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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 19:16:56 +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/t145020704696l0bpppv2ivj0i.htm/, Retrieved Sat, 18 May 2024 14:48:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286568, Retrieved Sat, 18 May 2024 14:48:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-12-15 19:16:56] [9d441e5437781f0cd4d5053adc3d2c6c] [Current]
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Dataseries X:
161193
157645
161694
163411
161834
159511
156359
154223
151497
160607
159672
155601
154668
153960
157307
165218
165616
162212
159787
157454
156485
165887
166836
163541
163973
164805
167521
174347
173374
172198
171055
168385
167281
177670
177280
174846
174476
174595
178392
185345
183293
181081
177795
173552
170734
179293
178659
175894
174815
173506
175376
179372
177688
175480
169705
164951
163405
169431
168389
164009
162245




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286568&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286568&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286568&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean167810.3934426231077.91405653097155.680680130181
Geometric Mean167602.489747861
Harmonic Mean167394.52804173
Quadratic Mean168017.981389386
Winsorized Mean ( 1 / 20 )167817.1311475411059.758426044158.354137153681
Winsorized Mean ( 2 / 20 )167753.2295081971041.31442010877161.097576552021
Winsorized Mean ( 3 / 20 )167691.065573771019.61640458392164.464856410584
Winsorized Mean ( 4 / 20 )167747.065573771005.95624704387166.753838516055
Winsorized Mean ( 5 / 20 )167757.229508197983.933428651692170.496524076917
Winsorized Mean ( 6 / 20 )167743.360655738976.735576197707171.738764045781
Winsorized Mean ( 7 / 20 )167769.180327869946.709396646335177.212966219815
Winsorized Mean ( 8 / 20 )167774.426229508940.700574435156178.350508960036
Winsorized Mean ( 9 / 20 )167799.950819672935.10704639151179.444643762654
Winsorized Mean ( 10 / 20 )168041.918032787871.089413482603192.910068050256
Winsorized Mean ( 11 / 20 )167821.016393443823.781016146783203.720422180183
Winsorized Mean ( 12 / 20 )167762.196721311806.908600474023207.90731022418
Winsorized Mean ( 13 / 20 )167914.786885246775.230058613928216.599943487059
Winsorized Mean ( 14 / 20 )167927.639344262735.08713175701228.44589721341
Winsorized Mean ( 15 / 20 )168043.213114754715.36632142784234.905122146857
Winsorized Mean ( 16 / 20 )168022.229508197700.886349616244239.728209288416
Winsorized Mean ( 17 / 20 )168094.409836066680.359100527448247.067188056646
Winsorized Mean ( 18 / 20 )168066.081967213673.019805932664249.719370047823
Winsorized Mean ( 19 / 20 )168179.770491803583.999852811496287.979131642159
Winsorized Mean ( 20 / 20 )168166.655737705581.421386218802289.233694741356
Trimmed Mean ( 1 / 20 )167789.6949152541036.8621993725161.824488361905
Trimmed Mean ( 2 / 20 )167760.3333333331008.62084655911166.326458456262
Trimmed Mean ( 3 / 20 )167764.272727273985.854891096736170.171365220534
Trimmed Mean ( 4 / 20 )167792.358490566967.595212363432173.411728733877
Trimmed Mean ( 5 / 20 )167805.901960784949.587211146229176.714576598214
Trimmed Mean ( 6 / 20 )167818.020408163933.719013860736179.730751882486
Trimmed Mean ( 7 / 20 )167834.170212766915.052538044273183.414791211306
Trimmed Mean ( 8 / 20 )167846.755555556899.001059063631186.703623831521
Trimmed Mean ( 9 / 20 )167859.581395349878.99545517842190.96751912247
Trimmed Mean ( 10 / 20 )167869.43902439853.539705056694196.674434744942
Trimmed Mean ( 11 / 20 )167842.461538462836.231950051125200.712806450651
Trimmed Mean ( 12 / 20 )167845.675675676824.163333193647203.655839705063
Trimmed Mean ( 13 / 20 )167857.8810.396883574686207.13036217461
Trimmed Mean ( 14 / 20 )167849.696969697797.976074398357210.344272660366
Trimmed Mean ( 15 / 20 )167838.741935484789.147566460835212.68359565272
Trimmed Mean ( 16 / 20 )167810.068965517778.96549265445215.426832828855
Trimmed Mean ( 17 / 20 )167780.111111111765.102749618562219.290953005668
Trimmed Mean ( 18 / 20 )167735747.271316189776224.463319233576
Trimmed Mean ( 19 / 20 )167686.217391304718.385423313238233.420963106302
Trimmed Mean ( 20 / 20 )167610.761904762704.204180701814238.014437428815
Median167281
Midrange168421
Midmean - Weighted Average at Xnp167606.2
Midmean - Weighted Average at X(n+1)p167838.741935484
Midmean - Empirical Distribution Function167838.741935484
Midmean - Empirical Distribution Function - Averaging167838.741935484
Midmean - Empirical Distribution Function - Interpolation167838.741935484
Midmean - Closest Observation167631.0625
Midmean - True Basic - Statistics Graphics Toolkit167838.741935484
Midmean - MS Excel (old versions)167838.741935484
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 167810.393442623 & 1077.91405653097 & 155.680680130181 \tabularnewline
Geometric Mean & 167602.489747861 &  &  \tabularnewline
Harmonic Mean & 167394.52804173 &  &  \tabularnewline
Quadratic Mean & 168017.981389386 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 167817.131147541 & 1059.758426044 & 158.354137153681 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 167753.229508197 & 1041.31442010877 & 161.097576552021 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 167691.06557377 & 1019.61640458392 & 164.464856410584 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 167747.06557377 & 1005.95624704387 & 166.753838516055 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 167757.229508197 & 983.933428651692 & 170.496524076917 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 167743.360655738 & 976.735576197707 & 171.738764045781 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 167769.180327869 & 946.709396646335 & 177.212966219815 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 167774.426229508 & 940.700574435156 & 178.350508960036 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 167799.950819672 & 935.10704639151 & 179.444643762654 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 168041.918032787 & 871.089413482603 & 192.910068050256 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 167821.016393443 & 823.781016146783 & 203.720422180183 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 167762.196721311 & 806.908600474023 & 207.90731022418 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 167914.786885246 & 775.230058613928 & 216.599943487059 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 167927.639344262 & 735.08713175701 & 228.44589721341 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 168043.213114754 & 715.36632142784 & 234.905122146857 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 168022.229508197 & 700.886349616244 & 239.728209288416 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 168094.409836066 & 680.359100527448 & 247.067188056646 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 168066.081967213 & 673.019805932664 & 249.719370047823 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 168179.770491803 & 583.999852811496 & 287.979131642159 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 168166.655737705 & 581.421386218802 & 289.233694741356 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 167789.694915254 & 1036.8621993725 & 161.824488361905 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 167760.333333333 & 1008.62084655911 & 166.326458456262 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 167764.272727273 & 985.854891096736 & 170.171365220534 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 167792.358490566 & 967.595212363432 & 173.411728733877 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 167805.901960784 & 949.587211146229 & 176.714576598214 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 167818.020408163 & 933.719013860736 & 179.730751882486 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 167834.170212766 & 915.052538044273 & 183.414791211306 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 167846.755555556 & 899.001059063631 & 186.703623831521 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 167859.581395349 & 878.99545517842 & 190.96751912247 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 167869.43902439 & 853.539705056694 & 196.674434744942 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 167842.461538462 & 836.231950051125 & 200.712806450651 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 167845.675675676 & 824.163333193647 & 203.655839705063 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 167857.8 & 810.396883574686 & 207.13036217461 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 167849.696969697 & 797.976074398357 & 210.344272660366 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 167838.741935484 & 789.147566460835 & 212.68359565272 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 167810.068965517 & 778.96549265445 & 215.426832828855 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 167780.111111111 & 765.102749618562 & 219.290953005668 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 167735 & 747.271316189776 & 224.463319233576 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 167686.217391304 & 718.385423313238 & 233.420963106302 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 167610.761904762 & 704.204180701814 & 238.014437428815 \tabularnewline
Median & 167281 &  &  \tabularnewline
Midrange & 168421 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 167606.2 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 167838.741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 167838.741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 167838.741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 167838.741935484 &  &  \tabularnewline
Midmean - Closest Observation & 167631.0625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 167838.741935484 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 167838.741935484 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286568&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]167810.393442623[/C][C]1077.91405653097[/C][C]155.680680130181[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]167602.489747861[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]167394.52804173[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]168017.981389386[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]167817.131147541[/C][C]1059.758426044[/C][C]158.354137153681[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]167753.229508197[/C][C]1041.31442010877[/C][C]161.097576552021[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]167691.06557377[/C][C]1019.61640458392[/C][C]164.464856410584[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]167747.06557377[/C][C]1005.95624704387[/C][C]166.753838516055[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]167757.229508197[/C][C]983.933428651692[/C][C]170.496524076917[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]167743.360655738[/C][C]976.735576197707[/C][C]171.738764045781[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]167769.180327869[/C][C]946.709396646335[/C][C]177.212966219815[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]167774.426229508[/C][C]940.700574435156[/C][C]178.350508960036[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]167799.950819672[/C][C]935.10704639151[/C][C]179.444643762654[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]168041.918032787[/C][C]871.089413482603[/C][C]192.910068050256[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]167821.016393443[/C][C]823.781016146783[/C][C]203.720422180183[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]167762.196721311[/C][C]806.908600474023[/C][C]207.90731022418[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]167914.786885246[/C][C]775.230058613928[/C][C]216.599943487059[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]167927.639344262[/C][C]735.08713175701[/C][C]228.44589721341[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]168043.213114754[/C][C]715.36632142784[/C][C]234.905122146857[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]168022.229508197[/C][C]700.886349616244[/C][C]239.728209288416[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]168094.409836066[/C][C]680.359100527448[/C][C]247.067188056646[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]168066.081967213[/C][C]673.019805932664[/C][C]249.719370047823[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]168179.770491803[/C][C]583.999852811496[/C][C]287.979131642159[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]168166.655737705[/C][C]581.421386218802[/C][C]289.233694741356[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]167789.694915254[/C][C]1036.8621993725[/C][C]161.824488361905[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]167760.333333333[/C][C]1008.62084655911[/C][C]166.326458456262[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]167764.272727273[/C][C]985.854891096736[/C][C]170.171365220534[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]167792.358490566[/C][C]967.595212363432[/C][C]173.411728733877[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]167805.901960784[/C][C]949.587211146229[/C][C]176.714576598214[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]167818.020408163[/C][C]933.719013860736[/C][C]179.730751882486[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]167834.170212766[/C][C]915.052538044273[/C][C]183.414791211306[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]167846.755555556[/C][C]899.001059063631[/C][C]186.703623831521[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]167859.581395349[/C][C]878.99545517842[/C][C]190.96751912247[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]167869.43902439[/C][C]853.539705056694[/C][C]196.674434744942[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]167842.461538462[/C][C]836.231950051125[/C][C]200.712806450651[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]167845.675675676[/C][C]824.163333193647[/C][C]203.655839705063[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]167857.8[/C][C]810.396883574686[/C][C]207.13036217461[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]167849.696969697[/C][C]797.976074398357[/C][C]210.344272660366[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]167838.741935484[/C][C]789.147566460835[/C][C]212.68359565272[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]167810.068965517[/C][C]778.96549265445[/C][C]215.426832828855[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]167780.111111111[/C][C]765.102749618562[/C][C]219.290953005668[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]167735[/C][C]747.271316189776[/C][C]224.463319233576[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]167686.217391304[/C][C]718.385423313238[/C][C]233.420963106302[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]167610.761904762[/C][C]704.204180701814[/C][C]238.014437428815[/C][/ROW]
[ROW][C]Median[/C][C]167281[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]168421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]167606.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]167838.741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]167838.741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]167838.741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]167838.741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]167631.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]167838.741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]167838.741935484[/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=286568&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286568&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 Mean167810.3934426231077.91405653097155.680680130181
Geometric Mean167602.489747861
Harmonic Mean167394.52804173
Quadratic Mean168017.981389386
Winsorized Mean ( 1 / 20 )167817.1311475411059.758426044158.354137153681
Winsorized Mean ( 2 / 20 )167753.2295081971041.31442010877161.097576552021
Winsorized Mean ( 3 / 20 )167691.065573771019.61640458392164.464856410584
Winsorized Mean ( 4 / 20 )167747.065573771005.95624704387166.753838516055
Winsorized Mean ( 5 / 20 )167757.229508197983.933428651692170.496524076917
Winsorized Mean ( 6 / 20 )167743.360655738976.735576197707171.738764045781
Winsorized Mean ( 7 / 20 )167769.180327869946.709396646335177.212966219815
Winsorized Mean ( 8 / 20 )167774.426229508940.700574435156178.350508960036
Winsorized Mean ( 9 / 20 )167799.950819672935.10704639151179.444643762654
Winsorized Mean ( 10 / 20 )168041.918032787871.089413482603192.910068050256
Winsorized Mean ( 11 / 20 )167821.016393443823.781016146783203.720422180183
Winsorized Mean ( 12 / 20 )167762.196721311806.908600474023207.90731022418
Winsorized Mean ( 13 / 20 )167914.786885246775.230058613928216.599943487059
Winsorized Mean ( 14 / 20 )167927.639344262735.08713175701228.44589721341
Winsorized Mean ( 15 / 20 )168043.213114754715.36632142784234.905122146857
Winsorized Mean ( 16 / 20 )168022.229508197700.886349616244239.728209288416
Winsorized Mean ( 17 / 20 )168094.409836066680.359100527448247.067188056646
Winsorized Mean ( 18 / 20 )168066.081967213673.019805932664249.719370047823
Winsorized Mean ( 19 / 20 )168179.770491803583.999852811496287.979131642159
Winsorized Mean ( 20 / 20 )168166.655737705581.421386218802289.233694741356
Trimmed Mean ( 1 / 20 )167789.6949152541036.8621993725161.824488361905
Trimmed Mean ( 2 / 20 )167760.3333333331008.62084655911166.326458456262
Trimmed Mean ( 3 / 20 )167764.272727273985.854891096736170.171365220534
Trimmed Mean ( 4 / 20 )167792.358490566967.595212363432173.411728733877
Trimmed Mean ( 5 / 20 )167805.901960784949.587211146229176.714576598214
Trimmed Mean ( 6 / 20 )167818.020408163933.719013860736179.730751882486
Trimmed Mean ( 7 / 20 )167834.170212766915.052538044273183.414791211306
Trimmed Mean ( 8 / 20 )167846.755555556899.001059063631186.703623831521
Trimmed Mean ( 9 / 20 )167859.581395349878.99545517842190.96751912247
Trimmed Mean ( 10 / 20 )167869.43902439853.539705056694196.674434744942
Trimmed Mean ( 11 / 20 )167842.461538462836.231950051125200.712806450651
Trimmed Mean ( 12 / 20 )167845.675675676824.163333193647203.655839705063
Trimmed Mean ( 13 / 20 )167857.8810.396883574686207.13036217461
Trimmed Mean ( 14 / 20 )167849.696969697797.976074398357210.344272660366
Trimmed Mean ( 15 / 20 )167838.741935484789.147566460835212.68359565272
Trimmed Mean ( 16 / 20 )167810.068965517778.96549265445215.426832828855
Trimmed Mean ( 17 / 20 )167780.111111111765.102749618562219.290953005668
Trimmed Mean ( 18 / 20 )167735747.271316189776224.463319233576
Trimmed Mean ( 19 / 20 )167686.217391304718.385423313238233.420963106302
Trimmed Mean ( 20 / 20 )167610.761904762704.204180701814238.014437428815
Median167281
Midrange168421
Midmean - Weighted Average at Xnp167606.2
Midmean - Weighted Average at X(n+1)p167838.741935484
Midmean - Empirical Distribution Function167838.741935484
Midmean - Empirical Distribution Function - Averaging167838.741935484
Midmean - Empirical Distribution Function - Interpolation167838.741935484
Midmean - Closest Observation167631.0625
Midmean - True Basic - Statistics Graphics Toolkit167838.741935484
Midmean - MS Excel (old versions)167838.741935484
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')