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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 computationThu, 22 Oct 2009 09:17:28 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t1256224758qzwoc1k2ltmxkog.htm/, Retrieved Thu, 02 May 2024 14:37:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49753, Retrieved Thu, 02 May 2024 14:37:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [workshop 3/part 2] [2009-10-22 15:17:28] [bebfa40a4e66abcf3fcee16e050bb8d6] [Current]
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Dataseries X:
27501
26577
25705
25147
24740
24281
23577
22598
21903
21360
24226
25468
26858
25684
24938
24347
25137
24479
23810
23301
23076
23049
25870
27291
28706
28220
26612
25453
26066
25696
23851
24203
22433
19195
21955
23326
24490
23996
22181
22550
23013
22826
20544
20814
18518
17964
21139
21818
23028
21890
21833
22289
22380
22316
22614
22775
21221
20915
23889
24703




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49753&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49753&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23605.75289.03281989174981.671520932609
Geometric Mean23499.7310296836
Harmonic Mean23391.7434050144
Quadratic Mean23709.9196824873
Winsorized Mean ( 1 / 20 )23606.8833333333283.77302051187583.1893154985304
Winsorized Mean ( 2 / 20 )23605.4833333333270.99339797623287.1072266321548
Winsorized Mean ( 3 / 20 )23662.4333333333251.97456082549693.908024904628
Winsorized Mean ( 4 / 20 )23651.5666666667241.51597175743097.929617219773
Winsorized Mean ( 5 / 20 )23639.4833333333235.349920381419100.443982708904
Winsorized Mean ( 6 / 20 )23658.3833333333230.324161261533102.717766142082
Winsorized Mean ( 7 / 20 )23608.3333333333216.381917624724109.104927031277
Winsorized Mean ( 8 / 20 )23600.7333333333208.023095831320113.452466607220
Winsorized Mean ( 9 / 20 )23644.6833333333191.627913780651123.388513013811
Winsorized Mean ( 10 / 20 )23645.6833333333190.951667342363123.830724614403
Winsorized Mean ( 11 / 20 )23653.9333333333188.883307572355125.230406208724
Winsorized Mean ( 12 / 20 )23613.3333333333180.774405509691130.623211105332
Winsorized Mean ( 13 / 20 )23621.35178.413880893501132.396368946764
Winsorized Mean ( 14 / 20 )23602.6833333333158.069548612887149.318344617637
Winsorized Mean ( 15 / 20 )23627.1833333333153.602018016674153.820787242317
Winsorized Mean ( 16 / 20 )23581.3166666667143.866723657984163.910847950682
Winsorized Mean ( 17 / 20 )23543.35132.375851282720177.852302907708
Winsorized Mean ( 18 / 20 )23548.15128.323531414504183.506093858467
Winsorized Mean ( 19 / 20 )23517.75112.814866655145208.463216748637
Winsorized Mean ( 20 / 20 )23530.0833333333109.966315571013213.975372468838
Trimmed Mean ( 1 / 20 )23615.0862068966268.24503507276288.0355015722505
Trimmed Mean ( 2 / 20 )23623.875248.82496855349894.941738111466
Trimmed Mean ( 3 / 20 )23634.0925925926233.499517442895101.216879809495
Trimmed Mean ( 4 / 20 )23623.1923076923224.039942770497105.441877977498
Trimmed Mean ( 5 / 20 )23614.68216.422722108604109.11368164083
Trimmed Mean ( 6 / 20 )23608.4791666667208.932827504931112.995547174651
Trimmed Mean ( 7 / 20 )23597.6304347826200.921962784496117.446744535802
Trimmed Mean ( 8 / 20 )23595.5454545455194.837891240785121.103473786757
Trimmed Mean ( 9 / 20 )23594.6190476190189.216997000758124.696086618078
Trimmed Mean ( 10 / 20 )23586.275186.121035156062126.725466469832
Trimmed Mean ( 11 / 20 )23576.8947368421181.881594319011129.627710957325
Trimmed Mean ( 12 / 20 )23565.2222222222176.431456680847133.565876888100
Trimmed Mean ( 13 / 20 )23558.1470588235171.072183180161137.708811689237
Trimmed Mean ( 14 / 20 )23549.03125163.975617067574143.613005830590
Trimmed Mean ( 15 / 20 )23541.3666666667159.907023871764147.219090798322
Trimmed Mean ( 16 / 20 )23529.1071428571154.848648919467151.949063211356
Trimmed Mean ( 17 / 20 )23521.5769230769150.227337193457156.573213387832
Trimmed Mean ( 18 / 20 )23518.375146.711325700398160.303745383825
Trimmed Mean ( 19 / 20 )23513.8636363636141.876284370936165.734983409112
Trimmed Mean ( 20 / 20 )23513.25139.714556281162168.294919483420
Median23451.5
Midrange23335
Midmean - Weighted Average at Xnp23497.4838709677
Midmean - Weighted Average at X(n+1)p23541.3666666667
Midmean - Empirical Distribution Function23497.4838709677
Midmean - Empirical Distribution Function - Averaging23541.3666666667
Midmean - Empirical Distribution Function - Interpolation23541.3666666667
Midmean - Closest Observation23497.4838709677
Midmean - True Basic - Statistics Graphics Toolkit23541.3666666667
Midmean - MS Excel (old versions)23549.03125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23605.75 & 289.032819891749 & 81.671520932609 \tabularnewline
Geometric Mean & 23499.7310296836 &  &  \tabularnewline
Harmonic Mean & 23391.7434050144 &  &  \tabularnewline
Quadratic Mean & 23709.9196824873 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 23606.8833333333 & 283.773020511875 & 83.1893154985304 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 23605.4833333333 & 270.993397976232 & 87.1072266321548 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 23662.4333333333 & 251.974560825496 & 93.908024904628 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 23651.5666666667 & 241.515971757430 & 97.929617219773 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 23639.4833333333 & 235.349920381419 & 100.443982708904 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 23658.3833333333 & 230.324161261533 & 102.717766142082 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 23608.3333333333 & 216.381917624724 & 109.104927031277 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 23600.7333333333 & 208.023095831320 & 113.452466607220 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 23644.6833333333 & 191.627913780651 & 123.388513013811 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 23645.6833333333 & 190.951667342363 & 123.830724614403 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 23653.9333333333 & 188.883307572355 & 125.230406208724 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 23613.3333333333 & 180.774405509691 & 130.623211105332 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 23621.35 & 178.413880893501 & 132.396368946764 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 23602.6833333333 & 158.069548612887 & 149.318344617637 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 23627.1833333333 & 153.602018016674 & 153.820787242317 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 23581.3166666667 & 143.866723657984 & 163.910847950682 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 23543.35 & 132.375851282720 & 177.852302907708 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 23548.15 & 128.323531414504 & 183.506093858467 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 23517.75 & 112.814866655145 & 208.463216748637 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 23530.0833333333 & 109.966315571013 & 213.975372468838 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 23615.0862068966 & 268.245035072762 & 88.0355015722505 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 23623.875 & 248.824968553498 & 94.941738111466 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 23634.0925925926 & 233.499517442895 & 101.216879809495 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 23623.1923076923 & 224.039942770497 & 105.441877977498 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 23614.68 & 216.422722108604 & 109.11368164083 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 23608.4791666667 & 208.932827504931 & 112.995547174651 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 23597.6304347826 & 200.921962784496 & 117.446744535802 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 23595.5454545455 & 194.837891240785 & 121.103473786757 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 23594.6190476190 & 189.216997000758 & 124.696086618078 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 23586.275 & 186.121035156062 & 126.725466469832 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 23576.8947368421 & 181.881594319011 & 129.627710957325 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 23565.2222222222 & 176.431456680847 & 133.565876888100 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 23558.1470588235 & 171.072183180161 & 137.708811689237 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 23549.03125 & 163.975617067574 & 143.613005830590 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 23541.3666666667 & 159.907023871764 & 147.219090798322 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 23529.1071428571 & 154.848648919467 & 151.949063211356 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 23521.5769230769 & 150.227337193457 & 156.573213387832 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 23518.375 & 146.711325700398 & 160.303745383825 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 23513.8636363636 & 141.876284370936 & 165.734983409112 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 23513.25 & 139.714556281162 & 168.294919483420 \tabularnewline
Median & 23451.5 &  &  \tabularnewline
Midrange & 23335 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 23497.4838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 23541.3666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 23497.4838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 23541.3666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 23541.3666666667 &  &  \tabularnewline
Midmean - Closest Observation & 23497.4838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 23541.3666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 23549.03125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49753&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]23605.75[/C][C]289.032819891749[/C][C]81.671520932609[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]23499.7310296836[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]23391.7434050144[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23709.9196824873[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]23606.8833333333[/C][C]283.773020511875[/C][C]83.1893154985304[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]23605.4833333333[/C][C]270.993397976232[/C][C]87.1072266321548[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]23662.4333333333[/C][C]251.974560825496[/C][C]93.908024904628[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]23651.5666666667[/C][C]241.515971757430[/C][C]97.929617219773[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]23639.4833333333[/C][C]235.349920381419[/C][C]100.443982708904[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]23658.3833333333[/C][C]230.324161261533[/C][C]102.717766142082[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]23608.3333333333[/C][C]216.381917624724[/C][C]109.104927031277[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]23600.7333333333[/C][C]208.023095831320[/C][C]113.452466607220[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]23644.6833333333[/C][C]191.627913780651[/C][C]123.388513013811[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]23645.6833333333[/C][C]190.951667342363[/C][C]123.830724614403[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]23653.9333333333[/C][C]188.883307572355[/C][C]125.230406208724[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]23613.3333333333[/C][C]180.774405509691[/C][C]130.623211105332[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]23621.35[/C][C]178.413880893501[/C][C]132.396368946764[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]23602.6833333333[/C][C]158.069548612887[/C][C]149.318344617637[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]23627.1833333333[/C][C]153.602018016674[/C][C]153.820787242317[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]23581.3166666667[/C][C]143.866723657984[/C][C]163.910847950682[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]23543.35[/C][C]132.375851282720[/C][C]177.852302907708[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]23548.15[/C][C]128.323531414504[/C][C]183.506093858467[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]23517.75[/C][C]112.814866655145[/C][C]208.463216748637[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]23530.0833333333[/C][C]109.966315571013[/C][C]213.975372468838[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]23615.0862068966[/C][C]268.245035072762[/C][C]88.0355015722505[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]23623.875[/C][C]248.824968553498[/C][C]94.941738111466[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]23634.0925925926[/C][C]233.499517442895[/C][C]101.216879809495[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]23623.1923076923[/C][C]224.039942770497[/C][C]105.441877977498[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]23614.68[/C][C]216.422722108604[/C][C]109.11368164083[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]23608.4791666667[/C][C]208.932827504931[/C][C]112.995547174651[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]23597.6304347826[/C][C]200.921962784496[/C][C]117.446744535802[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]23595.5454545455[/C][C]194.837891240785[/C][C]121.103473786757[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]23594.6190476190[/C][C]189.216997000758[/C][C]124.696086618078[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]23586.275[/C][C]186.121035156062[/C][C]126.725466469832[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]23576.8947368421[/C][C]181.881594319011[/C][C]129.627710957325[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]23565.2222222222[/C][C]176.431456680847[/C][C]133.565876888100[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]23558.1470588235[/C][C]171.072183180161[/C][C]137.708811689237[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]23549.03125[/C][C]163.975617067574[/C][C]143.613005830590[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]23541.3666666667[/C][C]159.907023871764[/C][C]147.219090798322[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]23529.1071428571[/C][C]154.848648919467[/C][C]151.949063211356[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]23521.5769230769[/C][C]150.227337193457[/C][C]156.573213387832[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]23518.375[/C][C]146.711325700398[/C][C]160.303745383825[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]23513.8636363636[/C][C]141.876284370936[/C][C]165.734983409112[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]23513.25[/C][C]139.714556281162[/C][C]168.294919483420[/C][/ROW]
[ROW][C]Median[/C][C]23451.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]23335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]23497.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]23541.3666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]23497.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]23541.3666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]23541.3666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]23497.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]23541.3666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]23549.03125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49753&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 Mean23605.75289.03281989174981.671520932609
Geometric Mean23499.7310296836
Harmonic Mean23391.7434050144
Quadratic Mean23709.9196824873
Winsorized Mean ( 1 / 20 )23606.8833333333283.77302051187583.1893154985304
Winsorized Mean ( 2 / 20 )23605.4833333333270.99339797623287.1072266321548
Winsorized Mean ( 3 / 20 )23662.4333333333251.97456082549693.908024904628
Winsorized Mean ( 4 / 20 )23651.5666666667241.51597175743097.929617219773
Winsorized Mean ( 5 / 20 )23639.4833333333235.349920381419100.443982708904
Winsorized Mean ( 6 / 20 )23658.3833333333230.324161261533102.717766142082
Winsorized Mean ( 7 / 20 )23608.3333333333216.381917624724109.104927031277
Winsorized Mean ( 8 / 20 )23600.7333333333208.023095831320113.452466607220
Winsorized Mean ( 9 / 20 )23644.6833333333191.627913780651123.388513013811
Winsorized Mean ( 10 / 20 )23645.6833333333190.951667342363123.830724614403
Winsorized Mean ( 11 / 20 )23653.9333333333188.883307572355125.230406208724
Winsorized Mean ( 12 / 20 )23613.3333333333180.774405509691130.623211105332
Winsorized Mean ( 13 / 20 )23621.35178.413880893501132.396368946764
Winsorized Mean ( 14 / 20 )23602.6833333333158.069548612887149.318344617637
Winsorized Mean ( 15 / 20 )23627.1833333333153.602018016674153.820787242317
Winsorized Mean ( 16 / 20 )23581.3166666667143.866723657984163.910847950682
Winsorized Mean ( 17 / 20 )23543.35132.375851282720177.852302907708
Winsorized Mean ( 18 / 20 )23548.15128.323531414504183.506093858467
Winsorized Mean ( 19 / 20 )23517.75112.814866655145208.463216748637
Winsorized Mean ( 20 / 20 )23530.0833333333109.966315571013213.975372468838
Trimmed Mean ( 1 / 20 )23615.0862068966268.24503507276288.0355015722505
Trimmed Mean ( 2 / 20 )23623.875248.82496855349894.941738111466
Trimmed Mean ( 3 / 20 )23634.0925925926233.499517442895101.216879809495
Trimmed Mean ( 4 / 20 )23623.1923076923224.039942770497105.441877977498
Trimmed Mean ( 5 / 20 )23614.68216.422722108604109.11368164083
Trimmed Mean ( 6 / 20 )23608.4791666667208.932827504931112.995547174651
Trimmed Mean ( 7 / 20 )23597.6304347826200.921962784496117.446744535802
Trimmed Mean ( 8 / 20 )23595.5454545455194.837891240785121.103473786757
Trimmed Mean ( 9 / 20 )23594.6190476190189.216997000758124.696086618078
Trimmed Mean ( 10 / 20 )23586.275186.121035156062126.725466469832
Trimmed Mean ( 11 / 20 )23576.8947368421181.881594319011129.627710957325
Trimmed Mean ( 12 / 20 )23565.2222222222176.431456680847133.565876888100
Trimmed Mean ( 13 / 20 )23558.1470588235171.072183180161137.708811689237
Trimmed Mean ( 14 / 20 )23549.03125163.975617067574143.613005830590
Trimmed Mean ( 15 / 20 )23541.3666666667159.907023871764147.219090798322
Trimmed Mean ( 16 / 20 )23529.1071428571154.848648919467151.949063211356
Trimmed Mean ( 17 / 20 )23521.5769230769150.227337193457156.573213387832
Trimmed Mean ( 18 / 20 )23518.375146.711325700398160.303745383825
Trimmed Mean ( 19 / 20 )23513.8636363636141.876284370936165.734983409112
Trimmed Mean ( 20 / 20 )23513.25139.714556281162168.294919483420
Median23451.5
Midrange23335
Midmean - Weighted Average at Xnp23497.4838709677
Midmean - Weighted Average at X(n+1)p23541.3666666667
Midmean - Empirical Distribution Function23497.4838709677
Midmean - Empirical Distribution Function - Averaging23541.3666666667
Midmean - Empirical Distribution Function - Interpolation23541.3666666667
Midmean - Closest Observation23497.4838709677
Midmean - True Basic - Statistics Graphics Toolkit23541.3666666667
Midmean - MS Excel (old versions)23549.03125
Number of observations60



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')