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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, 10 Nov 2011 18:50:22 -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/2011/Nov/10/t13209690658hi9e7l6e5nzemd.htm/, Retrieved Sat, 20 Apr 2024 03:27:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=141278, Retrieved Sat, 20 Apr 2024 03:27:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
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]
- RMPD    [Central Tendency] [Centrale Tendenti...] [2011-11-10 23:50:22] [614dd89c388120cee0dd25886939832b] [Current]
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Dataseries X:
79717000
82855667
79346667
76270333
89532667
83541333
82456000
85818333
92106667
96873333
96580000
87769000
88396000
90995667
92785000
98112667
105779667
103660333
105435000
105204000
107466333
118554333
123614333
125620000
121524333
130830333
138871333
135215667
122096333
130005333
126566000
134808667
138761333
133778333
122598667
116446000
100745333
104419333
103477000
102054333
102446667
99528000
106549667
107587333
117091333
114029667
109721333
114697000
115063667
121234667
118393000
121308000
117579000
117414000
117740333
109417000
116442333
113311000
109391333
107198667




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=141278&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=141278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141278&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108613877.7333332076637.2211028352.3027694147043
Geometric Mean107404568.012203
Harmonic Mean106159531.220845
Quadratic Mean109778902.085089
Winsorized Mean ( 1 / 20 )108663316.6333332063240.8239744452.666327348067
Winsorized Mean ( 2 / 20 )108557472.22032510.8884056253.4105243023602
Winsorized Mean ( 3 / 20 )108674072.21996269.1016834154.4385885191318
Winsorized Mean ( 4 / 20 )108632027.7333331975324.6246523554.9945190666835
Winsorized Mean ( 5 / 20 )108443499.91911781.1173112256.7238053132976
Winsorized Mean ( 6 / 20 )108588699.91846529.9268857458.8068995356819
Winsorized Mean ( 7 / 20 )108415022.21724270.2425355562.8758877382093
Winsorized Mean ( 8 / 20 )108372488.8666671685191.700401564.3087008088436
Winsorized Mean ( 9 / 20 )108242138.8666671600544.3711608867.6283274722078
Winsorized Mean ( 10 / 20 )108316694.5333331525698.3389103470.994830217023
Winsorized Mean ( 11 / 20 )108428283.31472407.6837453573.640123246431
Winsorized Mean ( 12 / 20 )108449549.91429188.7253908875.8818957729597
Winsorized Mean ( 13 / 20 )109224927.751275954.7677209885.6025076383308
Winsorized Mean ( 14 / 20 )109276261.0833331261757.0102619286.6064227855164
Winsorized Mean ( 15 / 20 )108916011.0833331106744.523069498.4111588655255
Winsorized Mean ( 16 / 20 )109250411.0833331039175.46982463105.131822541741
Winsorized Mean ( 17 / 20 )109410399.783333957929.890327563114.215456567412
Winsorized Mean ( 18 / 20 )109754699.883333891880.338304412123.059893989806
Winsorized Mean ( 19 / 20 )109826688.983333866052.324633911126.812994849657
Winsorized Mean ( 20 / 20 )110062577.65801315.700851564137.352328842472
Trimmed Mean ( 1 / 20 )108649844.7931032006061.6616545354.1607702644059
Trimmed Mean ( 2 / 20 )108635410.6785711935560.1953014756.126082227916
Trimmed Mean ( 3 / 20 )108678709.8333331868867.1449142158.1521860069524
Trimmed Mean ( 4 / 20 )108680493.5384621803465.7633196460.262022018324
Trimmed Mean ( 5 / 20 )108695033.281729547.1164347662.8459509701367
Trimmed Mean ( 6 / 20 )108757916.6251658565.8364481365.5734697019374
Trimmed Mean ( 7 / 20 )108794702.8695651589238.7236496968.4571180217143
Trimmed Mean ( 8 / 20 )108868666.6363641537071.3502029670.8286356531128
Trimmed Mean ( 9 / 20 )108957269.8095241479623.5357088673.6385081610131
Trimmed Mean ( 10 / 20 )109076458.31427126.6696820176.4308176822904
Trimmed Mean ( 11 / 20 )1091964211377249.9313016579.2858424010213
Trimmed Mean ( 12 / 20 )109312805.51323766.3237789282.5771161695271
Trimmed Mean ( 13 / 20 )109439754.8529411261359.2481460586.7633507375444
Trimmed Mean ( 14 / 20 )109470739.531251220983.0477945589.6578701309455
Trimmed Mean ( 15 / 20 )109498522.1666671165483.1809065493.9511817592218
Trimmed Mean ( 16 / 20 )109581738.0357141132683.1145626596.7452737900358
Trimmed Mean ( 17 / 20 )109629525.5769231103247.4748313399.3698404736291
Trimmed Mean ( 18 / 20 )109661749.9583331082144.06347651101.337477753223
Trimmed Mean ( 19 / 20 )109647666.6363641066867.95601446102.775292873149
Trimmed Mean ( 20 / 20 )109619399.951043356.71984876105.064162490744
Median108489333
Midrange107570833
Midmean - Weighted Average at Xnp109091258
Midmean - Weighted Average at X(n+1)p109498522.166667
Midmean - Empirical Distribution Function109091258
Midmean - Empirical Distribution Function - Averaging109498522.166667
Midmean - Empirical Distribution Function - Interpolation109498522.166667
Midmean - Closest Observation109091258
Midmean - True Basic - Statistics Graphics Toolkit109498522.166667
Midmean - MS Excel (old versions)109470739.53125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108613877.733333 & 2076637.22110283 & 52.3027694147043 \tabularnewline
Geometric Mean & 107404568.012203 &  &  \tabularnewline
Harmonic Mean & 106159531.220845 &  &  \tabularnewline
Quadratic Mean & 109778902.085089 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 108663316.633333 & 2063240.82397444 & 52.666327348067 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 108557472.2 & 2032510.88840562 & 53.4105243023602 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 108674072.2 & 1996269.10168341 & 54.4385885191318 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 108632027.733333 & 1975324.62465235 & 54.9945190666835 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 108443499.9 & 1911781.11731122 & 56.7238053132976 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 108588699.9 & 1846529.92688574 & 58.8068995356819 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 108415022.2 & 1724270.24253555 & 62.8758877382093 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 108372488.866667 & 1685191.7004015 & 64.3087008088436 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 108242138.866667 & 1600544.37116088 & 67.6283274722078 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 108316694.533333 & 1525698.33891034 & 70.994830217023 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 108428283.3 & 1472407.68374535 & 73.640123246431 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 108449549.9 & 1429188.72539088 & 75.8818957729597 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 109224927.75 & 1275954.76772098 & 85.6025076383308 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 109276261.083333 & 1261757.01026192 & 86.6064227855164 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 108916011.083333 & 1106744.5230694 & 98.4111588655255 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 109250411.083333 & 1039175.46982463 & 105.131822541741 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 109410399.783333 & 957929.890327563 & 114.215456567412 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 109754699.883333 & 891880.338304412 & 123.059893989806 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 109826688.983333 & 866052.324633911 & 126.812994849657 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110062577.65 & 801315.700851564 & 137.352328842472 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 108649844.793103 & 2006061.66165453 & 54.1607702644059 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 108635410.678571 & 1935560.19530147 & 56.126082227916 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 108678709.833333 & 1868867.14491421 & 58.1521860069524 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 108680493.538462 & 1803465.76331964 & 60.262022018324 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 108695033.28 & 1729547.11643476 & 62.8459509701367 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 108757916.625 & 1658565.83644813 & 65.5734697019374 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 108794702.869565 & 1589238.72364969 & 68.4571180217143 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 108868666.636364 & 1537071.35020296 & 70.8286356531128 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 108957269.809524 & 1479623.53570886 & 73.6385081610131 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 109076458.3 & 1427126.66968201 & 76.4308176822904 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109196421 & 1377249.93130165 & 79.2858424010213 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109312805.5 & 1323766.32377892 & 82.5771161695271 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 109439754.852941 & 1261359.24814605 & 86.7633507375444 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 109470739.53125 & 1220983.04779455 & 89.6578701309455 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 109498522.166667 & 1165483.18090654 & 93.9511817592218 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 109581738.035714 & 1132683.11456265 & 96.7452737900358 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 109629525.576923 & 1103247.47483133 & 99.3698404736291 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 109661749.958333 & 1082144.06347651 & 101.337477753223 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 109647666.636364 & 1066867.95601446 & 102.775292873149 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 109619399.95 & 1043356.71984876 & 105.064162490744 \tabularnewline
Median & 108489333 &  &  \tabularnewline
Midrange & 107570833 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109091258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109498522.166667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109091258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109498522.166667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109498522.166667 &  &  \tabularnewline
Midmean - Closest Observation & 109091258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109498522.166667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109470739.53125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=141278&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]108613877.733333[/C][C]2076637.22110283[/C][C]52.3027694147043[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107404568.012203[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106159531.220845[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109778902.085089[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]108663316.633333[/C][C]2063240.82397444[/C][C]52.666327348067[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]108557472.2[/C][C]2032510.88840562[/C][C]53.4105243023602[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]108674072.2[/C][C]1996269.10168341[/C][C]54.4385885191318[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]108632027.733333[/C][C]1975324.62465235[/C][C]54.9945190666835[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]108443499.9[/C][C]1911781.11731122[/C][C]56.7238053132976[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]108588699.9[/C][C]1846529.92688574[/C][C]58.8068995356819[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]108415022.2[/C][C]1724270.24253555[/C][C]62.8758877382093[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]108372488.866667[/C][C]1685191.7004015[/C][C]64.3087008088436[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]108242138.866667[/C][C]1600544.37116088[/C][C]67.6283274722078[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]108316694.533333[/C][C]1525698.33891034[/C][C]70.994830217023[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]108428283.3[/C][C]1472407.68374535[/C][C]73.640123246431[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]108449549.9[/C][C]1429188.72539088[/C][C]75.8818957729597[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]109224927.75[/C][C]1275954.76772098[/C][C]85.6025076383308[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]109276261.083333[/C][C]1261757.01026192[/C][C]86.6064227855164[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]108916011.083333[/C][C]1106744.5230694[/C][C]98.4111588655255[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]109250411.083333[/C][C]1039175.46982463[/C][C]105.131822541741[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]109410399.783333[/C][C]957929.890327563[/C][C]114.215456567412[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]109754699.883333[/C][C]891880.338304412[/C][C]123.059893989806[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]109826688.983333[/C][C]866052.324633911[/C][C]126.812994849657[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110062577.65[/C][C]801315.700851564[/C][C]137.352328842472[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]108649844.793103[/C][C]2006061.66165453[/C][C]54.1607702644059[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]108635410.678571[/C][C]1935560.19530147[/C][C]56.126082227916[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]108678709.833333[/C][C]1868867.14491421[/C][C]58.1521860069524[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]108680493.538462[/C][C]1803465.76331964[/C][C]60.262022018324[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]108695033.28[/C][C]1729547.11643476[/C][C]62.8459509701367[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]108757916.625[/C][C]1658565.83644813[/C][C]65.5734697019374[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]108794702.869565[/C][C]1589238.72364969[/C][C]68.4571180217143[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]108868666.636364[/C][C]1537071.35020296[/C][C]70.8286356531128[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]108957269.809524[/C][C]1479623.53570886[/C][C]73.6385081610131[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]109076458.3[/C][C]1427126.66968201[/C][C]76.4308176822904[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109196421[/C][C]1377249.93130165[/C][C]79.2858424010213[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109312805.5[/C][C]1323766.32377892[/C][C]82.5771161695271[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]109439754.852941[/C][C]1261359.24814605[/C][C]86.7633507375444[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]109470739.53125[/C][C]1220983.04779455[/C][C]89.6578701309455[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]109498522.166667[/C][C]1165483.18090654[/C][C]93.9511817592218[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]109581738.035714[/C][C]1132683.11456265[/C][C]96.7452737900358[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]109629525.576923[/C][C]1103247.47483133[/C][C]99.3698404736291[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]109661749.958333[/C][C]1082144.06347651[/C][C]101.337477753223[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]109647666.636364[/C][C]1066867.95601446[/C][C]102.775292873149[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]109619399.95[/C][C]1043356.71984876[/C][C]105.064162490744[/C][/ROW]
[ROW][C]Median[/C][C]108489333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107570833[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109091258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109498522.166667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109091258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109498522.166667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109498522.166667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109091258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109498522.166667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109470739.53125[/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=141278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=141278&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 Mean108613877.7333332076637.2211028352.3027694147043
Geometric Mean107404568.012203
Harmonic Mean106159531.220845
Quadratic Mean109778902.085089
Winsorized Mean ( 1 / 20 )108663316.6333332063240.8239744452.666327348067
Winsorized Mean ( 2 / 20 )108557472.22032510.8884056253.4105243023602
Winsorized Mean ( 3 / 20 )108674072.21996269.1016834154.4385885191318
Winsorized Mean ( 4 / 20 )108632027.7333331975324.6246523554.9945190666835
Winsorized Mean ( 5 / 20 )108443499.91911781.1173112256.7238053132976
Winsorized Mean ( 6 / 20 )108588699.91846529.9268857458.8068995356819
Winsorized Mean ( 7 / 20 )108415022.21724270.2425355562.8758877382093
Winsorized Mean ( 8 / 20 )108372488.8666671685191.700401564.3087008088436
Winsorized Mean ( 9 / 20 )108242138.8666671600544.3711608867.6283274722078
Winsorized Mean ( 10 / 20 )108316694.5333331525698.3389103470.994830217023
Winsorized Mean ( 11 / 20 )108428283.31472407.6837453573.640123246431
Winsorized Mean ( 12 / 20 )108449549.91429188.7253908875.8818957729597
Winsorized Mean ( 13 / 20 )109224927.751275954.7677209885.6025076383308
Winsorized Mean ( 14 / 20 )109276261.0833331261757.0102619286.6064227855164
Winsorized Mean ( 15 / 20 )108916011.0833331106744.523069498.4111588655255
Winsorized Mean ( 16 / 20 )109250411.0833331039175.46982463105.131822541741
Winsorized Mean ( 17 / 20 )109410399.783333957929.890327563114.215456567412
Winsorized Mean ( 18 / 20 )109754699.883333891880.338304412123.059893989806
Winsorized Mean ( 19 / 20 )109826688.983333866052.324633911126.812994849657
Winsorized Mean ( 20 / 20 )110062577.65801315.700851564137.352328842472
Trimmed Mean ( 1 / 20 )108649844.7931032006061.6616545354.1607702644059
Trimmed Mean ( 2 / 20 )108635410.6785711935560.1953014756.126082227916
Trimmed Mean ( 3 / 20 )108678709.8333331868867.1449142158.1521860069524
Trimmed Mean ( 4 / 20 )108680493.5384621803465.7633196460.262022018324
Trimmed Mean ( 5 / 20 )108695033.281729547.1164347662.8459509701367
Trimmed Mean ( 6 / 20 )108757916.6251658565.8364481365.5734697019374
Trimmed Mean ( 7 / 20 )108794702.8695651589238.7236496968.4571180217143
Trimmed Mean ( 8 / 20 )108868666.6363641537071.3502029670.8286356531128
Trimmed Mean ( 9 / 20 )108957269.8095241479623.5357088673.6385081610131
Trimmed Mean ( 10 / 20 )109076458.31427126.6696820176.4308176822904
Trimmed Mean ( 11 / 20 )1091964211377249.9313016579.2858424010213
Trimmed Mean ( 12 / 20 )109312805.51323766.3237789282.5771161695271
Trimmed Mean ( 13 / 20 )109439754.8529411261359.2481460586.7633507375444
Trimmed Mean ( 14 / 20 )109470739.531251220983.0477945589.6578701309455
Trimmed Mean ( 15 / 20 )109498522.1666671165483.1809065493.9511817592218
Trimmed Mean ( 16 / 20 )109581738.0357141132683.1145626596.7452737900358
Trimmed Mean ( 17 / 20 )109629525.5769231103247.4748313399.3698404736291
Trimmed Mean ( 18 / 20 )109661749.9583331082144.06347651101.337477753223
Trimmed Mean ( 19 / 20 )109647666.6363641066867.95601446102.775292873149
Trimmed Mean ( 20 / 20 )109619399.951043356.71984876105.064162490744
Median108489333
Midrange107570833
Midmean - Weighted Average at Xnp109091258
Midmean - Weighted Average at X(n+1)p109498522.166667
Midmean - Empirical Distribution Function109091258
Midmean - Empirical Distribution Function - Averaging109498522.166667
Midmean - Empirical Distribution Function - Interpolation109498522.166667
Midmean - Closest Observation109091258
Midmean - True Basic - Statistics Graphics Toolkit109498522.166667
Midmean - MS Excel (old versions)109470739.53125
Number of observations60



Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')