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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, 25 Nov 2015 11:24:52 +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/Nov/25/t1448450715uq0vygo9on6ngwo.htm/, Retrieved Wed, 15 May 2024 12:20:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284109, Retrieved Wed, 15 May 2024 12:20:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
- RM D  [Central Tendency] [Central Tendency ...] [2015-11-25 11:02:04] [22b6f4a061c8797aa483199554a73d13]
- RM      [Central Tendency] [Central Tendency ...] [2015-11-25 11:08:52] [22b6f4a061c8797aa483199554a73d13]
- RM D        [Central Tendency] [Central Tendency ...] [2015-11-25 11:24:52] [20fcaaf1d4bc4a12bf87c6c50d624c14] [Current]
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Dataseries X:
276444
268606
267679
269879
265641
262525
258597
253849
256221
286895
294610
280363
269926
264341
263269
271045
267915
262078
257751
253271
257638
287452
298152
284793
274560
268270
267577
271866
268546
264722
262425
258973
262751
296186
304659
295442
285466
279575
279985
286012
281337
276270
271472
265637
268974
299299
305452
295468
285584
278204
276505
279732
276980
271832
263105
256162
260705
285857
291870
280358
270981




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' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284109&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284109&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284109&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' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean274553.0983606561703.02832052039161.214640445182
Geometric Mean274240.727793306
Harmonic Mean273932.943342169
Quadratic Mean274869.827640404
Winsorized Mean ( 1 / 20 )274549.5737704921697.19089646646161.767055398483
Winsorized Mean ( 2 / 20 )274449.6721311481634.07657847745167.953984376219
Winsorized Mean ( 3 / 20 )274396.1639344261619.48944902657169.433745986649
Winsorized Mean ( 4 / 20 )274360.1639344261571.86658664747174.544179681045
Winsorized Mean ( 5 / 20 )274310.5737704921556.7484169204176.207388932594
Winsorized Mean ( 6 / 20 )274391.2295081971541.68595481541177.981273456597
Winsorized Mean ( 7 / 20 )274338.9016393441512.82313130607181.342349916674
Winsorized Mean ( 8 / 20 )274206.7049180331397.1955072337196.255072034217
Winsorized Mean ( 9 / 20 )273757.4426229511235.5032574598221.575654268851
Winsorized Mean ( 10 / 20 )273723.0163934431209.8746219403226.240811592913
Winsorized Mean ( 11 / 20 )273581.8196721311178.61540293569232.121367997308
Winsorized Mean ( 12 / 20 )273595.7868852461166.34362493599234.575626801459
Winsorized Mean ( 13 / 20 )273613.0491803281144.55739540682239.05576974851
Winsorized Mean ( 14 / 20 )273623.6065573771134.09676977425241.270069583077
Winsorized Mean ( 15 / 20 )273721.7213114751065.95920992791256.784423608467
Winsorized Mean ( 16 / 20 )272915.163934426901.383726557625302.773564569095
Winsorized Mean ( 17 / 20 )272898.721311475821.547249149632332.176538347548
Winsorized Mean ( 18 / 20 )272898.426229508821.149974141295332.336887077038
Winsorized Mean ( 19 / 20 )273385.262295082718.157329712282380.676003689344
Winsorized Mean ( 20 / 20 )273335.754098361700.993928887026389.925993413863
Trimmed Mean ( 1 / 20 )274390.1016949151640.18436382553167.29223113366
Trimmed Mean ( 2 / 20 )274219.4385964911569.81207929379174.6829714292
Trimmed Mean ( 3 / 20 )274091.7636363641525.33325474227179.693036117983
Trimmed Mean ( 4 / 20 )273974.9811320751476.85866989193185.51198345345
Trimmed Mean ( 5 / 20 )273859.8039215691434.8929743568190.857303517238
Trimmed Mean ( 6 / 20 )273747.5714285711386.77174919081197.399154971469
Trimmed Mean ( 7 / 20 )273608.3404255321329.60950889324205.780974485722
Trimmed Mean ( 8 / 20 )273466.8666666671264.50231460301216.264425543991
Trimmed Mean ( 9 / 20 )273335.6744186051214.45525694425225.068542340833
Trimmed Mean ( 10 / 20 )273265.9512195121193.8529145786228.894152606703
Trimmed Mean ( 11 / 20 )273194.4615384621171.52176422672233.196232354068
Trimmed Mean ( 12 / 20 )273136.4054054051148.09514420597237.903981027903
Trimmed Mean ( 13 / 20 )273069.6857142861117.43747274655244.371333854687
Trimmed Mean ( 14 / 20 )272992.4242424241079.16438372606252.966488108008
Trimmed Mean ( 15 / 20 )272903.7096774191026.23336778114265.927534852502
Trimmed Mean ( 16 / 20 )272789970.232608847454281.158350598057
Trimmed Mean ( 17 / 20 )272771.185185185944.487610431902288.803349215402
Trimmed Mean ( 18 / 20 )272752.88928.873222996551293.638435523093
Trimmed Mean ( 19 / 20 )272731.434782609899.336617230308303.258456908539
Trimmed Mean ( 20 / 20 )272631.476190476886.222294533825307.633285544782
Median271472
Midrange279361.5
Midmean - Weighted Average at Xnp272507.4
Midmean - Weighted Average at X(n+1)p272903.709677419
Midmean - Empirical Distribution Function272903.709677419
Midmean - Empirical Distribution Function - Averaging272903.709677419
Midmean - Empirical Distribution Function - Interpolation272903.709677419
Midmean - Closest Observation272602.625
Midmean - True Basic - Statistics Graphics Toolkit272903.709677419
Midmean - MS Excel (old versions)272903.709677419
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 274553.098360656 & 1703.02832052039 & 161.214640445182 \tabularnewline
Geometric Mean & 274240.727793306 &  &  \tabularnewline
Harmonic Mean & 273932.943342169 &  &  \tabularnewline
Quadratic Mean & 274869.827640404 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 274549.573770492 & 1697.19089646646 & 161.767055398483 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 274449.672131148 & 1634.07657847745 & 167.953984376219 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 274396.163934426 & 1619.48944902657 & 169.433745986649 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 274360.163934426 & 1571.86658664747 & 174.544179681045 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 274310.573770492 & 1556.7484169204 & 176.207388932594 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 274391.229508197 & 1541.68595481541 & 177.981273456597 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 274338.901639344 & 1512.82313130607 & 181.342349916674 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 274206.704918033 & 1397.1955072337 & 196.255072034217 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 273757.442622951 & 1235.5032574598 & 221.575654268851 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 273723.016393443 & 1209.8746219403 & 226.240811592913 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 273581.819672131 & 1178.61540293569 & 232.121367997308 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 273595.786885246 & 1166.34362493599 & 234.575626801459 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 273613.049180328 & 1144.55739540682 & 239.05576974851 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 273623.606557377 & 1134.09676977425 & 241.270069583077 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 273721.721311475 & 1065.95920992791 & 256.784423608467 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 272915.163934426 & 901.383726557625 & 302.773564569095 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 272898.721311475 & 821.547249149632 & 332.176538347548 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 272898.426229508 & 821.149974141295 & 332.336887077038 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 273385.262295082 & 718.157329712282 & 380.676003689344 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 273335.754098361 & 700.993928887026 & 389.925993413863 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 274390.101694915 & 1640.18436382553 & 167.29223113366 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 274219.438596491 & 1569.81207929379 & 174.6829714292 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 274091.763636364 & 1525.33325474227 & 179.693036117983 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 273974.981132075 & 1476.85866989193 & 185.51198345345 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 273859.803921569 & 1434.8929743568 & 190.857303517238 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 273747.571428571 & 1386.77174919081 & 197.399154971469 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 273608.340425532 & 1329.60950889324 & 205.780974485722 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 273466.866666667 & 1264.50231460301 & 216.264425543991 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 273335.674418605 & 1214.45525694425 & 225.068542340833 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 273265.951219512 & 1193.8529145786 & 228.894152606703 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 273194.461538462 & 1171.52176422672 & 233.196232354068 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 273136.405405405 & 1148.09514420597 & 237.903981027903 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 273069.685714286 & 1117.43747274655 & 244.371333854687 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 272992.424242424 & 1079.16438372606 & 252.966488108008 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 272903.709677419 & 1026.23336778114 & 265.927534852502 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 272789 & 970.232608847454 & 281.158350598057 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 272771.185185185 & 944.487610431902 & 288.803349215402 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 272752.88 & 928.873222996551 & 293.638435523093 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 272731.434782609 & 899.336617230308 & 303.258456908539 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 272631.476190476 & 886.222294533825 & 307.633285544782 \tabularnewline
Median & 271472 &  &  \tabularnewline
Midrange & 279361.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 272507.4 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 272903.709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 272903.709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 272903.709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 272903.709677419 &  &  \tabularnewline
Midmean - Closest Observation & 272602.625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 272903.709677419 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 272903.709677419 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284109&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]274553.098360656[/C][C]1703.02832052039[/C][C]161.214640445182[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]274240.727793306[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]273932.943342169[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]274869.827640404[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]274549.573770492[/C][C]1697.19089646646[/C][C]161.767055398483[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]274449.672131148[/C][C]1634.07657847745[/C][C]167.953984376219[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]274396.163934426[/C][C]1619.48944902657[/C][C]169.433745986649[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]274360.163934426[/C][C]1571.86658664747[/C][C]174.544179681045[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]274310.573770492[/C][C]1556.7484169204[/C][C]176.207388932594[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]274391.229508197[/C][C]1541.68595481541[/C][C]177.981273456597[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]274338.901639344[/C][C]1512.82313130607[/C][C]181.342349916674[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]274206.704918033[/C][C]1397.1955072337[/C][C]196.255072034217[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]273757.442622951[/C][C]1235.5032574598[/C][C]221.575654268851[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]273723.016393443[/C][C]1209.8746219403[/C][C]226.240811592913[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]273581.819672131[/C][C]1178.61540293569[/C][C]232.121367997308[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]273595.786885246[/C][C]1166.34362493599[/C][C]234.575626801459[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]273613.049180328[/C][C]1144.55739540682[/C][C]239.05576974851[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]273623.606557377[/C][C]1134.09676977425[/C][C]241.270069583077[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]273721.721311475[/C][C]1065.95920992791[/C][C]256.784423608467[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]272915.163934426[/C][C]901.383726557625[/C][C]302.773564569095[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]272898.721311475[/C][C]821.547249149632[/C][C]332.176538347548[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]272898.426229508[/C][C]821.149974141295[/C][C]332.336887077038[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]273385.262295082[/C][C]718.157329712282[/C][C]380.676003689344[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]273335.754098361[/C][C]700.993928887026[/C][C]389.925993413863[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]274390.101694915[/C][C]1640.18436382553[/C][C]167.29223113366[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]274219.438596491[/C][C]1569.81207929379[/C][C]174.6829714292[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]274091.763636364[/C][C]1525.33325474227[/C][C]179.693036117983[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]273974.981132075[/C][C]1476.85866989193[/C][C]185.51198345345[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]273859.803921569[/C][C]1434.8929743568[/C][C]190.857303517238[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]273747.571428571[/C][C]1386.77174919081[/C][C]197.399154971469[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]273608.340425532[/C][C]1329.60950889324[/C][C]205.780974485722[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]273466.866666667[/C][C]1264.50231460301[/C][C]216.264425543991[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]273335.674418605[/C][C]1214.45525694425[/C][C]225.068542340833[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]273265.951219512[/C][C]1193.8529145786[/C][C]228.894152606703[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]273194.461538462[/C][C]1171.52176422672[/C][C]233.196232354068[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]273136.405405405[/C][C]1148.09514420597[/C][C]237.903981027903[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]273069.685714286[/C][C]1117.43747274655[/C][C]244.371333854687[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]272992.424242424[/C][C]1079.16438372606[/C][C]252.966488108008[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]272903.709677419[/C][C]1026.23336778114[/C][C]265.927534852502[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]272789[/C][C]970.232608847454[/C][C]281.158350598057[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]272771.185185185[/C][C]944.487610431902[/C][C]288.803349215402[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]272752.88[/C][C]928.873222996551[/C][C]293.638435523093[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]272731.434782609[/C][C]899.336617230308[/C][C]303.258456908539[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]272631.476190476[/C][C]886.222294533825[/C][C]307.633285544782[/C][/ROW]
[ROW][C]Median[/C][C]271472[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]279361.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]272507.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]272903.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]272903.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]272903.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]272903.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]272602.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]272903.709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]272903.709677419[/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=284109&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284109&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 Mean274553.0983606561703.02832052039161.214640445182
Geometric Mean274240.727793306
Harmonic Mean273932.943342169
Quadratic Mean274869.827640404
Winsorized Mean ( 1 / 20 )274549.5737704921697.19089646646161.767055398483
Winsorized Mean ( 2 / 20 )274449.6721311481634.07657847745167.953984376219
Winsorized Mean ( 3 / 20 )274396.1639344261619.48944902657169.433745986649
Winsorized Mean ( 4 / 20 )274360.1639344261571.86658664747174.544179681045
Winsorized Mean ( 5 / 20 )274310.5737704921556.7484169204176.207388932594
Winsorized Mean ( 6 / 20 )274391.2295081971541.68595481541177.981273456597
Winsorized Mean ( 7 / 20 )274338.9016393441512.82313130607181.342349916674
Winsorized Mean ( 8 / 20 )274206.7049180331397.1955072337196.255072034217
Winsorized Mean ( 9 / 20 )273757.4426229511235.5032574598221.575654268851
Winsorized Mean ( 10 / 20 )273723.0163934431209.8746219403226.240811592913
Winsorized Mean ( 11 / 20 )273581.8196721311178.61540293569232.121367997308
Winsorized Mean ( 12 / 20 )273595.7868852461166.34362493599234.575626801459
Winsorized Mean ( 13 / 20 )273613.0491803281144.55739540682239.05576974851
Winsorized Mean ( 14 / 20 )273623.6065573771134.09676977425241.270069583077
Winsorized Mean ( 15 / 20 )273721.7213114751065.95920992791256.784423608467
Winsorized Mean ( 16 / 20 )272915.163934426901.383726557625302.773564569095
Winsorized Mean ( 17 / 20 )272898.721311475821.547249149632332.176538347548
Winsorized Mean ( 18 / 20 )272898.426229508821.149974141295332.336887077038
Winsorized Mean ( 19 / 20 )273385.262295082718.157329712282380.676003689344
Winsorized Mean ( 20 / 20 )273335.754098361700.993928887026389.925993413863
Trimmed Mean ( 1 / 20 )274390.1016949151640.18436382553167.29223113366
Trimmed Mean ( 2 / 20 )274219.4385964911569.81207929379174.6829714292
Trimmed Mean ( 3 / 20 )274091.7636363641525.33325474227179.693036117983
Trimmed Mean ( 4 / 20 )273974.9811320751476.85866989193185.51198345345
Trimmed Mean ( 5 / 20 )273859.8039215691434.8929743568190.857303517238
Trimmed Mean ( 6 / 20 )273747.5714285711386.77174919081197.399154971469
Trimmed Mean ( 7 / 20 )273608.3404255321329.60950889324205.780974485722
Trimmed Mean ( 8 / 20 )273466.8666666671264.50231460301216.264425543991
Trimmed Mean ( 9 / 20 )273335.6744186051214.45525694425225.068542340833
Trimmed Mean ( 10 / 20 )273265.9512195121193.8529145786228.894152606703
Trimmed Mean ( 11 / 20 )273194.4615384621171.52176422672233.196232354068
Trimmed Mean ( 12 / 20 )273136.4054054051148.09514420597237.903981027903
Trimmed Mean ( 13 / 20 )273069.6857142861117.43747274655244.371333854687
Trimmed Mean ( 14 / 20 )272992.4242424241079.16438372606252.966488108008
Trimmed Mean ( 15 / 20 )272903.7096774191026.23336778114265.927534852502
Trimmed Mean ( 16 / 20 )272789970.232608847454281.158350598057
Trimmed Mean ( 17 / 20 )272771.185185185944.487610431902288.803349215402
Trimmed Mean ( 18 / 20 )272752.88928.873222996551293.638435523093
Trimmed Mean ( 19 / 20 )272731.434782609899.336617230308303.258456908539
Trimmed Mean ( 20 / 20 )272631.476190476886.222294533825307.633285544782
Median271472
Midrange279361.5
Midmean - Weighted Average at Xnp272507.4
Midmean - Weighted Average at X(n+1)p272903.709677419
Midmean - Empirical Distribution Function272903.709677419
Midmean - Empirical Distribution Function - Averaging272903.709677419
Midmean - Empirical Distribution Function - Interpolation272903.709677419
Midmean - Closest Observation272602.625
Midmean - True Basic - Statistics Graphics Toolkit272903.709677419
Midmean - MS Excel (old versions)272903.709677419
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')