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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 05 Mar 2012 06:25:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/05/t1330946728b8yxka64v5in18i.htm/, Retrieved Thu, 02 May 2024 14:27:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163476, Retrieved Thu, 02 May 2024 14:27:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-05 11:25:09] [a77d50c199526ea1c5b38e78affe5e1d] [Current]
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Dataseries X:
4
4
4
4
4
4
4
4
4,06
4,07
4,07
4,07
4,07
4,07
4,3
4,44
4,52
4,52
4,52
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,61
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,66
4,7
4,72
4,73
4,73
4,74
4,74
4,74
4,76
4,88
4,88
4,88
4,88
4,89
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163476&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163476&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.54250.0418496265567311108.543381954489
Geometric Mean4.53079599586528
Harmonic Mean4.51877382304059
Quadratic Mean4.5538597182317
Winsorized Mean ( 1 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 2 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 3 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 4 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 5 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 6 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 7 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 8 / 20 )4.539833333333330.038368928450416118.320566059074
Winsorized Mean ( 9 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 10 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 11 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 12 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 13 / 20 )4.513833333333330.0342358813876311131.845103744404
Winsorized Mean ( 14 / 20 )4.562833333333330.0222671144953106204.913543436185
Winsorized Mean ( 15 / 20 )4.597833333333330.0156931948738426292.982618918281
Winsorized Mean ( 16 / 20 )4.619166666666670.0123834491025757373.011317638952
Winsorized Mean ( 17 / 20 )4.616333333333330.0119200886003861387.273407781868
Winsorized Mean ( 18 / 20 )4.616333333333330.0119200886003861387.273407781868
Winsorized Mean ( 19 / 20 )4.616333333333330.0109826948281094420.327925484932
Winsorized Mean ( 20 / 20 )4.609666666666670.00993472101936335463.995582531423
Trimmed Mean ( 1 / 20 )4.544482758620690.0416051008537099109.228980710798
Trimmed Mean ( 2 / 20 )4.546607142857140.041265907429202110.17829065452
Trimmed Mean ( 3 / 20 )4.548888888888890.0408099913317734111.465078536963
Trimmed Mean ( 4 / 20 )4.551346153846150.0402087584597479113.19290443654
Trimmed Mean ( 5 / 20 )4.5540.0394244304243665115.512131715805
Trimmed Mean ( 6 / 20 )4.5568750.0384059090759528118.65036161462
Trimmed Mean ( 7 / 20 )4.560.0370819695238551122.970814618315
Trimmed Mean ( 8 / 20 )4.563409090909090.0353492738379267129.094846808789
Trimmed Mean ( 9 / 20 )4.567619047619050.0341085401545732133.914234585224
Trimmed Mean ( 10 / 20 )4.572250.0325940208060879140.278796138769
Trimmed Mean ( 11 / 20 )4.577368421052630.0305163813726424149.997090584147
Trimmed Mean ( 12 / 20 )4.583055555555560.0275905995161005166.109313894434
Trimmed Mean ( 13 / 20 )4.589411764705880.0232476444534259197.414055170203
Trimmed Mean ( 14 / 20 )4.60031250.0174970295578071262.91962786034
Trimmed Mean ( 15 / 20 )4.605666666666670.0148995358512396309.114774624572
Trimmed Mean ( 16 / 20 )4.606785714285710.0139732697524129329.68559227093
Trimmed Mean ( 17 / 20 )4.6050.0137141140099141335.785454070965
Trimmed Mean ( 18 / 20 )4.603333333333330.0134146073673908343.158260786927
Trimmed Mean ( 19 / 20 )4.601363636363640.0128476833450896358.147341646793
Trimmed Mean ( 20 / 20 )4.5990.0122452998501895375.572673292179
Median4.63
Midrange4.485
Midmean - Weighted Average at Xnp4.6003125
Midmean - Weighted Average at X(n+1)p4.61
Midmean - Empirical Distribution Function4.6003125
Midmean - Empirical Distribution Function - Averaging4.61
Midmean - Empirical Distribution Function - Interpolation4.61
Midmean - Closest Observation4.6003125
Midmean - True Basic - Statistics Graphics Toolkit4.61
Midmean - MS Excel (old versions)4.6003125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Geometric Mean & 4.53079599586528 &  &  \tabularnewline
Harmonic Mean & 4.51877382304059 &  &  \tabularnewline
Quadratic Mean & 4.5538597182317 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4.5425 & 0.0418496265567311 & 108.543381954489 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4.53983333333333 & 0.038368928450416 & 118.320566059074 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4.53983333333333 & 0.0378216836639897 & 120.032555231161 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4.53983333333333 & 0.0378216836639897 & 120.032555231161 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4.53983333333333 & 0.0378216836639897 & 120.032555231161 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4.53983333333333 & 0.0378216836639897 & 120.032555231161 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4.51383333333333 & 0.0342358813876311 & 131.845103744404 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4.56283333333333 & 0.0222671144953106 & 204.913543436185 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4.59783333333333 & 0.0156931948738426 & 292.982618918281 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4.61916666666667 & 0.0123834491025757 & 373.011317638952 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4.61633333333333 & 0.0119200886003861 & 387.273407781868 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4.61633333333333 & 0.0119200886003861 & 387.273407781868 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4.61633333333333 & 0.0109826948281094 & 420.327925484932 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4.60966666666667 & 0.00993472101936335 & 463.995582531423 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4.54448275862069 & 0.0416051008537099 & 109.228980710798 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4.54660714285714 & 0.041265907429202 & 110.17829065452 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4.54888888888889 & 0.0408099913317734 & 111.465078536963 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4.55134615384615 & 0.0402087584597479 & 113.19290443654 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4.554 & 0.0394244304243665 & 115.512131715805 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4.556875 & 0.0384059090759528 & 118.65036161462 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4.56 & 0.0370819695238551 & 122.970814618315 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4.56340909090909 & 0.0353492738379267 & 129.094846808789 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4.56761904761905 & 0.0341085401545732 & 133.914234585224 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4.57225 & 0.0325940208060879 & 140.278796138769 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4.57736842105263 & 0.0305163813726424 & 149.997090584147 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4.58305555555556 & 0.0275905995161005 & 166.109313894434 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4.58941176470588 & 0.0232476444534259 & 197.414055170203 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4.6003125 & 0.0174970295578071 & 262.91962786034 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4.60566666666667 & 0.0148995358512396 & 309.114774624572 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4.60678571428571 & 0.0139732697524129 & 329.68559227093 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4.605 & 0.0137141140099141 & 335.785454070965 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4.60333333333333 & 0.0134146073673908 & 343.158260786927 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4.60136363636364 & 0.0128476833450896 & 358.147341646793 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4.599 & 0.0122452998501895 & 375.572673292179 \tabularnewline
Median & 4.63 &  &  \tabularnewline
Midrange & 4.485 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.6003125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.61 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.6003125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.61 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.61 &  &  \tabularnewline
Midmean - Closest Observation & 4.6003125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.61 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.6003125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163476&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]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.53079599586528[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.51877382304059[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.5538597182317[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4.5425[/C][C]0.0418496265567311[/C][C]108.543381954489[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4.53983333333333[/C][C]0.038368928450416[/C][C]118.320566059074[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4.53983333333333[/C][C]0.0378216836639897[/C][C]120.032555231161[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4.53983333333333[/C][C]0.0378216836639897[/C][C]120.032555231161[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4.53983333333333[/C][C]0.0378216836639897[/C][C]120.032555231161[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4.53983333333333[/C][C]0.0378216836639897[/C][C]120.032555231161[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4.51383333333333[/C][C]0.0342358813876311[/C][C]131.845103744404[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4.56283333333333[/C][C]0.0222671144953106[/C][C]204.913543436185[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4.59783333333333[/C][C]0.0156931948738426[/C][C]292.982618918281[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4.61916666666667[/C][C]0.0123834491025757[/C][C]373.011317638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4.61633333333333[/C][C]0.0119200886003861[/C][C]387.273407781868[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4.61633333333333[/C][C]0.0119200886003861[/C][C]387.273407781868[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4.61633333333333[/C][C]0.0109826948281094[/C][C]420.327925484932[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4.60966666666667[/C][C]0.00993472101936335[/C][C]463.995582531423[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4.54448275862069[/C][C]0.0416051008537099[/C][C]109.228980710798[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4.54660714285714[/C][C]0.041265907429202[/C][C]110.17829065452[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4.54888888888889[/C][C]0.0408099913317734[/C][C]111.465078536963[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4.55134615384615[/C][C]0.0402087584597479[/C][C]113.19290443654[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4.554[/C][C]0.0394244304243665[/C][C]115.512131715805[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4.556875[/C][C]0.0384059090759528[/C][C]118.65036161462[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4.56[/C][C]0.0370819695238551[/C][C]122.970814618315[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4.56340909090909[/C][C]0.0353492738379267[/C][C]129.094846808789[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4.56761904761905[/C][C]0.0341085401545732[/C][C]133.914234585224[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4.57225[/C][C]0.0325940208060879[/C][C]140.278796138769[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4.57736842105263[/C][C]0.0305163813726424[/C][C]149.997090584147[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4.58305555555556[/C][C]0.0275905995161005[/C][C]166.109313894434[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4.58941176470588[/C][C]0.0232476444534259[/C][C]197.414055170203[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4.6003125[/C][C]0.0174970295578071[/C][C]262.91962786034[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4.60566666666667[/C][C]0.0148995358512396[/C][C]309.114774624572[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4.60678571428571[/C][C]0.0139732697524129[/C][C]329.68559227093[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4.605[/C][C]0.0137141140099141[/C][C]335.785454070965[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4.60333333333333[/C][C]0.0134146073673908[/C][C]343.158260786927[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4.60136363636364[/C][C]0.0128476833450896[/C][C]358.147341646793[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4.599[/C][C]0.0122452998501895[/C][C]375.572673292179[/C][/ROW]
[ROW][C]Median[/C][C]4.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.6003125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.6003125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.6003125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.6003125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163476&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 Mean4.54250.0418496265567311108.543381954489
Geometric Mean4.53079599586528
Harmonic Mean4.51877382304059
Quadratic Mean4.5538597182317
Winsorized Mean ( 1 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 2 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 3 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 4 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 5 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 6 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 7 / 20 )4.54250.0418496265567311108.543381954489
Winsorized Mean ( 8 / 20 )4.539833333333330.038368928450416118.320566059074
Winsorized Mean ( 9 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 10 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 11 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 12 / 20 )4.539833333333330.0378216836639897120.032555231161
Winsorized Mean ( 13 / 20 )4.513833333333330.0342358813876311131.845103744404
Winsorized Mean ( 14 / 20 )4.562833333333330.0222671144953106204.913543436185
Winsorized Mean ( 15 / 20 )4.597833333333330.0156931948738426292.982618918281
Winsorized Mean ( 16 / 20 )4.619166666666670.0123834491025757373.011317638952
Winsorized Mean ( 17 / 20 )4.616333333333330.0119200886003861387.273407781868
Winsorized Mean ( 18 / 20 )4.616333333333330.0119200886003861387.273407781868
Winsorized Mean ( 19 / 20 )4.616333333333330.0109826948281094420.327925484932
Winsorized Mean ( 20 / 20 )4.609666666666670.00993472101936335463.995582531423
Trimmed Mean ( 1 / 20 )4.544482758620690.0416051008537099109.228980710798
Trimmed Mean ( 2 / 20 )4.546607142857140.041265907429202110.17829065452
Trimmed Mean ( 3 / 20 )4.548888888888890.0408099913317734111.465078536963
Trimmed Mean ( 4 / 20 )4.551346153846150.0402087584597479113.19290443654
Trimmed Mean ( 5 / 20 )4.5540.0394244304243665115.512131715805
Trimmed Mean ( 6 / 20 )4.5568750.0384059090759528118.65036161462
Trimmed Mean ( 7 / 20 )4.560.0370819695238551122.970814618315
Trimmed Mean ( 8 / 20 )4.563409090909090.0353492738379267129.094846808789
Trimmed Mean ( 9 / 20 )4.567619047619050.0341085401545732133.914234585224
Trimmed Mean ( 10 / 20 )4.572250.0325940208060879140.278796138769
Trimmed Mean ( 11 / 20 )4.577368421052630.0305163813726424149.997090584147
Trimmed Mean ( 12 / 20 )4.583055555555560.0275905995161005166.109313894434
Trimmed Mean ( 13 / 20 )4.589411764705880.0232476444534259197.414055170203
Trimmed Mean ( 14 / 20 )4.60031250.0174970295578071262.91962786034
Trimmed Mean ( 15 / 20 )4.605666666666670.0148995358512396309.114774624572
Trimmed Mean ( 16 / 20 )4.606785714285710.0139732697524129329.68559227093
Trimmed Mean ( 17 / 20 )4.6050.0137141140099141335.785454070965
Trimmed Mean ( 18 / 20 )4.603333333333330.0134146073673908343.158260786927
Trimmed Mean ( 19 / 20 )4.601363636363640.0128476833450896358.147341646793
Trimmed Mean ( 20 / 20 )4.5990.0122452998501895375.572673292179
Median4.63
Midrange4.485
Midmean - Weighted Average at Xnp4.6003125
Midmean - Weighted Average at X(n+1)p4.61
Midmean - Empirical Distribution Function4.6003125
Midmean - Empirical Distribution Function - Averaging4.61
Midmean - Empirical Distribution Function - Interpolation4.61
Midmean - Closest Observation4.6003125
Midmean - True Basic - Statistics Graphics Toolkit4.61
Midmean - MS Excel (old versions)4.6003125
Number of observations60



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')