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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Oct 2009 07:45:58 -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/22/t1256219224j6zulqsp0ctousi.htm/, Retrieved Fri, 03 May 2024 01:52:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49736, Retrieved Fri, 03 May 2024 01:52:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJSSHWWS3P2
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
-   PD      [Univariate Data Series] [verschil graf] [2009-10-20 19:39:37] [134dc66689e3d457a82860db6471d419]
- RM D          [Central Tendency] [Verbetering] [2009-10-22 13:45:58] [c8fd62404619100d8e91184019148412] [Current]
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Dataseries X:
103.8
103.33
106.88
112.85
113.04
113.22
112.63
116.65
110.54
111.37
107.68
103.76
104.82
108.31
107.23
109.6
105.95
105.93
106.25
106.38
102.36
103.32
112.58
105.68
103.92
106.46
103.23
103.58
104.34
106.28
107.7
107.67
106.71
114.19
110.93
113.44
110.85
111.71
116.32
118.49
121.2
123.62
122.22
119.88
128.15
133.29
136.09
131.24
135.45
135.75
133.07
130.17
128.96
127.5
121.48
121.66
122.46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49736&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49736&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49736&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean114.2485964912281.3322093187952885.7587429237795
Geometric Mean113.831173805273
Harmonic Mean113.431563809174
Quadratic Mean114.682734418413
Winsorized Mean ( 1 / 19 )114.2578947368421.3281264654856686.0293787572864
Winsorized Mean ( 2 / 19 )114.2505263157891.3246346358948686.2505956131872
Winsorized Mean ( 3 / 19 )114.1373684210531.2932651728911988.255193763465
Winsorized Mean ( 4 / 19 )114.1394736842111.2866008776468788.7139715721057
Winsorized Mean ( 5 / 19 )113.9947368421051.2432937676029591.6876926535913
Winsorized Mean ( 6 / 19 )113.8863157894741.2152429605253693.7148533164425
Winsorized Mean ( 7 / 19 )113.7524561403511.1781389651041296.5526644221448
Winsorized Mean ( 8 / 19 )113.6977192982461.1435031974169399.4292972289699
Winsorized Mean ( 9 / 19 )113.6708771929821.10956064711124102.446745465358
Winsorized Mean ( 10 / 19 )113.1410526315790.944300064488317119.814725092586
Winsorized Mean ( 11 / 19 )112.9654385964910.894074656062062126.348999863217
Winsorized Mean ( 12 / 19 )112.9191228070180.883944696012075127.744556097744
Winsorized Mean ( 13 / 19 )112.8598245614040.850578805262427132.685912067352
Winsorized Mean ( 14 / 19 )112.8229824561400.841410528220034134.087913892416
Winsorized Mean ( 15 / 19 )112.7756140350880.82426693403463136.819286785013
Winsorized Mean ( 16 / 19 )112.4275438596490.754591637172774148.991240190364
Winsorized Mean ( 17 / 19 )112.0875438596490.672113678655963166.768728890911
Winsorized Mean ( 18 / 19 )111.5601754385970.568200479729353196.339460135154
Winsorized Mean ( 19 / 19 )111.5668421052630.533602756855444209.082207076166
Trimmed Mean ( 1 / 19 )114.0676363636361.3033131043829587.521284010753
Trimmed Mean ( 2 / 19 )113.8630188679251.2714228280209989.5555879275472
Trimmed Mean ( 3 / 19 )113.6464705882351.2328149781994492.184531010662
Trimmed Mean ( 4 / 19 )113.4561224489801.1990465960435294.6219461556787
Trimmed Mean ( 5 / 19 )113.2489361702131.1576158245414397.829464464236
Trimmed Mean ( 6 / 19 )113.061.11959502959911100.982942055828
Trimmed Mean ( 7 / 19 )112.8774418604651.07883684406144104.628834732341
Trimmed Mean ( 8 / 19 )112.7036585365851.03648701685523108.736199010515
Trimmed Mean ( 9 / 19 )112.5220512820510.989838464682804113.677186022579
Trimmed Mean ( 10 / 19 )112.3254054054050.935993201076616120.006646710900
Trimmed Mean ( 11 / 19 )112.1925714285710.914218253813739122.719679858229
Trimmed Mean ( 12 / 19 )112.0712121212120.896896031859382124.954518851950
Trimmed Mean ( 13 / 19 )111.9412903225810.872815089845148128.253156510437
Trimmed Mean ( 14 / 19 )111.8024137931030.845938085864656132.163825770804
Trimmed Mean ( 15 / 19 )111.6485185185190.806211764031383138.485350251193
Trimmed Mean ( 16 / 19 )111.47720.748957390866352148.843180345746
Trimmed Mean ( 17 / 19 )111.330.689108664136609161.556523367017
Trimmed Mean ( 18 / 19 )111.2090476190480.631263624939957176.168946261754
Trimmed Mean ( 19 / 19 )111.1505263157890.589770732381992188.463957624465
Median111.37
Midrange119.225
Midmean - Weighted Average at Xnp111.456785714286
Midmean - Weighted Average at X(n+1)p111.802413793103
Midmean - Empirical Distribution Function111.802413793103
Midmean - Empirical Distribution Function - Averaging111.802413793103
Midmean - Empirical Distribution Function - Interpolation111.802413793103
Midmean - Closest Observation111.617333333333
Midmean - True Basic - Statistics Graphics Toolkit111.802413793103
Midmean - MS Excel (old versions)111.802413793103
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 114.248596491228 & 1.33220931879528 & 85.7587429237795 \tabularnewline
Geometric Mean & 113.831173805273 &  &  \tabularnewline
Harmonic Mean & 113.431563809174 &  &  \tabularnewline
Quadratic Mean & 114.682734418413 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 114.257894736842 & 1.32812646548566 & 86.0293787572864 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 114.250526315789 & 1.32463463589486 & 86.2505956131872 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 114.137368421053 & 1.29326517289119 & 88.255193763465 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 114.139473684211 & 1.28660087764687 & 88.7139715721057 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 113.994736842105 & 1.24329376760295 & 91.6876926535913 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 113.886315789474 & 1.21524296052536 & 93.7148533164425 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 113.752456140351 & 1.17813896510412 & 96.5526644221448 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 113.697719298246 & 1.14350319741693 & 99.4292972289699 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 113.670877192982 & 1.10956064711124 & 102.446745465358 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 113.141052631579 & 0.944300064488317 & 119.814725092586 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 112.965438596491 & 0.894074656062062 & 126.348999863217 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 112.919122807018 & 0.883944696012075 & 127.744556097744 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 112.859824561404 & 0.850578805262427 & 132.685912067352 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 112.822982456140 & 0.841410528220034 & 134.087913892416 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 112.775614035088 & 0.82426693403463 & 136.819286785013 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 112.427543859649 & 0.754591637172774 & 148.991240190364 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 112.087543859649 & 0.672113678655963 & 166.768728890911 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 111.560175438597 & 0.568200479729353 & 196.339460135154 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 111.566842105263 & 0.533602756855444 & 209.082207076166 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 114.067636363636 & 1.30331310438295 & 87.521284010753 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 113.863018867925 & 1.27142282802099 & 89.5555879275472 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 113.646470588235 & 1.23281497819944 & 92.184531010662 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 113.456122448980 & 1.19904659604352 & 94.6219461556787 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 113.248936170213 & 1.15761582454143 & 97.829464464236 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 113.06 & 1.11959502959911 & 100.982942055828 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 112.877441860465 & 1.07883684406144 & 104.628834732341 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 112.703658536585 & 1.03648701685523 & 108.736199010515 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 112.522051282051 & 0.989838464682804 & 113.677186022579 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 112.325405405405 & 0.935993201076616 & 120.006646710900 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 112.192571428571 & 0.914218253813739 & 122.719679858229 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 112.071212121212 & 0.896896031859382 & 124.954518851950 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 111.941290322581 & 0.872815089845148 & 128.253156510437 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 111.802413793103 & 0.845938085864656 & 132.163825770804 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 111.648518518519 & 0.806211764031383 & 138.485350251193 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 111.4772 & 0.748957390866352 & 148.843180345746 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 111.33 & 0.689108664136609 & 161.556523367017 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 111.209047619048 & 0.631263624939957 & 176.168946261754 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 111.150526315789 & 0.589770732381992 & 188.463957624465 \tabularnewline
Median & 111.37 &  &  \tabularnewline
Midrange & 119.225 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.456785714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.802413793103 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.802413793103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.802413793103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.802413793103 &  &  \tabularnewline
Midmean - Closest Observation & 111.617333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.802413793103 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.802413793103 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49736&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]114.248596491228[/C][C]1.33220931879528[/C][C]85.7587429237795[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.831173805273[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.431563809174[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.682734418413[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]114.257894736842[/C][C]1.32812646548566[/C][C]86.0293787572864[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]114.250526315789[/C][C]1.32463463589486[/C][C]86.2505956131872[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]114.137368421053[/C][C]1.29326517289119[/C][C]88.255193763465[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]114.139473684211[/C][C]1.28660087764687[/C][C]88.7139715721057[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]113.994736842105[/C][C]1.24329376760295[/C][C]91.6876926535913[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]113.886315789474[/C][C]1.21524296052536[/C][C]93.7148533164425[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]113.752456140351[/C][C]1.17813896510412[/C][C]96.5526644221448[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]113.697719298246[/C][C]1.14350319741693[/C][C]99.4292972289699[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]113.670877192982[/C][C]1.10956064711124[/C][C]102.446745465358[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]113.141052631579[/C][C]0.944300064488317[/C][C]119.814725092586[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]112.965438596491[/C][C]0.894074656062062[/C][C]126.348999863217[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]112.919122807018[/C][C]0.883944696012075[/C][C]127.744556097744[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]112.859824561404[/C][C]0.850578805262427[/C][C]132.685912067352[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]112.822982456140[/C][C]0.841410528220034[/C][C]134.087913892416[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]112.775614035088[/C][C]0.82426693403463[/C][C]136.819286785013[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]112.427543859649[/C][C]0.754591637172774[/C][C]148.991240190364[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]112.087543859649[/C][C]0.672113678655963[/C][C]166.768728890911[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]111.560175438597[/C][C]0.568200479729353[/C][C]196.339460135154[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]111.566842105263[/C][C]0.533602756855444[/C][C]209.082207076166[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]114.067636363636[/C][C]1.30331310438295[/C][C]87.521284010753[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]113.863018867925[/C][C]1.27142282802099[/C][C]89.5555879275472[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]113.646470588235[/C][C]1.23281497819944[/C][C]92.184531010662[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]113.456122448980[/C][C]1.19904659604352[/C][C]94.6219461556787[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]113.248936170213[/C][C]1.15761582454143[/C][C]97.829464464236[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]113.06[/C][C]1.11959502959911[/C][C]100.982942055828[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]112.877441860465[/C][C]1.07883684406144[/C][C]104.628834732341[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]112.703658536585[/C][C]1.03648701685523[/C][C]108.736199010515[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]112.522051282051[/C][C]0.989838464682804[/C][C]113.677186022579[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]112.325405405405[/C][C]0.935993201076616[/C][C]120.006646710900[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]112.192571428571[/C][C]0.914218253813739[/C][C]122.719679858229[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]112.071212121212[/C][C]0.896896031859382[/C][C]124.954518851950[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]111.941290322581[/C][C]0.872815089845148[/C][C]128.253156510437[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]111.802413793103[/C][C]0.845938085864656[/C][C]132.163825770804[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]111.648518518519[/C][C]0.806211764031383[/C][C]138.485350251193[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]111.4772[/C][C]0.748957390866352[/C][C]148.843180345746[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]111.33[/C][C]0.689108664136609[/C][C]161.556523367017[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]111.209047619048[/C][C]0.631263624939957[/C][C]176.168946261754[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]111.150526315789[/C][C]0.589770732381992[/C][C]188.463957624465[/C][/ROW]
[ROW][C]Median[/C][C]111.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]119.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.456785714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.802413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.802413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.802413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.802413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.617333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.802413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.802413793103[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]57[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49736&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49736&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 Mean114.2485964912281.3322093187952885.7587429237795
Geometric Mean113.831173805273
Harmonic Mean113.431563809174
Quadratic Mean114.682734418413
Winsorized Mean ( 1 / 19 )114.2578947368421.3281264654856686.0293787572864
Winsorized Mean ( 2 / 19 )114.2505263157891.3246346358948686.2505956131872
Winsorized Mean ( 3 / 19 )114.1373684210531.2932651728911988.255193763465
Winsorized Mean ( 4 / 19 )114.1394736842111.2866008776468788.7139715721057
Winsorized Mean ( 5 / 19 )113.9947368421051.2432937676029591.6876926535913
Winsorized Mean ( 6 / 19 )113.8863157894741.2152429605253693.7148533164425
Winsorized Mean ( 7 / 19 )113.7524561403511.1781389651041296.5526644221448
Winsorized Mean ( 8 / 19 )113.6977192982461.1435031974169399.4292972289699
Winsorized Mean ( 9 / 19 )113.6708771929821.10956064711124102.446745465358
Winsorized Mean ( 10 / 19 )113.1410526315790.944300064488317119.814725092586
Winsorized Mean ( 11 / 19 )112.9654385964910.894074656062062126.348999863217
Winsorized Mean ( 12 / 19 )112.9191228070180.883944696012075127.744556097744
Winsorized Mean ( 13 / 19 )112.8598245614040.850578805262427132.685912067352
Winsorized Mean ( 14 / 19 )112.8229824561400.841410528220034134.087913892416
Winsorized Mean ( 15 / 19 )112.7756140350880.82426693403463136.819286785013
Winsorized Mean ( 16 / 19 )112.4275438596490.754591637172774148.991240190364
Winsorized Mean ( 17 / 19 )112.0875438596490.672113678655963166.768728890911
Winsorized Mean ( 18 / 19 )111.5601754385970.568200479729353196.339460135154
Winsorized Mean ( 19 / 19 )111.5668421052630.533602756855444209.082207076166
Trimmed Mean ( 1 / 19 )114.0676363636361.3033131043829587.521284010753
Trimmed Mean ( 2 / 19 )113.8630188679251.2714228280209989.5555879275472
Trimmed Mean ( 3 / 19 )113.6464705882351.2328149781994492.184531010662
Trimmed Mean ( 4 / 19 )113.4561224489801.1990465960435294.6219461556787
Trimmed Mean ( 5 / 19 )113.2489361702131.1576158245414397.829464464236
Trimmed Mean ( 6 / 19 )113.061.11959502959911100.982942055828
Trimmed Mean ( 7 / 19 )112.8774418604651.07883684406144104.628834732341
Trimmed Mean ( 8 / 19 )112.7036585365851.03648701685523108.736199010515
Trimmed Mean ( 9 / 19 )112.5220512820510.989838464682804113.677186022579
Trimmed Mean ( 10 / 19 )112.3254054054050.935993201076616120.006646710900
Trimmed Mean ( 11 / 19 )112.1925714285710.914218253813739122.719679858229
Trimmed Mean ( 12 / 19 )112.0712121212120.896896031859382124.954518851950
Trimmed Mean ( 13 / 19 )111.9412903225810.872815089845148128.253156510437
Trimmed Mean ( 14 / 19 )111.8024137931030.845938085864656132.163825770804
Trimmed Mean ( 15 / 19 )111.6485185185190.806211764031383138.485350251193
Trimmed Mean ( 16 / 19 )111.47720.748957390866352148.843180345746
Trimmed Mean ( 17 / 19 )111.330.689108664136609161.556523367017
Trimmed Mean ( 18 / 19 )111.2090476190480.631263624939957176.168946261754
Trimmed Mean ( 19 / 19 )111.1505263157890.589770732381992188.463957624465
Median111.37
Midrange119.225
Midmean - Weighted Average at Xnp111.456785714286
Midmean - Weighted Average at X(n+1)p111.802413793103
Midmean - Empirical Distribution Function111.802413793103
Midmean - Empirical Distribution Function - Averaging111.802413793103
Midmean - Empirical Distribution Function - Interpolation111.802413793103
Midmean - Closest Observation111.617333333333
Midmean - True Basic - Statistics Graphics Toolkit111.802413793103
Midmean - MS Excel (old versions)111.802413793103
Number of observations57



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')