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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 computationWed, 15 Dec 2010 15:45:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/15/t129242777014lox2fnraq1gfx.htm/, Retrieved Fri, 03 May 2024 09:58:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110492, Retrieved Fri, 03 May 2024 09:58:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2010-12-13 22:17:35] [2db311435ed525bc1ed0ddec922afb8f]
-    D    [Central Tendency] [] [2010-12-15 15:45:08] [6fde1c772c7be11768d9b6a0344566b2] [Current]
-    D      [Central Tendency] [] [2010-12-15 20:17:31] [2db311435ed525bc1ed0ddec922afb8f]
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Dataseries X:
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110492&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110492&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110492&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean118.1311475409842.1515625799473154.9048159890735
Geometric Mean116.975985331462
Harmonic Mean115.838379798453
Quadratic Mean119.300969449018
Winsorized Mean ( 1 / 20 )118.1803278688522.1390856783195955.248057180062
Winsorized Mean ( 2 / 20 )118.1475409836072.0299446902979258.2023448955483
Winsorized Mean ( 3 / 20 )118.0983606557382.0172351524121358.5446671968412
Winsorized Mean ( 4 / 20 )118.2295081967211.9908799496983559.3855537169054
Winsorized Mean ( 5 / 20 )118.0655737704921.9494806443677560.5625780956561
Winsorized Mean ( 6 / 20 )118.1639344262301.803939272945465.5032772989614
Winsorized Mean ( 7 / 20 )117.5901639344261.5848285231025974.1974050947937
Winsorized Mean ( 8 / 20 )117.7213114754101.5623876829648675.3470555093061
Winsorized Mean ( 9 / 20 )117.5737704918031.4785273681461179.5208617877841
Winsorized Mean ( 10 / 20 )117.7377049180331.3945447264886184.4273422584947
Winsorized Mean ( 11 / 20 )117.3770491803281.3263129250279988.4987599573086
Winsorized Mean ( 12 / 20 )117.1803278688521.2906786872100390.7896977226401
Winsorized Mean ( 13 / 20 )116.9672131147541.2531854958257293.3359135613718
Winsorized Mean ( 14 / 20 )117.1967213114751.2173202837773396.2743518474988
Winsorized Mean ( 15 / 20 )116.7049180327871.05461366357364110.661299074509
Winsorized Mean ( 16 / 20 )116.1803278688520.972155566921158119.507959242365
Winsorized Mean ( 17 / 20 )116.1803278688520.887222040431841130.948423928134
Winsorized Mean ( 18 / 20 )116.4754098360660.842714374917372138.214575783742
Winsorized Mean ( 19 / 20 )116.4754098360660.842714374917372138.214575783742
Winsorized Mean ( 20 / 20 )116.1475409836070.79473543234045146.146171741153
Trimmed Mean ( 1 / 20 )118.0508474576272.0418508078924757.8156087610901
Trimmed Mean ( 2 / 20 )117.9122807017541.9214331114042261.3668412404853
Trimmed Mean ( 3 / 20 )117.7818181818181.8471364514011763.7645465187336
Trimmed Mean ( 4 / 20 )117.6603773584911.7607112372908366.8254821497771
Trimmed Mean ( 5 / 20 )117.4901960784311.6623565953824370.6768911103593
Trimmed Mean ( 6 / 20 )117.3469387755101.5525245570834275.5845942919953
Trimmed Mean ( 7 / 20 )117.1702127659571.4619184324642480.148255992951
Trimmed Mean ( 8 / 20 )117.0888888888891.4152210885644082.7354042665264
Trimmed Mean ( 9 / 20 )116.9767441860471.3601219621934686.0045991738847
Trimmed Mean ( 10 / 20 )116.8780487804881.3113924464938089.1251502118822
Trimmed Mean ( 11 / 20 )116.7435897435901.2687024350552792.018101737547
Trimmed Mean ( 12 / 20 )116.6486486486491.2297709790791694.8539611302213
Trimmed Mean ( 13 / 20 )116.5714285714291.1855472191707798.3271072517584
Trimmed Mean ( 14 / 20 )116.5151515151521.13411393470684102.736725076277
Trimmed Mean ( 15 / 20 )116.4193548387101.07039756813415108.762723594043
Trimmed Mean ( 16 / 20 )116.3793103448281.03201676522384112.768817587557
Trimmed Mean ( 17 / 20 )116.4074074074071.00036924701245116.364440185513
Trimmed Mean ( 18 / 20 )116.440.978229693545096119.031348944257
Trimmed Mean ( 19 / 20 )116.4347826086960.95517332193009121.899114993517
Trimmed Mean ( 20 / 20 )116.4285714285710.911752442830181127.697570041232
Median117
Midrange120.5
Midmean - Weighted Average at Xnp116.066666666667
Midmean - Weighted Average at X(n+1)p116.419354838710
Midmean - Empirical Distribution Function116.419354838710
Midmean - Empirical Distribution Function - Averaging116.419354838710
Midmean - Empirical Distribution Function - Interpolation116.419354838710
Midmean - Closest Observation116.09375
Midmean - True Basic - Statistics Graphics Toolkit116.419354838710
Midmean - MS Excel (old versions)116.419354838710
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 118.131147540984 & 2.15156257994731 & 54.9048159890735 \tabularnewline
Geometric Mean & 116.975985331462 &  &  \tabularnewline
Harmonic Mean & 115.838379798453 &  &  \tabularnewline
Quadratic Mean & 119.300969449018 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 118.180327868852 & 2.13908567831959 & 55.248057180062 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 118.147540983607 & 2.02994469029792 & 58.2023448955483 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 118.098360655738 & 2.01723515241213 & 58.5446671968412 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 118.229508196721 & 1.99087994969835 & 59.3855537169054 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 118.065573770492 & 1.94948064436775 & 60.5625780956561 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 118.163934426230 & 1.8039392729454 & 65.5032772989614 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 117.590163934426 & 1.58482852310259 & 74.1974050947937 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 117.721311475410 & 1.56238768296486 & 75.3470555093061 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 117.573770491803 & 1.47852736814611 & 79.5208617877841 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 117.737704918033 & 1.39454472648861 & 84.4273422584947 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 117.377049180328 & 1.32631292502799 & 88.4987599573086 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 117.180327868852 & 1.29067868721003 & 90.7896977226401 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.967213114754 & 1.25318549582572 & 93.3359135613718 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 117.196721311475 & 1.21732028377733 & 96.2743518474988 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.704918032787 & 1.05461366357364 & 110.661299074509 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.180327868852 & 0.972155566921158 & 119.507959242365 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 116.180327868852 & 0.887222040431841 & 130.948423928134 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 116.475409836066 & 0.842714374917372 & 138.214575783742 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.475409836066 & 0.842714374917372 & 138.214575783742 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 116.147540983607 & 0.79473543234045 & 146.146171741153 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 118.050847457627 & 2.04185080789247 & 57.8156087610901 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 117.912280701754 & 1.92143311140422 & 61.3668412404853 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 117.781818181818 & 1.84713645140117 & 63.7645465187336 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 117.660377358491 & 1.76071123729083 & 66.8254821497771 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 117.490196078431 & 1.66235659538243 & 70.6768911103593 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 117.346938775510 & 1.55252455708342 & 75.5845942919953 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 117.170212765957 & 1.46191843246424 & 80.148255992951 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 117.088888888889 & 1.41522108856440 & 82.7354042665264 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.976744186047 & 1.36012196219346 & 86.0045991738847 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.878048780488 & 1.31139244649380 & 89.1251502118822 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.743589743590 & 1.26870243505527 & 92.018101737547 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.648648648649 & 1.22977097907916 & 94.8539611302213 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.571428571429 & 1.18554721917077 & 98.3271072517584 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.515151515152 & 1.13411393470684 & 102.736725076277 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.419354838710 & 1.07039756813415 & 108.762723594043 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.379310344828 & 1.03201676522384 & 112.768817587557 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.407407407407 & 1.00036924701245 & 116.364440185513 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.44 & 0.978229693545096 & 119.031348944257 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 116.434782608696 & 0.95517332193009 & 121.899114993517 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 116.428571428571 & 0.911752442830181 & 127.697570041232 \tabularnewline
Median & 117 &  &  \tabularnewline
Midrange & 120.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.066666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.419354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.419354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.419354838710 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.419354838710 &  &  \tabularnewline
Midmean - Closest Observation & 116.09375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.419354838710 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.419354838710 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110492&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]118.131147540984[/C][C]2.15156257994731[/C][C]54.9048159890735[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]116.975985331462[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.838379798453[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]119.300969449018[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]118.180327868852[/C][C]2.13908567831959[/C][C]55.248057180062[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]118.147540983607[/C][C]2.02994469029792[/C][C]58.2023448955483[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]118.098360655738[/C][C]2.01723515241213[/C][C]58.5446671968412[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]118.229508196721[/C][C]1.99087994969835[/C][C]59.3855537169054[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]118.065573770492[/C][C]1.94948064436775[/C][C]60.5625780956561[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]118.163934426230[/C][C]1.8039392729454[/C][C]65.5032772989614[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]117.590163934426[/C][C]1.58482852310259[/C][C]74.1974050947937[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]117.721311475410[/C][C]1.56238768296486[/C][C]75.3470555093061[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]117.573770491803[/C][C]1.47852736814611[/C][C]79.5208617877841[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]117.737704918033[/C][C]1.39454472648861[/C][C]84.4273422584947[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]117.377049180328[/C][C]1.32631292502799[/C][C]88.4987599573086[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]117.180327868852[/C][C]1.29067868721003[/C][C]90.7896977226401[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.967213114754[/C][C]1.25318549582572[/C][C]93.3359135613718[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]117.196721311475[/C][C]1.21732028377733[/C][C]96.2743518474988[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.704918032787[/C][C]1.05461366357364[/C][C]110.661299074509[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.180327868852[/C][C]0.972155566921158[/C][C]119.507959242365[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]116.180327868852[/C][C]0.887222040431841[/C][C]130.948423928134[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]116.475409836066[/C][C]0.842714374917372[/C][C]138.214575783742[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.475409836066[/C][C]0.842714374917372[/C][C]138.214575783742[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]116.147540983607[/C][C]0.79473543234045[/C][C]146.146171741153[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]118.050847457627[/C][C]2.04185080789247[/C][C]57.8156087610901[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]117.912280701754[/C][C]1.92143311140422[/C][C]61.3668412404853[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]117.781818181818[/C][C]1.84713645140117[/C][C]63.7645465187336[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]117.660377358491[/C][C]1.76071123729083[/C][C]66.8254821497771[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]117.490196078431[/C][C]1.66235659538243[/C][C]70.6768911103593[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]117.346938775510[/C][C]1.55252455708342[/C][C]75.5845942919953[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]117.170212765957[/C][C]1.46191843246424[/C][C]80.148255992951[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]117.088888888889[/C][C]1.41522108856440[/C][C]82.7354042665264[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.976744186047[/C][C]1.36012196219346[/C][C]86.0045991738847[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.878048780488[/C][C]1.31139244649380[/C][C]89.1251502118822[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.743589743590[/C][C]1.26870243505527[/C][C]92.018101737547[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.648648648649[/C][C]1.22977097907916[/C][C]94.8539611302213[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.571428571429[/C][C]1.18554721917077[/C][C]98.3271072517584[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.515151515152[/C][C]1.13411393470684[/C][C]102.736725076277[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.419354838710[/C][C]1.07039756813415[/C][C]108.762723594043[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.379310344828[/C][C]1.03201676522384[/C][C]112.768817587557[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.407407407407[/C][C]1.00036924701245[/C][C]116.364440185513[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.44[/C][C]0.978229693545096[/C][C]119.031348944257[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]116.434782608696[/C][C]0.95517332193009[/C][C]121.899114993517[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]116.428571428571[/C][C]0.911752442830181[/C][C]127.697570041232[/C][/ROW]
[ROW][C]Median[/C][C]117[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]120.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.09375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.419354838710[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110492&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110492&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 Mean118.1311475409842.1515625799473154.9048159890735
Geometric Mean116.975985331462
Harmonic Mean115.838379798453
Quadratic Mean119.300969449018
Winsorized Mean ( 1 / 20 )118.1803278688522.1390856783195955.248057180062
Winsorized Mean ( 2 / 20 )118.1475409836072.0299446902979258.2023448955483
Winsorized Mean ( 3 / 20 )118.0983606557382.0172351524121358.5446671968412
Winsorized Mean ( 4 / 20 )118.2295081967211.9908799496983559.3855537169054
Winsorized Mean ( 5 / 20 )118.0655737704921.9494806443677560.5625780956561
Winsorized Mean ( 6 / 20 )118.1639344262301.803939272945465.5032772989614
Winsorized Mean ( 7 / 20 )117.5901639344261.5848285231025974.1974050947937
Winsorized Mean ( 8 / 20 )117.7213114754101.5623876829648675.3470555093061
Winsorized Mean ( 9 / 20 )117.5737704918031.4785273681461179.5208617877841
Winsorized Mean ( 10 / 20 )117.7377049180331.3945447264886184.4273422584947
Winsorized Mean ( 11 / 20 )117.3770491803281.3263129250279988.4987599573086
Winsorized Mean ( 12 / 20 )117.1803278688521.2906786872100390.7896977226401
Winsorized Mean ( 13 / 20 )116.9672131147541.2531854958257293.3359135613718
Winsorized Mean ( 14 / 20 )117.1967213114751.2173202837773396.2743518474988
Winsorized Mean ( 15 / 20 )116.7049180327871.05461366357364110.661299074509
Winsorized Mean ( 16 / 20 )116.1803278688520.972155566921158119.507959242365
Winsorized Mean ( 17 / 20 )116.1803278688520.887222040431841130.948423928134
Winsorized Mean ( 18 / 20 )116.4754098360660.842714374917372138.214575783742
Winsorized Mean ( 19 / 20 )116.4754098360660.842714374917372138.214575783742
Winsorized Mean ( 20 / 20 )116.1475409836070.79473543234045146.146171741153
Trimmed Mean ( 1 / 20 )118.0508474576272.0418508078924757.8156087610901
Trimmed Mean ( 2 / 20 )117.9122807017541.9214331114042261.3668412404853
Trimmed Mean ( 3 / 20 )117.7818181818181.8471364514011763.7645465187336
Trimmed Mean ( 4 / 20 )117.6603773584911.7607112372908366.8254821497771
Trimmed Mean ( 5 / 20 )117.4901960784311.6623565953824370.6768911103593
Trimmed Mean ( 6 / 20 )117.3469387755101.5525245570834275.5845942919953
Trimmed Mean ( 7 / 20 )117.1702127659571.4619184324642480.148255992951
Trimmed Mean ( 8 / 20 )117.0888888888891.4152210885644082.7354042665264
Trimmed Mean ( 9 / 20 )116.9767441860471.3601219621934686.0045991738847
Trimmed Mean ( 10 / 20 )116.8780487804881.3113924464938089.1251502118822
Trimmed Mean ( 11 / 20 )116.7435897435901.2687024350552792.018101737547
Trimmed Mean ( 12 / 20 )116.6486486486491.2297709790791694.8539611302213
Trimmed Mean ( 13 / 20 )116.5714285714291.1855472191707798.3271072517584
Trimmed Mean ( 14 / 20 )116.5151515151521.13411393470684102.736725076277
Trimmed Mean ( 15 / 20 )116.4193548387101.07039756813415108.762723594043
Trimmed Mean ( 16 / 20 )116.3793103448281.03201676522384112.768817587557
Trimmed Mean ( 17 / 20 )116.4074074074071.00036924701245116.364440185513
Trimmed Mean ( 18 / 20 )116.440.978229693545096119.031348944257
Trimmed Mean ( 19 / 20 )116.4347826086960.95517332193009121.899114993517
Trimmed Mean ( 20 / 20 )116.4285714285710.911752442830181127.697570041232
Median117
Midrange120.5
Midmean - Weighted Average at Xnp116.066666666667
Midmean - Weighted Average at X(n+1)p116.419354838710
Midmean - Empirical Distribution Function116.419354838710
Midmean - Empirical Distribution Function - Averaging116.419354838710
Midmean - Empirical Distribution Function - Interpolation116.419354838710
Midmean - Closest Observation116.09375
Midmean - True Basic - Statistics Graphics Toolkit116.419354838710
Midmean - MS Excel (old versions)116.419354838710
Number of observations61



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')