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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 computationFri, 17 Dec 2010 12:21:08 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/17/t1292588491oksi8vaq8pvj4yb.htm/, Retrieved Mon, 06 May 2024 13:55:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111422, Retrieved Mon, 06 May 2024 13:55:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper CT Werklozen] [2010-12-17 12:21:08] [514029464b0621595fe21c9fa38c7009] [Current]
-    D    [Central Tendency] [Paper CT Failliss...] [2010-12-17 12:29:04] [945bcebba5e7ac34a41d6888338a1ba9]
- RM D      [Variability] [Paper V Werklozen] [2010-12-17 13:31:46] [945bcebba5e7ac34a41d6888338a1ba9]
- RM        [Variability] [Paper V Faillisse...] [2010-12-17 13:35:21] [945bcebba5e7ac34a41d6888338a1ba9]
- RMPD      [Notched Boxplots] [Paper V Notched B...] [2010-12-17 14:04:15] [945bcebba5e7ac34a41d6888338a1ba9]
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Dataseries X:
36700
35600
80900
174000
169422
153452
173570
193036
174652
105367
95963
82896
121747
120196
103983
81103
70944
57248
47830
60095
60931
82955
99559
77911
70753
69287
88426
91756
96933
174484
232595
266197
290435
304296
322310
415555
490042
545109
545720
505944
477930
466106
424476
383018
364696
391116
435721
511435
553997
555252
544897
540562
505282
507626
474427
469740
491480
538974
576612




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111422&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111422&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111422&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean274292.35593220324997.070394073110.9729800975893
Geometric Mean199076.359829430
Harmonic Mean137818.437465181
Quadratic Mean333882.915351236
Winsorized Mean ( 1 / 19 )273948.96610169524921.026977331610.9926836623098
Winsorized Mean ( 2 / 19 )274283.71186440724852.157153537611.0366158627547
Winsorized Mean ( 3 / 19 )274341.72881355924697.543525298311.1080573066930
Winsorized Mean ( 4 / 19 )274493.32203389824660.608463934511.1308414159909
Winsorized Mean ( 5 / 19 )274546.20338983024646.606621106711.1393104783324
Winsorized Mean ( 6 / 19 )274955.11864406824438.464498213511.250916303034
Winsorized Mean ( 7 / 19 )274940.64406779724378.042975538911.2782081951236
Winsorized Mean ( 8 / 19 )271232.44067796623699.053294626111.4448639490367
Winsorized Mean ( 9 / 19 )271714.16949152523444.708579262411.5895733390290
Winsorized Mean ( 10 / 19 )271935.69491525423323.446304668211.6593273293761
Winsorized Mean ( 11 / 19 )271850.11864406823296.766031629511.6690066885242
Winsorized Mean ( 12 / 19 )269407.61016949122766.663649845311.8334251479716
Winsorized Mean ( 13 / 19 )269103.76271186422711.61221348411.8487300761545
Winsorized Mean ( 14 / 19 )267527.9322033922051.487068736312.1319678518498
Winsorized Mean ( 15 / 19 )267483.94915254221787.160658117412.2771366746627
Winsorized Mean ( 16 / 19 )267353.77966101721421.533570799212.4806087658197
Winsorized Mean ( 17 / 19 )266586.18644067821212.802435125112.5672309095404
Winsorized Mean ( 18 / 19 )258117.33898305119625.867495627813.1518945106785
Winsorized Mean ( 19 / 19 )255920.74576271218866.243760788513.5650079055278
Trimmed Mean ( 1 / 19 )273176.08771929824967.438322980410.9412941842681
Trimmed Mean ( 2 / 19 )27234724986.737048212210.8996624679126
Trimmed Mean ( 3 / 19 )271269.01886792525014.399191545610.8445146649618
Trimmed Mean ( 4 / 19 )270084.11764705925074.671533573210.7711926469480
Trimmed Mean ( 5 / 19 )268756.85714285725114.232251757910.7013765919141
Trimmed Mean ( 6 / 19 )267303.36170212825116.934152269810.6423562717336
Trimmed Mean ( 7 / 19 )265631.31111111125125.076736157410.5723582021480
Trimmed Mean ( 8 / 19 )263806.55813953525092.041117475610.5135551509918
Trimmed Mean ( 9 / 19 )262470.80487804925163.945938250510.4304311224528
Trimmed Mean ( 10 / 19 )260917.07692307725241.480267561310.3368373866089
Trimmed Mean ( 11 / 19 )259160.05405405425286.222531357410.2490616671854
Trimmed Mean ( 12 / 19 )257215.34285714325259.30811280710.1829924124774
Trimmed Mean ( 13 / 19 )255398.81818181825261.563398568110.1101746614897
Trimmed Mean ( 14 / 19 )253392.38709677425165.339326515410.0691027372632
Trimmed Mean ( 15 / 19 )251338.20689655225091.219875895610.0169783748938
Trimmed Mean ( 16 / 19 )248986.11111111124916.550745149.9928001133815
Trimmed Mean ( 17 / 19 )246276.8824613.477656311310.0057733993900
Trimmed Mean ( 18 / 19 )243212.30434782624049.090339631810.1131602448606
Trimmed Mean ( 19 / 19 )240885.85714285723646.201563412910.1870846569951
Median193036
Midrange306106
Midmean - Weighted Average at Xnp245907.8
Midmean - Weighted Average at X(n+1)p253392.387096774
Midmean - Empirical Distribution Function253392.387096774
Midmean - Empirical Distribution Function - Averaging253392.387096774
Midmean - Empirical Distribution Function - Interpolation251338.206896552
Midmean - Closest Observation245907.8
Midmean - True Basic - Statistics Graphics Toolkit253392.387096774
Midmean - MS Excel (old versions)253392.387096774
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 274292.355932203 & 24997.0703940731 & 10.9729800975893 \tabularnewline
Geometric Mean & 199076.359829430 &  &  \tabularnewline
Harmonic Mean & 137818.437465181 &  &  \tabularnewline
Quadratic Mean & 333882.915351236 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 273948.966101695 & 24921.0269773316 & 10.9926836623098 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 274283.711864407 & 24852.1571535376 & 11.0366158627547 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 274341.728813559 & 24697.5435252983 & 11.1080573066930 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 274493.322033898 & 24660.6084639345 & 11.1308414159909 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 274546.203389830 & 24646.6066211067 & 11.1393104783324 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 274955.118644068 & 24438.4644982135 & 11.250916303034 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 274940.644067797 & 24378.0429755389 & 11.2782081951236 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 271232.440677966 & 23699.0532946261 & 11.4448639490367 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 271714.169491525 & 23444.7085792624 & 11.5895733390290 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 271935.694915254 & 23323.4463046682 & 11.6593273293761 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 271850.118644068 & 23296.7660316295 & 11.6690066885242 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 269407.610169491 & 22766.6636498453 & 11.8334251479716 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 269103.762711864 & 22711.612213484 & 11.8487300761545 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 267527.93220339 & 22051.4870687363 & 12.1319678518498 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 267483.949152542 & 21787.1606581174 & 12.2771366746627 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 267353.779661017 & 21421.5335707992 & 12.4806087658197 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 266586.186440678 & 21212.8024351251 & 12.5672309095404 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 258117.338983051 & 19625.8674956278 & 13.1518945106785 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 255920.745762712 & 18866.2437607885 & 13.5650079055278 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 273176.087719298 & 24967.4383229804 & 10.9412941842681 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 272347 & 24986.7370482122 & 10.8996624679126 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 271269.018867925 & 25014.3991915456 & 10.8445146649618 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 270084.117647059 & 25074.6715335732 & 10.7711926469480 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 268756.857142857 & 25114.2322517579 & 10.7013765919141 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 267303.361702128 & 25116.9341522698 & 10.6423562717336 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 265631.311111111 & 25125.0767361574 & 10.5723582021480 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 263806.558139535 & 25092.0411174756 & 10.5135551509918 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 262470.804878049 & 25163.9459382505 & 10.4304311224528 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 260917.076923077 & 25241.4802675613 & 10.3368373866089 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 259160.054054054 & 25286.2225313574 & 10.2490616671854 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 257215.342857143 & 25259.308112807 & 10.1829924124774 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 255398.818181818 & 25261.5633985681 & 10.1101746614897 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 253392.387096774 & 25165.3393265154 & 10.0691027372632 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 251338.206896552 & 25091.2198758956 & 10.0169783748938 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 248986.111111111 & 24916.55074514 & 9.9928001133815 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 246276.88 & 24613.4776563113 & 10.0057733993900 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 243212.304347826 & 24049.0903396318 & 10.1131602448606 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 240885.857142857 & 23646.2015634129 & 10.1870846569951 \tabularnewline
Median & 193036 &  &  \tabularnewline
Midrange & 306106 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 245907.8 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 253392.387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 253392.387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 253392.387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 251338.206896552 &  &  \tabularnewline
Midmean - Closest Observation & 245907.8 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 253392.387096774 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 253392.387096774 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111422&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]274292.355932203[/C][C]24997.0703940731[/C][C]10.9729800975893[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]199076.359829430[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]137818.437465181[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]333882.915351236[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]273948.966101695[/C][C]24921.0269773316[/C][C]10.9926836623098[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]274283.711864407[/C][C]24852.1571535376[/C][C]11.0366158627547[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]274341.728813559[/C][C]24697.5435252983[/C][C]11.1080573066930[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]274493.322033898[/C][C]24660.6084639345[/C][C]11.1308414159909[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]274546.203389830[/C][C]24646.6066211067[/C][C]11.1393104783324[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]274955.118644068[/C][C]24438.4644982135[/C][C]11.250916303034[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]274940.644067797[/C][C]24378.0429755389[/C][C]11.2782081951236[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]271232.440677966[/C][C]23699.0532946261[/C][C]11.4448639490367[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]271714.169491525[/C][C]23444.7085792624[/C][C]11.5895733390290[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]271935.694915254[/C][C]23323.4463046682[/C][C]11.6593273293761[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]271850.118644068[/C][C]23296.7660316295[/C][C]11.6690066885242[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]269407.610169491[/C][C]22766.6636498453[/C][C]11.8334251479716[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]269103.762711864[/C][C]22711.612213484[/C][C]11.8487300761545[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]267527.93220339[/C][C]22051.4870687363[/C][C]12.1319678518498[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]267483.949152542[/C][C]21787.1606581174[/C][C]12.2771366746627[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]267353.779661017[/C][C]21421.5335707992[/C][C]12.4806087658197[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]266586.186440678[/C][C]21212.8024351251[/C][C]12.5672309095404[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]258117.338983051[/C][C]19625.8674956278[/C][C]13.1518945106785[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]255920.745762712[/C][C]18866.2437607885[/C][C]13.5650079055278[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]273176.087719298[/C][C]24967.4383229804[/C][C]10.9412941842681[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]272347[/C][C]24986.7370482122[/C][C]10.8996624679126[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]271269.018867925[/C][C]25014.3991915456[/C][C]10.8445146649618[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]270084.117647059[/C][C]25074.6715335732[/C][C]10.7711926469480[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]268756.857142857[/C][C]25114.2322517579[/C][C]10.7013765919141[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]267303.361702128[/C][C]25116.9341522698[/C][C]10.6423562717336[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]265631.311111111[/C][C]25125.0767361574[/C][C]10.5723582021480[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]263806.558139535[/C][C]25092.0411174756[/C][C]10.5135551509918[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]262470.804878049[/C][C]25163.9459382505[/C][C]10.4304311224528[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]260917.076923077[/C][C]25241.4802675613[/C][C]10.3368373866089[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]259160.054054054[/C][C]25286.2225313574[/C][C]10.2490616671854[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]257215.342857143[/C][C]25259.308112807[/C][C]10.1829924124774[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]255398.818181818[/C][C]25261.5633985681[/C][C]10.1101746614897[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]253392.387096774[/C][C]25165.3393265154[/C][C]10.0691027372632[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]251338.206896552[/C][C]25091.2198758956[/C][C]10.0169783748938[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]248986.111111111[/C][C]24916.55074514[/C][C]9.9928001133815[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]246276.88[/C][C]24613.4776563113[/C][C]10.0057733993900[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]243212.304347826[/C][C]24049.0903396318[/C][C]10.1131602448606[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]240885.857142857[/C][C]23646.2015634129[/C][C]10.1870846569951[/C][/ROW]
[ROW][C]Median[/C][C]193036[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]306106[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]245907.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]253392.387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]253392.387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]253392.387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]251338.206896552[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]245907.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]253392.387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]253392.387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111422&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111422&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 Mean274292.35593220324997.070394073110.9729800975893
Geometric Mean199076.359829430
Harmonic Mean137818.437465181
Quadratic Mean333882.915351236
Winsorized Mean ( 1 / 19 )273948.96610169524921.026977331610.9926836623098
Winsorized Mean ( 2 / 19 )274283.71186440724852.157153537611.0366158627547
Winsorized Mean ( 3 / 19 )274341.72881355924697.543525298311.1080573066930
Winsorized Mean ( 4 / 19 )274493.32203389824660.608463934511.1308414159909
Winsorized Mean ( 5 / 19 )274546.20338983024646.606621106711.1393104783324
Winsorized Mean ( 6 / 19 )274955.11864406824438.464498213511.250916303034
Winsorized Mean ( 7 / 19 )274940.64406779724378.042975538911.2782081951236
Winsorized Mean ( 8 / 19 )271232.44067796623699.053294626111.4448639490367
Winsorized Mean ( 9 / 19 )271714.16949152523444.708579262411.5895733390290
Winsorized Mean ( 10 / 19 )271935.69491525423323.446304668211.6593273293761
Winsorized Mean ( 11 / 19 )271850.11864406823296.766031629511.6690066885242
Winsorized Mean ( 12 / 19 )269407.61016949122766.663649845311.8334251479716
Winsorized Mean ( 13 / 19 )269103.76271186422711.61221348411.8487300761545
Winsorized Mean ( 14 / 19 )267527.9322033922051.487068736312.1319678518498
Winsorized Mean ( 15 / 19 )267483.94915254221787.160658117412.2771366746627
Winsorized Mean ( 16 / 19 )267353.77966101721421.533570799212.4806087658197
Winsorized Mean ( 17 / 19 )266586.18644067821212.802435125112.5672309095404
Winsorized Mean ( 18 / 19 )258117.33898305119625.867495627813.1518945106785
Winsorized Mean ( 19 / 19 )255920.74576271218866.243760788513.5650079055278
Trimmed Mean ( 1 / 19 )273176.08771929824967.438322980410.9412941842681
Trimmed Mean ( 2 / 19 )27234724986.737048212210.8996624679126
Trimmed Mean ( 3 / 19 )271269.01886792525014.399191545610.8445146649618
Trimmed Mean ( 4 / 19 )270084.11764705925074.671533573210.7711926469480
Trimmed Mean ( 5 / 19 )268756.85714285725114.232251757910.7013765919141
Trimmed Mean ( 6 / 19 )267303.36170212825116.934152269810.6423562717336
Trimmed Mean ( 7 / 19 )265631.31111111125125.076736157410.5723582021480
Trimmed Mean ( 8 / 19 )263806.55813953525092.041117475610.5135551509918
Trimmed Mean ( 9 / 19 )262470.80487804925163.945938250510.4304311224528
Trimmed Mean ( 10 / 19 )260917.07692307725241.480267561310.3368373866089
Trimmed Mean ( 11 / 19 )259160.05405405425286.222531357410.2490616671854
Trimmed Mean ( 12 / 19 )257215.34285714325259.30811280710.1829924124774
Trimmed Mean ( 13 / 19 )255398.81818181825261.563398568110.1101746614897
Trimmed Mean ( 14 / 19 )253392.38709677425165.339326515410.0691027372632
Trimmed Mean ( 15 / 19 )251338.20689655225091.219875895610.0169783748938
Trimmed Mean ( 16 / 19 )248986.11111111124916.550745149.9928001133815
Trimmed Mean ( 17 / 19 )246276.8824613.477656311310.0057733993900
Trimmed Mean ( 18 / 19 )243212.30434782624049.090339631810.1131602448606
Trimmed Mean ( 19 / 19 )240885.85714285723646.201563412910.1870846569951
Median193036
Midrange306106
Midmean - Weighted Average at Xnp245907.8
Midmean - Weighted Average at X(n+1)p253392.387096774
Midmean - Empirical Distribution Function253392.387096774
Midmean - Empirical Distribution Function - Averaging253392.387096774
Midmean - Empirical Distribution Function - Interpolation251338.206896552
Midmean - Closest Observation245907.8
Midmean - True Basic - Statistics Graphics Toolkit253392.387096774
Midmean - MS Excel (old versions)253392.387096774
Number of observations59



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')