Mean ( 3 / 24 )2.875833333333330.11776241798299624.4206376073951
Winsorized Mean ( 4 / 24 )2.881944444444440.1158476683953924.8770172448212
Winsorized Mean ( 5 / 24 )2.882638888888890.11439932823700525.1980403496498
Winsorized Mean ( 6 / 24 )2.893472222222220.11203362026869225.8268206925989
Winsorized Mean ( 7 / 24 )2.882777777777780.10881496804226926.4924746075188
Winsorized Mean ( 8 / 24 )2.937222222222220.099696766817477429.4615594465528
Winsorized Mean ( 9 / 24 )2.938472222222220.099143763821156629.6384977629342
Winsorized Mean ( 10 / 24 )2.946805555555560.097629538839561230.1835447609577
Winsorized Mean ( 11 / 24 )2.946805555555560.096721658793108530.4668632892131
Winsorized Mean ( 12 / 24 )2.935138888888890.094291276366006731.1284246221854
Winsorized Mean ( 13 / 24 )2.938750.093838742557918731.3170223715025
Winsorized Mean ( 14 / 24 )2.930972222222220.092020265450649931.8513776054481
Winsorized Mean ( 15 / 24 )2.926805555555560.090177148382126832.4561777353302
Winsorized Mean ( 16 / 24 )2.920138888888890.087275868331955633.4587205455474
Winsorized Mean ( 17 / 24 )2.915416666666670.085899215223751333.9399685907788
Winsorized Mean ( 18 / 24 )2.915416666666670.085216041726928634.2120639211218
Winsorized Mean ( 19 / 24 )2.918055555555560.084184070363746234.6627995409
Winsorized Mean ( 20 / 24 )2.898611111111110.08124840327203335.6759147795937
Winsorized Mean ( 21 / 24 )2.884027777777780.079086791858118336.4666173708465
Winsorized Mean ( 22 / 24 )2.884027777777780.076649482591995337.6261871607071
Winsorized Mean ( 23 / 24 )2.880833333333330.075339541789955838.2379991288638
Winsorized Mean ( 24 / 24 )2.854166666666670.071489777878785339.9241227397021
Trimmed Mean ( 1 / 24 )2.873714285714290.11816701718962724.3190896585189
Trimmed Mean ( 2 / 24 )2.881470588235290.1151927545769225.0143387821427
Trimmed Mean ( 3 / 24 )2.887727272727270.11255349320380825.6564873335230
Trimmed Mean ( 4 / 24 )2.89218750.11004473944746126.2819241930309
Trimmed Mean ( 5 / 24 )2.895161290322580.10771354325282626.8783404843255
Trimmed Mean ( 6 / 24 )2.898166666666670.10532743985157627.5157800355792
Trimmed Mean ( 7 / 24 )2.899137931034480.10307354239145328.1268874996468
Trimmed Mean ( 8 / 24 )2.902142857142860.10111511836224128.7013742766541
Trimmed Mean ( 9 / 24 )2.896296296296300.10077071839911328.741447340141
Trimmed Mean ( 10 / 24 )2.889807692307690.10032469548285028.8045498508558
Trimmed Mean ( 11 / 24 )2.88160.099923382893993328.8380949137504
Trimmed Mean ( 12 / 24 )2.872708333333330.09943802178154728.8894356692284
Trimmed Mean ( 13 / 24 )2.864565217391300.09915620162622728.8894206354272
Trimmed Mean ( 14 / 24 )2.855227272727270.098671668499729328.9366473288643
Trimmed Mean ( 15 / 24 )2.845952380952380.098217008021962528.9761665343745
Trimmed Mean ( 16 / 24 )2.836250.097771113858481829.0090793494008
Trimmed Mean ( 17 / 24 )2.826315789473680.097534631886112928.9775614550312
Trimmed Mean ( 18 / 24 )2.815833333333330.097205701544191428.9677795499805
Trimmed Mean ( 19 / 24 )2.804117647058820.09655576431970129.0414318276664
Trimmed Mean ( 20 / 24 )2.7906250.09551002470185229.2181371401728
Trimmed Mean ( 21 / 24 )2.777666666666670.094487952565798729.3970457739824
Trimmed Mean ( 22 / 24 )2.764642857142860.093230501944478229.6538450344212
Trimmed Mean ( 23 / 24 )2.749615384615380.091585152927133330.0225014288399
Trimmed Mean ( 24 / 24 )2.73250.088941541621938230.7224267779726
Median2.67
Midrange2.625
Midmean - Weighted Average at Xnp2.79864864864865
Midmean - Weighted Average at X(n+1)p2.81583333333333
Midmean - Empirical Distribution Function2.79864864864865
Midmean - Empirical Distribution Function - Averaging2.81583333333333
Midmean - Empirical Distribution Function - Interpolation2.81583333333333
Midmean - Closest Observation2.79864864864865
Midmean - True Basic - Statistics Graphics Toolkit2.81583333333333
Midmean - MS Excel (old versions)2.82631578947368
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')