Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 14 Mar 2010 15:34:37 -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/2010/Mar/14/t1268602562gat8ocz8l9ms0ao.htm/, Retrieved Wed, 19 Jan 2022 10:18:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74428, Retrieved Wed, 19 Jan 2022 10:18:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-03-14 21:34:37] [6be1587f4b9760ef373df169f4355671] [Current]
Feedback Forum

Post a new message
Dataseries X:
132.8
132.5
131.4
131.4
130.7
131.5
131.2
130.1
130.5
129
128.2
128.4
127.3
127.7
127
123.9
125.4
124.6
124.5
124.8
124.1
124.2
122.8
122.3
121.1
121.7
122.2
122.2
122.7
121.7
121
119.8
120.2
116.6
116
118
117.1
116.2
113.3
114.3
113.6
113
112.9
112.7
112.5
113
111.9
110.9
109.8
108.3
109.2
109.2
108.7
109.8
110.8
110
109.6
109.5
110.8
111.6
113.1
114.3
114.1
113.8
112.6
112.7
111.5
110.7
110.4
109.7
110
111.3
109
108.2
107.2
108.7
110.3
110.3
109.5
109.5
109.4
109.6
111.3
110
109.5
110.693
109.195
108.095
108.199
106.87
105.278
108.711
111.192
109.641
109.42
109.935
111.126
110.733
110.34
111.766
111.294
111.54
112.008
111.007
114.963
112.045
110.703
108.894
107.51
111.35
112.964
115.203
115.182
115.191
112.346
110.774
113.07
111.138
109.092
107.971
107.051




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74428&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74428&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean115.1850413223140.663489801208794173.604840816636
Geometric Mean114.964728959010
Harmonic Mean114.753338580080
Quadratic Mean115.414123877367
Winsorized Mean ( 1 / 40 )115.1957190082640.661436444729507174.159921072044
Winsorized Mean ( 2 / 40 )115.1821818181820.657614429703508175.151542629794
Winsorized Mean ( 3 / 40 )115.1833966942150.656725551555613175.390460172252
Winsorized Mean ( 4 / 40 )115.1936446280990.655706102891438175.678774560942
Winsorized Mean ( 5 / 40 )115.2044297520660.652199889379109176.639756657641
Winsorized Mean ( 6 / 40 )115.1857851239670.646622332964547178.134560549245
Winsorized Mean ( 7 / 40 )115.1802314049590.643771643329268178.914732573966
Winsorized Mean ( 8 / 40 )115.1538512396690.638564073840369180.332492786708
Winsorized Mean ( 9 / 40 )115.0794710743800.622278885804616184.932308808101
Winsorized Mean ( 10 / 40 )115.0629421487600.610202463611427188.56518780303
Winsorized Mean ( 11 / 40 )115.0447603305790.606904491765077189.559909164604
Winsorized Mean ( 12 / 40 )114.996264462810.597940395668777192.320614723128
Winsorized Mean ( 13 / 40 )114.9729504132230.588678803764454195.306760967101
Winsorized Mean ( 14 / 40 )114.9505041322310.581603138304286197.644229478162
Winsorized Mean ( 15 / 40 )114.7635619834710.547412296696679209.647394981815
Winsorized Mean ( 16 / 40 )114.6978429752070.533554566288913214.969283784743
Winsorized Mean ( 17 / 40 )114.6704462809920.529079971894454216.735564323851
Winsorized Mean ( 18 / 40 )114.6555702479340.5267582902953217.662583314366
Winsorized Mean ( 19 / 40 )114.6398677685950.516776277976877221.836552206687
Winsorized Mean ( 20 / 40 )114.6266446280990.513953544847819223.029193547133
Winsorized Mean ( 21 / 40 )114.6058181818180.507470631944846225.837341054790
Winsorized Mean ( 22 / 40 )114.4058181818180.477541449746402239.572540232002
Winsorized Mean ( 23 / 40 )114.3868099173550.47476241605265240.934846672172
Winsorized Mean ( 24 / 40 )114.3074710743800.463269587853044246.740718733819
Winsorized Mean ( 25 / 40 )114.3074710743800.458525280429132249.293716079079
Winsorized Mean ( 26 / 40 )114.3074710743800.458525280429132249.293716079079
Winsorized Mean ( 27 / 40 )114.2050495867770.44185069244573258.469776192110
Winsorized Mean ( 28 / 40 )114.2187024793390.440679761766285259.187537956224
Winsorized Mean ( 29 / 40 )114.0988677685950.418428715149251272.684124290793
Winsorized Mean ( 30 / 40 )114.0740743801650.414976021439642274.893170897965
Winsorized Mean ( 31 / 40 )113.9037024793390.383726371145486296.835742978304
Winsorized Mean ( 32 / 40 )113.8151074380170.367837597751762309.416732094976
Winsorized Mean ( 33 / 40 )113.3241983471070.302807806109335374.244639869652
Winsorized Mean ( 34 / 40 )113.0713057851240.270829064050175417.500633403864
Winsorized Mean ( 35 / 40 )113.0134545454550.244922519372694461.425330896111
Winsorized Mean ( 36 / 40 )112.8944462809920.230546960117925489.680914566152
Winsorized Mean ( 37 / 40 )112.8455206611570.222125563880799508.025815172334
Winsorized Mean ( 38 / 40 )112.6140661157020.191360889181871588.490503974787
Winsorized Mean ( 39 / 40 )112.7046363636360.182016065043403619.201587160788
Winsorized Mean ( 40 / 40 )112.7039752066120.181464398402109621.080367273307
Trimmed Mean ( 1 / 40 )115.1202689075630.652749395628556176.362122551963
Trimmed Mean ( 2 / 40 )115.0422393162390.643050192711454178.90087060103
Trimmed Mean ( 3 / 40 )114.9686173913040.634434274814288181.214385721765
Trimmed Mean ( 4 / 40 )114.8919557522120.625133294179224183.787932624931
Trimmed Mean ( 5 / 40 )114.8097387387390.614998173786827186.683056360643
Trimmed Mean ( 6 / 40 )114.7221100917430.604508898092348189.777372101175
Trimmed Mean ( 7 / 40 )114.6347196261680.593996971232095192.988727515542
Trimmed Mean ( 8 / 40 )114.5449142857140.582706570788402196.573919066564
Trimmed Mean ( 9 / 40 )114.4554951456310.570951966694384200.464315427949
Trimmed Mean ( 10 / 40 )114.3724356435640.560646810410029204.000867426532
Trimmed Mean ( 11 / 40 )114.2880404040400.550952280288839207.437276317514
Trimmed Mean ( 12 / 40 )114.2022268041240.540413923050704211.323620530422
Trimmed Mean ( 13 / 40 )114.1179473684210.529798009507006215.398973421232
Trimmed Mean ( 14 / 40 )114.0323763440860.519015259754798219.709101420176
Trimmed Mean ( 15 / 40 )113.9451758241760.507647523827033224.457267052482
Trimmed Mean ( 16 / 40 )113.8710.499662323921751227.895909994272
Trimmed Mean ( 17 / 40 )113.7991264367820.492336183262546231.141098918778
Trimmed Mean ( 18 / 40 )113.7261647058820.484397377165462234.778655019504
Trimmed Mean ( 19 / 40 )113.6508915662650.47541736184493239.054987653849
Trimmed Mean ( 20 / 40 )113.5731358024690.466213401156186243.607617286018
Trimmed Mean ( 21 / 40 )113.4924556962030.455747375742055249.024924194928
Trimmed Mean ( 22 / 40 )113.4091428571430.444279197928884255.265480323696
Trimmed Mean ( 23 / 40 )113.3360533333330.435211649823097260.415945619566
Trimmed Mean ( 24 / 40 )113.2603287671230.424784740479026266.629937411124
Trimmed Mean ( 25 / 40 )113.1859718309860.41407706053475273.345187692394
Trimmed Mean ( 26 / 40 )113.1073043478260.401833064498099281.478340984957
Trimmed Mean ( 27 / 40 )113.0239402985070.386969004961396292.074917756741
Trimmed Mean ( 28 / 40 )112.9425076923080.371788526871147303.781584232293
Trimmed Mean ( 29 / 40 )112.8549682539680.353221152066819319.502293658278
Trimmed Mean ( 30 / 40 )112.7698852459020.334524307968875337.105204493522
Trimmed Mean ( 31 / 40 )112.7698852459020.311738889928992361.744680850016
Trimmed Mean ( 32 / 40 )112.5969824561400.289799220197510388.534456301852
Trimmed Mean ( 33 / 40 )112.5132363636360.265313546751746424.076485129179
Trimmed Mean ( 34 / 40 )112.4571320754720.250162745341022449.535888815778
Trimmed Mean ( 35 / 40 )112.4142745098040.238283848001449471.766237840512
Trimmed Mean ( 36 / 40 )112.3720.228412254844755491.970100625187
Trimmed Mean ( 37 / 40 )112.3346382978720.219005130960832512.93153637557
Trimmed Mean ( 38 / 40 )112.2975111111110.208676751189712538.140978670974
Trimmed Mean ( 39 / 40 )112.2740697674420.202633561754275554.074403052698
Trimmed Mean ( 40 / 40 )112.2414878048780.196157015013394572.202262545717
Median112.008
Midrange119.039
Midmean - Weighted Average at Xnp112.586278688525
Midmean - Weighted Average at X(n+1)p112.721983870968
Midmean - Empirical Distribution Function112.721983870968
Midmean - Empirical Distribution Function - Averaging112.721983870968
Midmean - Empirical Distribution Function - Interpolation112.721983870968
Midmean - Closest Observation112.721983870968
Midmean - True Basic - Statistics Graphics Toolkit112.721983870968
Midmean - MS Excel (old versions)112.721983870968
Number of observations121

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.185041322314 & 0.663489801208794 & 173.604840816636 \tabularnewline
Geometric Mean & 114.964728959010 &  &  \tabularnewline
Harmonic Mean & 114.753338580080 &  &  \tabularnewline
Quadratic Mean & 115.414123877367 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 115.195719008264 & 0.661436444729507 & 174.159921072044 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 115.182181818182 & 0.657614429703508 & 175.151542629794 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 115.183396694215 & 0.656725551555613 & 175.390460172252 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 115.193644628099 & 0.655706102891438 & 175.678774560942 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 115.204429752066 & 0.652199889379109 & 176.639756657641 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 115.185785123967 & 0.646622332964547 & 178.134560549245 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 115.180231404959 & 0.643771643329268 & 178.914732573966 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 115.153851239669 & 0.638564073840369 & 180.332492786708 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 115.079471074380 & 0.622278885804616 & 184.932308808101 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 115.062942148760 & 0.610202463611427 & 188.56518780303 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 115.044760330579 & 0.606904491765077 & 189.559909164604 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 114.99626446281 & 0.597940395668777 & 192.320614723128 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 114.972950413223 & 0.588678803764454 & 195.306760967101 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 114.950504132231 & 0.581603138304286 & 197.644229478162 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 114.763561983471 & 0.547412296696679 & 209.647394981815 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 114.697842975207 & 0.533554566288913 & 214.969283784743 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 114.670446280992 & 0.529079971894454 & 216.735564323851 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 114.655570247934 & 0.5267582902953 & 217.662583314366 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 114.639867768595 & 0.516776277976877 & 221.836552206687 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 114.626644628099 & 0.513953544847819 & 223.029193547133 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 114.605818181818 & 0.507470631944846 & 225.837341054790 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 114.405818181818 & 0.477541449746402 & 239.572540232002 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 114.386809917355 & 0.47476241605265 & 240.934846672172 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 114.307471074380 & 0.463269587853044 & 246.740718733819 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 114.307471074380 & 0.458525280429132 & 249.293716079079 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 114.307471074380 & 0.458525280429132 & 249.293716079079 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 114.205049586777 & 0.44185069244573 & 258.469776192110 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 114.218702479339 & 0.440679761766285 & 259.187537956224 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 114.098867768595 & 0.418428715149251 & 272.684124290793 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 114.074074380165 & 0.414976021439642 & 274.893170897965 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 113.903702479339 & 0.383726371145486 & 296.835742978304 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 113.815107438017 & 0.367837597751762 & 309.416732094976 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 113.324198347107 & 0.302807806109335 & 374.244639869652 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 113.071305785124 & 0.270829064050175 & 417.500633403864 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 113.013454545455 & 0.244922519372694 & 461.425330896111 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 112.894446280992 & 0.230546960117925 & 489.680914566152 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 112.845520661157 & 0.222125563880799 & 508.025815172334 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 112.614066115702 & 0.191360889181871 & 588.490503974787 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 112.704636363636 & 0.182016065043403 & 619.201587160788 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 112.703975206612 & 0.181464398402109 & 621.080367273307 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 115.120268907563 & 0.652749395628556 & 176.362122551963 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 115.042239316239 & 0.643050192711454 & 178.90087060103 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 114.968617391304 & 0.634434274814288 & 181.214385721765 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 114.891955752212 & 0.625133294179224 & 183.787932624931 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 114.809738738739 & 0.614998173786827 & 186.683056360643 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 114.722110091743 & 0.604508898092348 & 189.777372101175 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 114.634719626168 & 0.593996971232095 & 192.988727515542 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 114.544914285714 & 0.582706570788402 & 196.573919066564 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 114.455495145631 & 0.570951966694384 & 200.464315427949 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 114.372435643564 & 0.560646810410029 & 204.000867426532 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 114.288040404040 & 0.550952280288839 & 207.437276317514 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 114.202226804124 & 0.540413923050704 & 211.323620530422 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 114.117947368421 & 0.529798009507006 & 215.398973421232 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 114.032376344086 & 0.519015259754798 & 219.709101420176 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 113.945175824176 & 0.507647523827033 & 224.457267052482 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 113.871 & 0.499662323921751 & 227.895909994272 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 113.799126436782 & 0.492336183262546 & 231.141098918778 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 113.726164705882 & 0.484397377165462 & 234.778655019504 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 113.650891566265 & 0.47541736184493 & 239.054987653849 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 113.573135802469 & 0.466213401156186 & 243.607617286018 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 113.492455696203 & 0.455747375742055 & 249.024924194928 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 113.409142857143 & 0.444279197928884 & 255.265480323696 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 113.336053333333 & 0.435211649823097 & 260.415945619566 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 113.260328767123 & 0.424784740479026 & 266.629937411124 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 113.185971830986 & 0.41407706053475 & 273.345187692394 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 113.107304347826 & 0.401833064498099 & 281.478340984957 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 113.023940298507 & 0.386969004961396 & 292.074917756741 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 112.942507692308 & 0.371788526871147 & 303.781584232293 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 112.854968253968 & 0.353221152066819 & 319.502293658278 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 112.769885245902 & 0.334524307968875 & 337.105204493522 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 112.769885245902 & 0.311738889928992 & 361.744680850016 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 112.596982456140 & 0.289799220197510 & 388.534456301852 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 112.513236363636 & 0.265313546751746 & 424.076485129179 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 112.457132075472 & 0.250162745341022 & 449.535888815778 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 112.414274509804 & 0.238283848001449 & 471.766237840512 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 112.372 & 0.228412254844755 & 491.970100625187 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 112.334638297872 & 0.219005130960832 & 512.93153637557 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 112.297511111111 & 0.208676751189712 & 538.140978670974 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 112.274069767442 & 0.202633561754275 & 554.074403052698 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 112.241487804878 & 0.196157015013394 & 572.202262545717 \tabularnewline
Median & 112.008 &  &  \tabularnewline
Midrange & 119.039 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.586278688525 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.721983870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.721983870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.721983870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.721983870968 &  &  \tabularnewline
Midmean - Closest Observation & 112.721983870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.721983870968 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.721983870968 &  &  \tabularnewline
Number of observations & 121 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74428&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]115.185041322314[/C][C]0.663489801208794[/C][C]173.604840816636[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.964728959010[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]114.753338580080[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.414123877367[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]115.195719008264[/C][C]0.661436444729507[/C][C]174.159921072044[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]115.182181818182[/C][C]0.657614429703508[/C][C]175.151542629794[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]115.183396694215[/C][C]0.656725551555613[/C][C]175.390460172252[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]115.193644628099[/C][C]0.655706102891438[/C][C]175.678774560942[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]115.204429752066[/C][C]0.652199889379109[/C][C]176.639756657641[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]115.185785123967[/C][C]0.646622332964547[/C][C]178.134560549245[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]115.180231404959[/C][C]0.643771643329268[/C][C]178.914732573966[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]115.153851239669[/C][C]0.638564073840369[/C][C]180.332492786708[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]115.079471074380[/C][C]0.622278885804616[/C][C]184.932308808101[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]115.062942148760[/C][C]0.610202463611427[/C][C]188.56518780303[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]115.044760330579[/C][C]0.606904491765077[/C][C]189.559909164604[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]114.99626446281[/C][C]0.597940395668777[/C][C]192.320614723128[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]114.972950413223[/C][C]0.588678803764454[/C][C]195.306760967101[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]114.950504132231[/C][C]0.581603138304286[/C][C]197.644229478162[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]114.763561983471[/C][C]0.547412296696679[/C][C]209.647394981815[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]114.697842975207[/C][C]0.533554566288913[/C][C]214.969283784743[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]114.670446280992[/C][C]0.529079971894454[/C][C]216.735564323851[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]114.655570247934[/C][C]0.5267582902953[/C][C]217.662583314366[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]114.639867768595[/C][C]0.516776277976877[/C][C]221.836552206687[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]114.626644628099[/C][C]0.513953544847819[/C][C]223.029193547133[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]114.605818181818[/C][C]0.507470631944846[/C][C]225.837341054790[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]114.405818181818[/C][C]0.477541449746402[/C][C]239.572540232002[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]114.386809917355[/C][C]0.47476241605265[/C][C]240.934846672172[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]114.307471074380[/C][C]0.463269587853044[/C][C]246.740718733819[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]114.307471074380[/C][C]0.458525280429132[/C][C]249.293716079079[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]114.307471074380[/C][C]0.458525280429132[/C][C]249.293716079079[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]114.205049586777[/C][C]0.44185069244573[/C][C]258.469776192110[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]114.218702479339[/C][C]0.440679761766285[/C][C]259.187537956224[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]114.098867768595[/C][C]0.418428715149251[/C][C]272.684124290793[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]114.074074380165[/C][C]0.414976021439642[/C][C]274.893170897965[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]113.903702479339[/C][C]0.383726371145486[/C][C]296.835742978304[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]113.815107438017[/C][C]0.367837597751762[/C][C]309.416732094976[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]113.324198347107[/C][C]0.302807806109335[/C][C]374.244639869652[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]113.071305785124[/C][C]0.270829064050175[/C][C]417.500633403864[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]113.013454545455[/C][C]0.244922519372694[/C][C]461.425330896111[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]112.894446280992[/C][C]0.230546960117925[/C][C]489.680914566152[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]112.845520661157[/C][C]0.222125563880799[/C][C]508.025815172334[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]112.614066115702[/C][C]0.191360889181871[/C][C]588.490503974787[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]112.704636363636[/C][C]0.182016065043403[/C][C]619.201587160788[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]112.703975206612[/C][C]0.181464398402109[/C][C]621.080367273307[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]115.120268907563[/C][C]0.652749395628556[/C][C]176.362122551963[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]115.042239316239[/C][C]0.643050192711454[/C][C]178.90087060103[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]114.968617391304[/C][C]0.634434274814288[/C][C]181.214385721765[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]114.891955752212[/C][C]0.625133294179224[/C][C]183.787932624931[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]114.809738738739[/C][C]0.614998173786827[/C][C]186.683056360643[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]114.722110091743[/C][C]0.604508898092348[/C][C]189.777372101175[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]114.634719626168[/C][C]0.593996971232095[/C][C]192.988727515542[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]114.544914285714[/C][C]0.582706570788402[/C][C]196.573919066564[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]114.455495145631[/C][C]0.570951966694384[/C][C]200.464315427949[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]114.372435643564[/C][C]0.560646810410029[/C][C]204.000867426532[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]114.288040404040[/C][C]0.550952280288839[/C][C]207.437276317514[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]114.202226804124[/C][C]0.540413923050704[/C][C]211.323620530422[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]114.117947368421[/C][C]0.529798009507006[/C][C]215.398973421232[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]114.032376344086[/C][C]0.519015259754798[/C][C]219.709101420176[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]113.945175824176[/C][C]0.507647523827033[/C][C]224.457267052482[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]113.871[/C][C]0.499662323921751[/C][C]227.895909994272[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]113.799126436782[/C][C]0.492336183262546[/C][C]231.141098918778[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]113.726164705882[/C][C]0.484397377165462[/C][C]234.778655019504[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]113.650891566265[/C][C]0.47541736184493[/C][C]239.054987653849[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]113.573135802469[/C][C]0.466213401156186[/C][C]243.607617286018[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]113.492455696203[/C][C]0.455747375742055[/C][C]249.024924194928[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]113.409142857143[/C][C]0.444279197928884[/C][C]255.265480323696[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]113.336053333333[/C][C]0.435211649823097[/C][C]260.415945619566[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]113.260328767123[/C][C]0.424784740479026[/C][C]266.629937411124[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]113.185971830986[/C][C]0.41407706053475[/C][C]273.345187692394[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]113.107304347826[/C][C]0.401833064498099[/C][C]281.478340984957[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]113.023940298507[/C][C]0.386969004961396[/C][C]292.074917756741[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]112.942507692308[/C][C]0.371788526871147[/C][C]303.781584232293[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]112.854968253968[/C][C]0.353221152066819[/C][C]319.502293658278[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]112.769885245902[/C][C]0.334524307968875[/C][C]337.105204493522[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]112.769885245902[/C][C]0.311738889928992[/C][C]361.744680850016[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]112.596982456140[/C][C]0.289799220197510[/C][C]388.534456301852[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]112.513236363636[/C][C]0.265313546751746[/C][C]424.076485129179[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]112.457132075472[/C][C]0.250162745341022[/C][C]449.535888815778[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]112.414274509804[/C][C]0.238283848001449[/C][C]471.766237840512[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]112.372[/C][C]0.228412254844755[/C][C]491.970100625187[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]112.334638297872[/C][C]0.219005130960832[/C][C]512.93153637557[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]112.297511111111[/C][C]0.208676751189712[/C][C]538.140978670974[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]112.274069767442[/C][C]0.202633561754275[/C][C]554.074403052698[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]112.241487804878[/C][C]0.196157015013394[/C][C]572.202262545717[/C][/ROW]
[ROW][C]Median[/C][C]112.008[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]119.039[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.586278688525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.721983870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.721983870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.721983870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.721983870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.721983870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.721983870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.721983870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]121[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74428&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 Mean115.1850413223140.663489801208794173.604840816636
Geometric Mean114.964728959010
Harmonic Mean114.753338580080
Quadratic Mean115.414123877367
Winsorized Mean ( 1 / 40 )115.1957190082640.661436444729507174.159921072044
Winsorized Mean ( 2 / 40 )115.1821818181820.657614429703508175.151542629794
Winsorized Mean ( 3 / 40 )115.1833966942150.656725551555613175.390460172252
Winsorized Mean ( 4 / 40 )115.1936446280990.655706102891438175.678774560942
Winsorized Mean ( 5 / 40 )115.2044297520660.652199889379109176.639756657641
Winsorized Mean ( 6 / 40 )115.1857851239670.646622332964547178.134560549245
Winsorized Mean ( 7 / 40 )115.1802314049590.643771643329268178.914732573966
Winsorized Mean ( 8 / 40 )115.1538512396690.638564073840369180.332492786708
Winsorized Mean ( 9 / 40 )115.0794710743800.622278885804616184.932308808101
Winsorized Mean ( 10 / 40 )115.0629421487600.610202463611427188.56518780303
Winsorized Mean ( 11 / 40 )115.0447603305790.606904491765077189.559909164604
Winsorized Mean ( 12 / 40 )114.996264462810.597940395668777192.320614723128
Winsorized Mean ( 13 / 40 )114.9729504132230.588678803764454195.306760967101
Winsorized Mean ( 14 / 40 )114.9505041322310.581603138304286197.644229478162
Winsorized Mean ( 15 / 40 )114.7635619834710.547412296696679209.647394981815
Winsorized Mean ( 16 / 40 )114.6978429752070.533554566288913214.969283784743
Winsorized Mean ( 17 / 40 )114.6704462809920.529079971894454216.735564323851
Winsorized Mean ( 18 / 40 )114.6555702479340.5267582902953217.662583314366
Winsorized Mean ( 19 / 40 )114.6398677685950.516776277976877221.836552206687
Winsorized Mean ( 20 / 40 )114.6266446280990.513953544847819223.029193547133
Winsorized Mean ( 21 / 40 )114.6058181818180.507470631944846225.837341054790
Winsorized Mean ( 22 / 40 )114.4058181818180.477541449746402239.572540232002
Winsorized Mean ( 23 / 40 )114.3868099173550.47476241605265240.934846672172
Winsorized Mean ( 24 / 40 )114.3074710743800.463269587853044246.740718733819
Winsorized Mean ( 25 / 40 )114.3074710743800.458525280429132249.293716079079
Winsorized Mean ( 26 / 40 )114.3074710743800.458525280429132249.293716079079
Winsorized Mean ( 27 / 40 )114.2050495867770.44185069244573258.469776192110
Winsorized Mean ( 28 / 40 )114.2187024793390.440679761766285259.187537956224
Winsorized Mean ( 29 / 40 )114.0988677685950.418428715149251272.684124290793
Winsorized Mean ( 30 / 40 )114.0740743801650.414976021439642274.893170897965
Winsorized Mean ( 31 / 40 )113.9037024793390.383726371145486296.835742978304
Winsorized Mean ( 32 / 40 )113.8151074380170.367837597751762309.416732094976
Winsorized Mean ( 33 / 40 )113.3241983471070.302807806109335374.244639869652
Winsorized Mean ( 34 / 40 )113.0713057851240.270829064050175417.500633403864
Winsorized Mean ( 35 / 40 )113.0134545454550.244922519372694461.425330896111
Winsorized Mean ( 36 / 40 )112.8944462809920.230546960117925489.680914566152
Winsorized Mean ( 37 / 40 )112.8455206611570.222125563880799508.025815172334
Winsorized Mean ( 38 / 40 )112.6140661157020.191360889181871588.490503974787
Winsorized Mean ( 39 / 40 )112.7046363636360.182016065043403619.201587160788
Winsorized Mean ( 40 / 40 )112.7039752066120.181464398402109621.080367273307
Trimmed Mean ( 1 / 40 )115.1202689075630.652749395628556176.362122551963
Trimmed Mean ( 2 / 40 )115.0422393162390.643050192711454178.90087060103
Trimmed Mean ( 3 / 40 )114.9686173913040.634434274814288181.214385721765
Trimmed Mean ( 4 / 40 )114.8919557522120.625133294179224183.787932624931
Trimmed Mean ( 5 / 40 )114.8097387387390.614998173786827186.683056360643
Trimmed Mean ( 6 / 40 )114.7221100917430.604508898092348189.777372101175
Trimmed Mean ( 7 / 40 )114.6347196261680.593996971232095192.988727515542
Trimmed Mean ( 8 / 40 )114.5449142857140.582706570788402196.573919066564
Trimmed Mean ( 9 / 40 )114.4554951456310.570951966694384200.464315427949
Trimmed Mean ( 10 / 40 )114.3724356435640.560646810410029204.000867426532
Trimmed Mean ( 11 / 40 )114.2880404040400.550952280288839207.437276317514
Trimmed Mean ( 12 / 40 )114.2022268041240.540413923050704211.323620530422
Trimmed Mean ( 13 / 40 )114.1179473684210.529798009507006215.398973421232
Trimmed Mean ( 14 / 40 )114.0323763440860.519015259754798219.709101420176
Trimmed Mean ( 15 / 40 )113.9451758241760.507647523827033224.457267052482
Trimmed Mean ( 16 / 40 )113.8710.499662323921751227.895909994272
Trimmed Mean ( 17 / 40 )113.7991264367820.492336183262546231.141098918778
Trimmed Mean ( 18 / 40 )113.7261647058820.484397377165462234.778655019504
Trimmed Mean ( 19 / 40 )113.6508915662650.47541736184493239.054987653849
Trimmed Mean ( 20 / 40 )113.5731358024690.466213401156186243.607617286018
Trimmed Mean ( 21 / 40 )113.4924556962030.455747375742055249.024924194928
Trimmed Mean ( 22 / 40 )113.4091428571430.444279197928884255.265480323696
Trimmed Mean ( 23 / 40 )113.3360533333330.435211649823097260.415945619566
Trimmed Mean ( 24 / 40 )113.2603287671230.424784740479026266.629937411124
Trimmed Mean ( 25 / 40 )113.1859718309860.41407706053475273.345187692394
Trimmed Mean ( 26 / 40 )113.1073043478260.401833064498099281.478340984957
Trimmed Mean ( 27 / 40 )113.0239402985070.386969004961396292.074917756741
Trimmed Mean ( 28 / 40 )112.9425076923080.371788526871147303.781584232293
Trimmed Mean ( 29 / 40 )112.8549682539680.353221152066819319.502293658278
Trimmed Mean ( 30 / 40 )112.7698852459020.334524307968875337.105204493522
Trimmed Mean ( 31 / 40 )112.7698852459020.311738889928992361.744680850016
Trimmed Mean ( 32 / 40 )112.5969824561400.289799220197510388.534456301852
Trimmed Mean ( 33 / 40 )112.5132363636360.265313546751746424.076485129179
Trimmed Mean ( 34 / 40 )112.4571320754720.250162745341022449.535888815778
Trimmed Mean ( 35 / 40 )112.4142745098040.238283848001449471.766237840512
Trimmed Mean ( 36 / 40 )112.3720.228412254844755491.970100625187
Trimmed Mean ( 37 / 40 )112.3346382978720.219005130960832512.93153637557
Trimmed Mean ( 38 / 40 )112.2975111111110.208676751189712538.140978670974
Trimmed Mean ( 39 / 40 )112.2740697674420.202633561754275554.074403052698
Trimmed Mean ( 40 / 40 )112.2414878048780.196157015013394572.202262545717
Median112.008
Midrange119.039
Midmean - Weighted Average at Xnp112.586278688525
Midmean - Weighted Average at X(n+1)p112.721983870968
Midmean - Empirical Distribution Function112.721983870968
Midmean - Empirical Distribution Function - Averaging112.721983870968
Midmean - Empirical Distribution Function - Interpolation112.721983870968
Midmean - Closest Observation112.721983870968
Midmean - True Basic - Statistics Graphics Toolkit112.721983870968
Midmean - MS Excel (old versions)112.721983870968
Number of observations121



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')