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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 computationThu, 15 Oct 2015 10:31:57 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/15/t14449015906wn8lz8kdxwomcd.htm/, Retrieved Tue, 14 May 2024 20:33:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282416, Retrieved Tue, 14 May 2024 20:33:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2015-10-10 10:31:19] [40c71f3c51e02adf0ccb0527bfc20d8f]
- R  D    [Central Tendency] [] [2015-10-15 09:31:57] [4b96c7bb02a36edde4d8c72e28fc1c90] [Current]
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Dataseries X:
103.4
103.49
103.51
103.27
103.35
103.34
103.07
103.08
103.1
103.13
103.13
103.18
103.2
103.21
103
102.46
102.52
102.55
102.78
102.81
102.81
102.68
102.72
102.73
102.87
102.93
103.2
102.62
102.18
101.19
100.91
100.72
100.86
100.89
100.47
100.45
100.64
100.63
100.66
100.38
99.68
99.71
99.63
99.63
99.71
99.77
99.76
99.79
98.13
98.13
97.87
97.72
97.72
97.6
97.31
97.31
97.44
96.94
96.94
96.94




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=282416&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=282416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282416&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 Mean101.0308333333330.281185172482664359.303559434885
Geometric Mean101.007556451641
Harmonic Mean100.98409188542
Quadratic Mean101.053916920622
Winsorized Mean ( 1 / 20 )101.03050.281135552985641359.365789659339
Winsorized Mean ( 2 / 20 )101.02750.280698244093703359.914969636486
Winsorized Mean ( 3 / 20 )101.04350.275936394967747366.184025894121
Winsorized Mean ( 4 / 20 )101.0428333333330.275842120125634366.306760139868
Winsorized Mean ( 5 / 20 )101.0478333333330.272569598396205370.723051755945
Winsorized Mean ( 6 / 20 )101.0578333333330.26820370153652376.795073126806
Winsorized Mean ( 7 / 20 )101.0706666666670.265015069038207381.377055400934
Winsorized Mean ( 8 / 20 )101.0706666666670.265015069038207381.377055400934
Winsorized Mean ( 9 / 20 )101.0901666666670.259831919994127389.059845568442
Winsorized Mean ( 10 / 20 )101.1251666666670.249738562924664404.924115372491
Winsorized Mean ( 11 / 20 )101.1251666666670.249738562924664404.924115372491
Winsorized Mean ( 12 / 20 )101.4191666666670.194080956325669522.561144517882
Winsorized Mean ( 13 / 20 )101.4148333333330.193446804563572524.251788816731
Winsorized Mean ( 14 / 20 )101.4241666666670.191292701989059530.204056987327
Winsorized Mean ( 15 / 20 )101.4141666666670.18760598385688540.569999856898
Winsorized Mean ( 16 / 20 )101.39550.18495615986889548.213696001669
Winsorized Mean ( 17 / 20 )101.3926666666670.180400193334649562.043004458312
Winsorized Mean ( 18 / 20 )101.3776666666670.177459212575905571.273055904629
Winsorized Mean ( 19 / 20 )101.3840.176488216024414574.451950865521
Winsorized Mean ( 20 / 20 )101.5706666666670.146353003066529694.011496439843
Trimmed Mean ( 1 / 20 )101.0586206896550.278795096593909362.483493878862
Trimmed Mean ( 2 / 20 )101.088750.27565683806162366.719544165282
Trimmed Mean ( 3 / 20 )101.1227777777780.271794566318002372.055921307357
Trimmed Mean ( 4 / 20 )101.1532692307690.268982457943423376.058981705213
Trimmed Mean ( 5 / 20 )101.18640.265167603524985381.594126337027
Trimmed Mean ( 6 / 20 )101.2210416666670.261130289954758387.62658167386
Trimmed Mean ( 7 / 20 )101.256521739130.256987982085462394.012672956268
Trimmed Mean ( 8 / 20 )101.2927272727270.252227782980018401.592267417867
Trimmed Mean ( 9 / 20 )101.3323809523810.245634074727244412.533892396249
Trimmed Mean ( 10 / 20 )101.372750.23809042332586425.774160018428
Trimmed Mean ( 11 / 20 )101.4118421052630.230606799054166439.760850595924
Trimmed Mean ( 12 / 20 )101.4552777777780.219992599482711461.175866898882
Trimmed Mean ( 13 / 20 )101.4605882352940.221287329520116458.501571035818
Trimmed Mean ( 14 / 20 )101.46718750.222175930350742456.697479964715
Trimmed Mean ( 15 / 20 )101.4733333333330.222842314917988455.35935744824
Trimmed Mean ( 16 / 20 )101.4817857142860.223491446974484454.07458356056
Trimmed Mean ( 17 / 20 )101.4942307692310.223677083917469453.753370670191
Trimmed Mean ( 18 / 20 )101.5091666666670.223666674766194453.841265234428
Trimmed Mean ( 19 / 20 )101.5290909090910.222584104529363456.138101702125
Trimmed Mean ( 20 / 20 )101.5520.218929933516351463.856167902301
Median101.05
Midrange100.225
Midmean - Weighted Average at Xnp101.415483870968
Midmean - Weighted Average at X(n+1)p101.473333333333
Midmean - Empirical Distribution Function101.415483870968
Midmean - Empirical Distribution Function - Averaging101.473333333333
Midmean - Empirical Distribution Function - Interpolation101.473333333333
Midmean - Closest Observation101.415483870968
Midmean - True Basic - Statistics Graphics Toolkit101.473333333333
Midmean - MS Excel (old versions)101.4671875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.030833333333 & 0.281185172482664 & 359.303559434885 \tabularnewline
Geometric Mean & 101.007556451641 &  &  \tabularnewline
Harmonic Mean & 100.98409188542 &  &  \tabularnewline
Quadratic Mean & 101.053916920622 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.0305 & 0.281135552985641 & 359.365789659339 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.0275 & 0.280698244093703 & 359.914969636486 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.0435 & 0.275936394967747 & 366.184025894121 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.042833333333 & 0.275842120125634 & 366.306760139868 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.047833333333 & 0.272569598396205 & 370.723051755945 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.057833333333 & 0.26820370153652 & 376.795073126806 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.070666666667 & 0.265015069038207 & 381.377055400934 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.070666666667 & 0.265015069038207 & 381.377055400934 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.090166666667 & 0.259831919994127 & 389.059845568442 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.125166666667 & 0.249738562924664 & 404.924115372491 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.125166666667 & 0.249738562924664 & 404.924115372491 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.419166666667 & 0.194080956325669 & 522.561144517882 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.414833333333 & 0.193446804563572 & 524.251788816731 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.424166666667 & 0.191292701989059 & 530.204056987327 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.414166666667 & 0.18760598385688 & 540.569999856898 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.3955 & 0.18495615986889 & 548.213696001669 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.392666666667 & 0.180400193334649 & 562.043004458312 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.377666666667 & 0.177459212575905 & 571.273055904629 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.384 & 0.176488216024414 & 574.451950865521 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.570666666667 & 0.146353003066529 & 694.011496439843 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.058620689655 & 0.278795096593909 & 362.483493878862 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.08875 & 0.27565683806162 & 366.719544165282 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.122777777778 & 0.271794566318002 & 372.055921307357 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.153269230769 & 0.268982457943423 & 376.058981705213 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.1864 & 0.265167603524985 & 381.594126337027 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.221041666667 & 0.261130289954758 & 387.62658167386 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.25652173913 & 0.256987982085462 & 394.012672956268 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.292727272727 & 0.252227782980018 & 401.592267417867 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.332380952381 & 0.245634074727244 & 412.533892396249 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.37275 & 0.23809042332586 & 425.774160018428 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.411842105263 & 0.230606799054166 & 439.760850595924 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.455277777778 & 0.219992599482711 & 461.175866898882 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.460588235294 & 0.221287329520116 & 458.501571035818 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.4671875 & 0.222175930350742 & 456.697479964715 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.473333333333 & 0.222842314917988 & 455.35935744824 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.481785714286 & 0.223491446974484 & 454.07458356056 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.494230769231 & 0.223677083917469 & 453.753370670191 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.509166666667 & 0.223666674766194 & 453.841265234428 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.529090909091 & 0.222584104529363 & 456.138101702125 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.552 & 0.218929933516351 & 463.856167902301 \tabularnewline
Median & 101.05 &  &  \tabularnewline
Midrange & 100.225 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.415483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.473333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.415483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.473333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.473333333333 &  &  \tabularnewline
Midmean - Closest Observation & 101.415483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.473333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.4671875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282416&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]101.030833333333[/C][C]0.281185172482664[/C][C]359.303559434885[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.007556451641[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.98409188542[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.053916920622[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.0305[/C][C]0.281135552985641[/C][C]359.365789659339[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.0275[/C][C]0.280698244093703[/C][C]359.914969636486[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.0435[/C][C]0.275936394967747[/C][C]366.184025894121[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.042833333333[/C][C]0.275842120125634[/C][C]366.306760139868[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.047833333333[/C][C]0.272569598396205[/C][C]370.723051755945[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.057833333333[/C][C]0.26820370153652[/C][C]376.795073126806[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.070666666667[/C][C]0.265015069038207[/C][C]381.377055400934[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.070666666667[/C][C]0.265015069038207[/C][C]381.377055400934[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.090166666667[/C][C]0.259831919994127[/C][C]389.059845568442[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.125166666667[/C][C]0.249738562924664[/C][C]404.924115372491[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.125166666667[/C][C]0.249738562924664[/C][C]404.924115372491[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.419166666667[/C][C]0.194080956325669[/C][C]522.561144517882[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.414833333333[/C][C]0.193446804563572[/C][C]524.251788816731[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.424166666667[/C][C]0.191292701989059[/C][C]530.204056987327[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.414166666667[/C][C]0.18760598385688[/C][C]540.569999856898[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.3955[/C][C]0.18495615986889[/C][C]548.213696001669[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.392666666667[/C][C]0.180400193334649[/C][C]562.043004458312[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.377666666667[/C][C]0.177459212575905[/C][C]571.273055904629[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.384[/C][C]0.176488216024414[/C][C]574.451950865521[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.570666666667[/C][C]0.146353003066529[/C][C]694.011496439843[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.058620689655[/C][C]0.278795096593909[/C][C]362.483493878862[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.08875[/C][C]0.27565683806162[/C][C]366.719544165282[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.122777777778[/C][C]0.271794566318002[/C][C]372.055921307357[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.153269230769[/C][C]0.268982457943423[/C][C]376.058981705213[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.1864[/C][C]0.265167603524985[/C][C]381.594126337027[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.221041666667[/C][C]0.261130289954758[/C][C]387.62658167386[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.25652173913[/C][C]0.256987982085462[/C][C]394.012672956268[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.292727272727[/C][C]0.252227782980018[/C][C]401.592267417867[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.332380952381[/C][C]0.245634074727244[/C][C]412.533892396249[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.37275[/C][C]0.23809042332586[/C][C]425.774160018428[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.411842105263[/C][C]0.230606799054166[/C][C]439.760850595924[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.455277777778[/C][C]0.219992599482711[/C][C]461.175866898882[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.460588235294[/C][C]0.221287329520116[/C][C]458.501571035818[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.4671875[/C][C]0.222175930350742[/C][C]456.697479964715[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.473333333333[/C][C]0.222842314917988[/C][C]455.35935744824[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.481785714286[/C][C]0.223491446974484[/C][C]454.07458356056[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.494230769231[/C][C]0.223677083917469[/C][C]453.753370670191[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.509166666667[/C][C]0.223666674766194[/C][C]453.841265234428[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.529090909091[/C][C]0.222584104529363[/C][C]456.138101702125[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.552[/C][C]0.218929933516351[/C][C]463.856167902301[/C][/ROW]
[ROW][C]Median[/C][C]101.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.415483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.473333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.415483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.473333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.473333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.415483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.473333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.4671875[/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=282416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282416&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 Mean101.0308333333330.281185172482664359.303559434885
Geometric Mean101.007556451641
Harmonic Mean100.98409188542
Quadratic Mean101.053916920622
Winsorized Mean ( 1 / 20 )101.03050.281135552985641359.365789659339
Winsorized Mean ( 2 / 20 )101.02750.280698244093703359.914969636486
Winsorized Mean ( 3 / 20 )101.04350.275936394967747366.184025894121
Winsorized Mean ( 4 / 20 )101.0428333333330.275842120125634366.306760139868
Winsorized Mean ( 5 / 20 )101.0478333333330.272569598396205370.723051755945
Winsorized Mean ( 6 / 20 )101.0578333333330.26820370153652376.795073126806
Winsorized Mean ( 7 / 20 )101.0706666666670.265015069038207381.377055400934
Winsorized Mean ( 8 / 20 )101.0706666666670.265015069038207381.377055400934
Winsorized Mean ( 9 / 20 )101.0901666666670.259831919994127389.059845568442
Winsorized Mean ( 10 / 20 )101.1251666666670.249738562924664404.924115372491
Winsorized Mean ( 11 / 20 )101.1251666666670.249738562924664404.924115372491
Winsorized Mean ( 12 / 20 )101.4191666666670.194080956325669522.561144517882
Winsorized Mean ( 13 / 20 )101.4148333333330.193446804563572524.251788816731
Winsorized Mean ( 14 / 20 )101.4241666666670.191292701989059530.204056987327
Winsorized Mean ( 15 / 20 )101.4141666666670.18760598385688540.569999856898
Winsorized Mean ( 16 / 20 )101.39550.18495615986889548.213696001669
Winsorized Mean ( 17 / 20 )101.3926666666670.180400193334649562.043004458312
Winsorized Mean ( 18 / 20 )101.3776666666670.177459212575905571.273055904629
Winsorized Mean ( 19 / 20 )101.3840.176488216024414574.451950865521
Winsorized Mean ( 20 / 20 )101.5706666666670.146353003066529694.011496439843
Trimmed Mean ( 1 / 20 )101.0586206896550.278795096593909362.483493878862
Trimmed Mean ( 2 / 20 )101.088750.27565683806162366.719544165282
Trimmed Mean ( 3 / 20 )101.1227777777780.271794566318002372.055921307357
Trimmed Mean ( 4 / 20 )101.1532692307690.268982457943423376.058981705213
Trimmed Mean ( 5 / 20 )101.18640.265167603524985381.594126337027
Trimmed Mean ( 6 / 20 )101.2210416666670.261130289954758387.62658167386
Trimmed Mean ( 7 / 20 )101.256521739130.256987982085462394.012672956268
Trimmed Mean ( 8 / 20 )101.2927272727270.252227782980018401.592267417867
Trimmed Mean ( 9 / 20 )101.3323809523810.245634074727244412.533892396249
Trimmed Mean ( 10 / 20 )101.372750.23809042332586425.774160018428
Trimmed Mean ( 11 / 20 )101.4118421052630.230606799054166439.760850595924
Trimmed Mean ( 12 / 20 )101.4552777777780.219992599482711461.175866898882
Trimmed Mean ( 13 / 20 )101.4605882352940.221287329520116458.501571035818
Trimmed Mean ( 14 / 20 )101.46718750.222175930350742456.697479964715
Trimmed Mean ( 15 / 20 )101.4733333333330.222842314917988455.35935744824
Trimmed Mean ( 16 / 20 )101.4817857142860.223491446974484454.07458356056
Trimmed Mean ( 17 / 20 )101.4942307692310.223677083917469453.753370670191
Trimmed Mean ( 18 / 20 )101.5091666666670.223666674766194453.841265234428
Trimmed Mean ( 19 / 20 )101.5290909090910.222584104529363456.138101702125
Trimmed Mean ( 20 / 20 )101.5520.218929933516351463.856167902301
Median101.05
Midrange100.225
Midmean - Weighted Average at Xnp101.415483870968
Midmean - Weighted Average at X(n+1)p101.473333333333
Midmean - Empirical Distribution Function101.415483870968
Midmean - Empirical Distribution Function - Averaging101.473333333333
Midmean - Empirical Distribution Function - Interpolation101.473333333333
Midmean - Closest Observation101.415483870968
Midmean - True Basic - Statistics Graphics Toolkit101.473333333333
Midmean - MS Excel (old versions)101.4671875
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')