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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 computationTue, 15 Dec 2015 19:40:07 +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/2015/Dec/15/t1450208413to47dj88ll2cj9t.htm/, Retrieved Sat, 18 May 2024 14:37:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286579, Retrieved Sat, 18 May 2024 14:37:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-12-15 19:40:07] [9d441e5437781f0cd4d5053adc3d2c6c] [Current]
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Dataseries X:
156209
152539
153769
155094
152729
151606
149974
147955
149158
163391
166540
156816
152363
150083
150829
155755
153866
151148
149249
146921
149763
164849
168530
159513
155122
152847
153809
158166
155661
153965
152954
151608
153817
170179
173839
166808
162583
160290
161538
165579
162893
160799
158734
155668
157466
171491
173947
166698
162173
158608
158635
160630
158579
155376
150347
147207
149905
161333
163547
155522
151682




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286579&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286579&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286579&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean157354.983606557864.226805794315182.076027440426
Geometric Mean157214.963438057
Harmonic Mean157077.303921126
Quadratic Mean157497.314720382
Winsorized Mean ( 1 / 20 )157357.901639344862.730258075726182.395250620191
Winsorized Mean ( 2 / 20 )157305.442622951834.856451299103188.422144164031
Winsorized Mean ( 3 / 20 )157300.081967213806.617080723775195.012089039905
Winsorized Mean ( 4 / 20 )157197.918032787778.07331762048202.034839741752
Winsorized Mean ( 5 / 20 )157098.901639344738.354108814116212.769049110682
Winsorized Mean ( 6 / 20 )157102.049180328733.69099167917214.125634581903
Winsorized Mean ( 7 / 20 )157091.836065574728.463118388734215.648304080295
Winsorized Mean ( 8 / 20 )156980.098360656699.578972018256224.392248251509
Winsorized Mean ( 9 / 20 )156911.344262295671.55592351437233.653428952202
Winsorized Mean ( 10 / 20 )156776.918032787618.213953668933253.596537416146
Winsorized Mean ( 11 / 20 )156806.31147541603.986491788378259.618904739265
Winsorized Mean ( 12 / 20 )156798.442622951572.541052301767273.864104578317
Winsorized Mean ( 13 / 20 )156732.803278689560.872249960521279.444745732599
Winsorized Mean ( 14 / 20 )156655.68852459542.117578711555288.969947989719
Winsorized Mean ( 15 / 20 )156667490.879249617376319.155882270674
Winsorized Mean ( 16 / 20 )156659.393442623475.317874815898329.588685263101
Winsorized Mean ( 17 / 20 )156563.524590164443.631957812616352.913088953556
Winsorized Mean ( 18 / 20 )156548.475409836430.724168203529363.454124394206
Winsorized Mean ( 19 / 20 )156475.901639344409.359242544051382.245923328593
Winsorized Mean ( 20 / 20 )156488.360655738332.780101858239470.245545878222
Trimmed Mean ( 1 / 20 )157250.610169492828.48262855619189.8055610937
Trimmed Mean ( 2 / 20 )157135.789473684785.999826513163199.918351344639
Trimmed Mean ( 3 / 20 )157041.709090909752.36063629907208.731958470623
Trimmed Mean ( 4 / 20 )156942.58490566724.317442292377216.67652294684
Trimmed Mean ( 5 / 20 )156866.235294118700.738942516684223.858309816117
Trimmed Mean ( 6 / 20 )156808.306122449684.709192208362229.01446030935
Trimmed Mean ( 7 / 20 )156744.765957447665.326288750186235.590820034921
Trimmed Mean ( 8 / 20 )156677.555555556641.587265103497244.203032194352
Trimmed Mean ( 9 / 20 )156623.906976744619.08915501224252.990874914692
Trimmed Mean ( 10 / 20 )156576.390243902597.272166867579262.152497520643
Trimmed Mean ( 11 / 20 )156545.025641026582.80787996471268.6048542283
Trimmed Mean ( 12 / 20 )156505.864864865566.409304517049276.312312698165
Trimmed Mean ( 13 / 20 )156463.371428571551.898331408317283.50035237344
Trimmed Mean ( 14 / 20 )156425.060606061534.2362892616292.801263692261
Trimmed Mean ( 15 / 20 )156392.64516129514.126547219331304.19095455612
Trimmed Mean ( 16 / 20 )156354.172413793500.083291261988312.656261758365
Trimmed Mean ( 17 / 20 )156311.074074074482.858921094662323.719967148397
Trimmed Mean ( 18 / 20 )156274.84466.668450044211334.873377416439
Trimmed Mean ( 19 / 20 )156234.52173913444.360293715238351.594244465171
Trimmed Mean ( 20 / 20 )156197.619047619415.976896543606375.495899761455
Median155668
Midrange160434
Midmean - Weighted Average at Xnp156221.133333333
Midmean - Weighted Average at X(n+1)p156392.64516129
Midmean - Empirical Distribution Function156392.64516129
Midmean - Empirical Distribution Function - Averaging156392.64516129
Midmean - Empirical Distribution Function - Interpolation156392.64516129
Midmean - Closest Observation156245.4375
Midmean - True Basic - Statistics Graphics Toolkit156392.64516129
Midmean - MS Excel (old versions)156392.64516129
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 157354.983606557 & 864.226805794315 & 182.076027440426 \tabularnewline
Geometric Mean & 157214.963438057 &  &  \tabularnewline
Harmonic Mean & 157077.303921126 &  &  \tabularnewline
Quadratic Mean & 157497.314720382 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 157357.901639344 & 862.730258075726 & 182.395250620191 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 157305.442622951 & 834.856451299103 & 188.422144164031 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 157300.081967213 & 806.617080723775 & 195.012089039905 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 157197.918032787 & 778.07331762048 & 202.034839741752 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 157098.901639344 & 738.354108814116 & 212.769049110682 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 157102.049180328 & 733.69099167917 & 214.125634581903 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 157091.836065574 & 728.463118388734 & 215.648304080295 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 156980.098360656 & 699.578972018256 & 224.392248251509 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 156911.344262295 & 671.55592351437 & 233.653428952202 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 156776.918032787 & 618.213953668933 & 253.596537416146 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 156806.31147541 & 603.986491788378 & 259.618904739265 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 156798.442622951 & 572.541052301767 & 273.864104578317 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 156732.803278689 & 560.872249960521 & 279.444745732599 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 156655.68852459 & 542.117578711555 & 288.969947989719 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 156667 & 490.879249617376 & 319.155882270674 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 156659.393442623 & 475.317874815898 & 329.588685263101 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 156563.524590164 & 443.631957812616 & 352.913088953556 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 156548.475409836 & 430.724168203529 & 363.454124394206 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 156475.901639344 & 409.359242544051 & 382.245923328593 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 156488.360655738 & 332.780101858239 & 470.245545878222 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 157250.610169492 & 828.48262855619 & 189.8055610937 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 157135.789473684 & 785.999826513163 & 199.918351344639 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 157041.709090909 & 752.36063629907 & 208.731958470623 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 156942.58490566 & 724.317442292377 & 216.67652294684 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 156866.235294118 & 700.738942516684 & 223.858309816117 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 156808.306122449 & 684.709192208362 & 229.01446030935 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 156744.765957447 & 665.326288750186 & 235.590820034921 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 156677.555555556 & 641.587265103497 & 244.203032194352 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 156623.906976744 & 619.08915501224 & 252.990874914692 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 156576.390243902 & 597.272166867579 & 262.152497520643 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 156545.025641026 & 582.80787996471 & 268.6048542283 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 156505.864864865 & 566.409304517049 & 276.312312698165 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 156463.371428571 & 551.898331408317 & 283.50035237344 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 156425.060606061 & 534.2362892616 & 292.801263692261 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 156392.64516129 & 514.126547219331 & 304.19095455612 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 156354.172413793 & 500.083291261988 & 312.656261758365 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 156311.074074074 & 482.858921094662 & 323.719967148397 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 156274.84 & 466.668450044211 & 334.873377416439 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 156234.52173913 & 444.360293715238 & 351.594244465171 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 156197.619047619 & 415.976896543606 & 375.495899761455 \tabularnewline
Median & 155668 &  &  \tabularnewline
Midrange & 160434 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 156221.133333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 156392.64516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 156392.64516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 156392.64516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 156392.64516129 &  &  \tabularnewline
Midmean - Closest Observation & 156245.4375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 156392.64516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 156392.64516129 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286579&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]157354.983606557[/C][C]864.226805794315[/C][C]182.076027440426[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]157214.963438057[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]157077.303921126[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]157497.314720382[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]157357.901639344[/C][C]862.730258075726[/C][C]182.395250620191[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]157305.442622951[/C][C]834.856451299103[/C][C]188.422144164031[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]157300.081967213[/C][C]806.617080723775[/C][C]195.012089039905[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]157197.918032787[/C][C]778.07331762048[/C][C]202.034839741752[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]157098.901639344[/C][C]738.354108814116[/C][C]212.769049110682[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]157102.049180328[/C][C]733.69099167917[/C][C]214.125634581903[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]157091.836065574[/C][C]728.463118388734[/C][C]215.648304080295[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]156980.098360656[/C][C]699.578972018256[/C][C]224.392248251509[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]156911.344262295[/C][C]671.55592351437[/C][C]233.653428952202[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]156776.918032787[/C][C]618.213953668933[/C][C]253.596537416146[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]156806.31147541[/C][C]603.986491788378[/C][C]259.618904739265[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]156798.442622951[/C][C]572.541052301767[/C][C]273.864104578317[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]156732.803278689[/C][C]560.872249960521[/C][C]279.444745732599[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]156655.68852459[/C][C]542.117578711555[/C][C]288.969947989719[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]156667[/C][C]490.879249617376[/C][C]319.155882270674[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]156659.393442623[/C][C]475.317874815898[/C][C]329.588685263101[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]156563.524590164[/C][C]443.631957812616[/C][C]352.913088953556[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]156548.475409836[/C][C]430.724168203529[/C][C]363.454124394206[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]156475.901639344[/C][C]409.359242544051[/C][C]382.245923328593[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]156488.360655738[/C][C]332.780101858239[/C][C]470.245545878222[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]157250.610169492[/C][C]828.48262855619[/C][C]189.8055610937[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]157135.789473684[/C][C]785.999826513163[/C][C]199.918351344639[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]157041.709090909[/C][C]752.36063629907[/C][C]208.731958470623[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]156942.58490566[/C][C]724.317442292377[/C][C]216.67652294684[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]156866.235294118[/C][C]700.738942516684[/C][C]223.858309816117[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]156808.306122449[/C][C]684.709192208362[/C][C]229.01446030935[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]156744.765957447[/C][C]665.326288750186[/C][C]235.590820034921[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]156677.555555556[/C][C]641.587265103497[/C][C]244.203032194352[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]156623.906976744[/C][C]619.08915501224[/C][C]252.990874914692[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]156576.390243902[/C][C]597.272166867579[/C][C]262.152497520643[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]156545.025641026[/C][C]582.80787996471[/C][C]268.6048542283[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]156505.864864865[/C][C]566.409304517049[/C][C]276.312312698165[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]156463.371428571[/C][C]551.898331408317[/C][C]283.50035237344[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]156425.060606061[/C][C]534.2362892616[/C][C]292.801263692261[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]156392.64516129[/C][C]514.126547219331[/C][C]304.19095455612[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]156354.172413793[/C][C]500.083291261988[/C][C]312.656261758365[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]156311.074074074[/C][C]482.858921094662[/C][C]323.719967148397[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]156274.84[/C][C]466.668450044211[/C][C]334.873377416439[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]156234.52173913[/C][C]444.360293715238[/C][C]351.594244465171[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]156197.619047619[/C][C]415.976896543606[/C][C]375.495899761455[/C][/ROW]
[ROW][C]Median[/C][C]155668[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]160434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]156221.133333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]156392.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]156392.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]156392.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]156392.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]156245.4375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]156392.64516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]156392.64516129[/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=286579&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286579&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 Mean157354.983606557864.226805794315182.076027440426
Geometric Mean157214.963438057
Harmonic Mean157077.303921126
Quadratic Mean157497.314720382
Winsorized Mean ( 1 / 20 )157357.901639344862.730258075726182.395250620191
Winsorized Mean ( 2 / 20 )157305.442622951834.856451299103188.422144164031
Winsorized Mean ( 3 / 20 )157300.081967213806.617080723775195.012089039905
Winsorized Mean ( 4 / 20 )157197.918032787778.07331762048202.034839741752
Winsorized Mean ( 5 / 20 )157098.901639344738.354108814116212.769049110682
Winsorized Mean ( 6 / 20 )157102.049180328733.69099167917214.125634581903
Winsorized Mean ( 7 / 20 )157091.836065574728.463118388734215.648304080295
Winsorized Mean ( 8 / 20 )156980.098360656699.578972018256224.392248251509
Winsorized Mean ( 9 / 20 )156911.344262295671.55592351437233.653428952202
Winsorized Mean ( 10 / 20 )156776.918032787618.213953668933253.596537416146
Winsorized Mean ( 11 / 20 )156806.31147541603.986491788378259.618904739265
Winsorized Mean ( 12 / 20 )156798.442622951572.541052301767273.864104578317
Winsorized Mean ( 13 / 20 )156732.803278689560.872249960521279.444745732599
Winsorized Mean ( 14 / 20 )156655.68852459542.117578711555288.969947989719
Winsorized Mean ( 15 / 20 )156667490.879249617376319.155882270674
Winsorized Mean ( 16 / 20 )156659.393442623475.317874815898329.588685263101
Winsorized Mean ( 17 / 20 )156563.524590164443.631957812616352.913088953556
Winsorized Mean ( 18 / 20 )156548.475409836430.724168203529363.454124394206
Winsorized Mean ( 19 / 20 )156475.901639344409.359242544051382.245923328593
Winsorized Mean ( 20 / 20 )156488.360655738332.780101858239470.245545878222
Trimmed Mean ( 1 / 20 )157250.610169492828.48262855619189.8055610937
Trimmed Mean ( 2 / 20 )157135.789473684785.999826513163199.918351344639
Trimmed Mean ( 3 / 20 )157041.709090909752.36063629907208.731958470623
Trimmed Mean ( 4 / 20 )156942.58490566724.317442292377216.67652294684
Trimmed Mean ( 5 / 20 )156866.235294118700.738942516684223.858309816117
Trimmed Mean ( 6 / 20 )156808.306122449684.709192208362229.01446030935
Trimmed Mean ( 7 / 20 )156744.765957447665.326288750186235.590820034921
Trimmed Mean ( 8 / 20 )156677.555555556641.587265103497244.203032194352
Trimmed Mean ( 9 / 20 )156623.906976744619.08915501224252.990874914692
Trimmed Mean ( 10 / 20 )156576.390243902597.272166867579262.152497520643
Trimmed Mean ( 11 / 20 )156545.025641026582.80787996471268.6048542283
Trimmed Mean ( 12 / 20 )156505.864864865566.409304517049276.312312698165
Trimmed Mean ( 13 / 20 )156463.371428571551.898331408317283.50035237344
Trimmed Mean ( 14 / 20 )156425.060606061534.2362892616292.801263692261
Trimmed Mean ( 15 / 20 )156392.64516129514.126547219331304.19095455612
Trimmed Mean ( 16 / 20 )156354.172413793500.083291261988312.656261758365
Trimmed Mean ( 17 / 20 )156311.074074074482.858921094662323.719967148397
Trimmed Mean ( 18 / 20 )156274.84466.668450044211334.873377416439
Trimmed Mean ( 19 / 20 )156234.52173913444.360293715238351.594244465171
Trimmed Mean ( 20 / 20 )156197.619047619415.976896543606375.495899761455
Median155668
Midrange160434
Midmean - Weighted Average at Xnp156221.133333333
Midmean - Weighted Average at X(n+1)p156392.64516129
Midmean - Empirical Distribution Function156392.64516129
Midmean - Empirical Distribution Function - Averaging156392.64516129
Midmean - Empirical Distribution Function - Interpolation156392.64516129
Midmean - Closest Observation156245.4375
Midmean - True Basic - Statistics Graphics Toolkit156392.64516129
Midmean - MS Excel (old versions)156392.64516129
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')