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of Irreproducible Research!

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, 20 Oct 2009 12:24:04 -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/20/t12560631070d0jnghrxd68wqm.htm/, Retrieved Fri, 03 May 2024 02:02:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48952, Retrieved Fri, 03 May 2024 02:02:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [central tendency ...] [2009-10-15 15:33:43] [757146c69eaf0537be37c7b0c18216d8]
-    D          [Central Tendency] [central tendency ...] [2009-10-20 18:24:04] [a931a0a30926b49d162330b43e89b999] [Current]
Feedback Forum

Post a new message
Dataseries X:
40061
39409
45240
40793
39624
36609
35173
34354
32800
33176
39042
46217
46512
43632
35745
32450
31829
33028
29256
26127
23773
24071
39320
39963
44357
35316
30613
26090
25552
22508
20502
21277
19213
18924
27918
38250
42605
32331
25784
23002
20048
19840
17483
18462
16073
18249
23902
32511
36924
24007
15978
9340
4611
-416
-4056
-9770
-11391
-11263
-7772
1150
4832
-6075




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48952&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48952&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24759.88709677421971.3015045772712.5601725759773
Geometric MeanNaN
Harmonic Mean41304816.0558504
Quadratic Mean29156.471253975
Winsorized Mean ( 1 / 20 )24757.19354838711969.8265026316312.5682102029352
Winsorized Mean ( 2 / 20 )24773.83870967741950.0878686617212.7039602203561
Winsorized Mean ( 3 / 20 )24827.79032258061915.3106034360712.9628010611123
Winsorized Mean ( 4 / 20 )24890.51877.4932779793813.2573044558583
Winsorized Mean ( 5 / 20 )24970.51820.8403531386813.7137228735935
Winsorized Mean ( 6 / 20 )25147.40322580651704.2736803722514.7554958545823
Winsorized Mean ( 7 / 20 )25241.56451612901649.0452741008515.3067747214473
Winsorized Mean ( 8 / 20 )25675.51543.6091567644916.6334203755422
Winsorized Mean ( 9 / 20 )25658.37096774191529.0212739457516.7809116883827
Winsorized Mean ( 10 / 20 )26350.79032258061368.0420046791019.2616821942990
Winsorized Mean ( 11 / 20 )27512.70967741941146.2907297063124.0015111039660
Winsorized Mean ( 12 / 20 )27477.29032258061134.2187508217024.2257415535357
Winsorized Mean ( 13 / 20 )27606.87096774191059.0821261913126.0667896143448
Winsorized Mean ( 14 / 20 )27480.4193548387983.95956065314727.9284032126253
Winsorized Mean ( 15 / 20 )27455.7419354839964.12976681752228.477226697514
Winsorized Mean ( 16 / 20 )27352911.78934034315529.9981572384976
Winsorized Mean ( 17 / 20 )27313.6129032258882.1974712582630.9608832411058
Winsorized Mean ( 18 / 20 )27454.1290322581848.92737855995632.3397851519747
Winsorized Mean ( 19 / 20 )27266.8870967742802.6573798556433.9707673299886
Winsorized Mean ( 20 / 20 )27033.3387096774727.20815897144837.1741410986271
Trimmed Mean ( 1 / 20 )24999.86666666671909.9403638553713.0893441176364
Trimmed Mean ( 2 / 20 )25259.27586206901836.0181340339713.7576396408303
Trimmed Mean ( 3 / 20 )255281757.5513241845514.5247536437346
Trimmed Mean ( 4 / 20 )25795.98148148151676.7806021136315.3842318124177
Trimmed Mean ( 5 / 20 )26065.88461538461590.5438663677316.3880325255728
Trimmed Mean ( 6 / 20 )26337.541501.6383572917317.5392030125689
Trimmed Mean ( 7 / 20 )26593.751427.4234998629518.6305956168953
Trimmed Mean ( 8 / 20 )26854.10869565221348.6110160770319.9124197974951
Trimmed Mean ( 9 / 20 )27061.70454545451279.2705748091221.1540115737380
Trimmed Mean ( 10 / 20 )27291.88095238101190.8781689338322.9174416530071
Trimmed Mean ( 11 / 20 )27437.751124.3741465697124.4026866712547
Trimmed Mean ( 12 / 20 )27426.63157894741099.4827546479424.9450311639764
Trimmed Mean ( 13 / 20 )27419.36111111111067.4984838120025.6856206607409
Trimmed Mean ( 14 / 20 )27393.05882352941042.6635574396926.2721935835125
Trimmed Mean ( 15 / 20 )27380.968751026.5242084692126.6734759142519
Trimmed Mean ( 16 / 20 )27370.66666666671006.0816142636727.2052150428161
Trimmed Mean ( 17 / 20 )27373.25988.78523840376227.6837162781574
Trimmed Mean ( 18 / 20 )27381.6153846154968.31303437699328.2776482526981
Trimmed Mean ( 19 / 20 )27371.2083333333943.9695612323628.9958590376580
Trimmed Mean ( 20 / 20 )27386.6818181818918.16837572132429.8275158918064
Median26108.5
Midrange17560.5
Midmean - Weighted Average at Xnp27083.2903225806
Midmean - Weighted Average at X(n+1)p27380.96875
Midmean - Empirical Distribution Function27380.96875
Midmean - Empirical Distribution Function - Averaging27380.96875
Midmean - Empirical Distribution Function - Interpolation27370.6666666667
Midmean - Closest Observation27380.96875
Midmean - True Basic - Statistics Graphics Toolkit27380.96875
Midmean - MS Excel (old versions)27380.96875
Number of observations62

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24759.8870967742 & 1971.30150457727 & 12.5601725759773 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 41304816.0558504 &  &  \tabularnewline
Quadratic Mean & 29156.471253975 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 24757.1935483871 & 1969.82650263163 & 12.5682102029352 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 24773.8387096774 & 1950.08786866172 & 12.7039602203561 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 24827.7903225806 & 1915.31060343607 & 12.9628010611123 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 24890.5 & 1877.49327797938 & 13.2573044558583 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 24970.5 & 1820.84035313868 & 13.7137228735935 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 25147.4032258065 & 1704.27368037225 & 14.7554958545823 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 25241.5645161290 & 1649.04527410085 & 15.3067747214473 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 25675.5 & 1543.60915676449 & 16.6334203755422 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 25658.3709677419 & 1529.02127394575 & 16.7809116883827 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 26350.7903225806 & 1368.04200467910 & 19.2616821942990 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 27512.7096774194 & 1146.29072970631 & 24.0015111039660 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 27477.2903225806 & 1134.21875082170 & 24.2257415535357 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 27606.8709677419 & 1059.08212619131 & 26.0667896143448 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 27480.4193548387 & 983.959560653147 & 27.9284032126253 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 27455.7419354839 & 964.129766817522 & 28.477226697514 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 27352 & 911.789340343155 & 29.9981572384976 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 27313.6129032258 & 882.19747125826 & 30.9608832411058 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 27454.1290322581 & 848.927378559956 & 32.3397851519747 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 27266.8870967742 & 802.65737985564 & 33.9707673299886 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 27033.3387096774 & 727.208158971448 & 37.1741410986271 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 24999.8666666667 & 1909.94036385537 & 13.0893441176364 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 25259.2758620690 & 1836.01813403397 & 13.7576396408303 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 25528 & 1757.55132418455 & 14.5247536437346 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 25795.9814814815 & 1676.78060211363 & 15.3842318124177 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 26065.8846153846 & 1590.54386636773 & 16.3880325255728 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 26337.54 & 1501.63835729173 & 17.5392030125689 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 26593.75 & 1427.42349986295 & 18.6305956168953 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 26854.1086956522 & 1348.61101607703 & 19.9124197974951 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 27061.7045454545 & 1279.27057480912 & 21.1540115737380 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 27291.8809523810 & 1190.87816893383 & 22.9174416530071 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 27437.75 & 1124.37414656971 & 24.4026866712547 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 27426.6315789474 & 1099.48275464794 & 24.9450311639764 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 27419.3611111111 & 1067.49848381200 & 25.6856206607409 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 27393.0588235294 & 1042.66355743969 & 26.2721935835125 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 27380.96875 & 1026.52420846921 & 26.6734759142519 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 27370.6666666667 & 1006.08161426367 & 27.2052150428161 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 27373.25 & 988.785238403762 & 27.6837162781574 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 27381.6153846154 & 968.313034376993 & 28.2776482526981 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 27371.2083333333 & 943.96956123236 & 28.9958590376580 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 27386.6818181818 & 918.168375721324 & 29.8275158918064 \tabularnewline
Median & 26108.5 &  &  \tabularnewline
Midrange & 17560.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 27083.2903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 27380.96875 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 27380.96875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 27380.96875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 27370.6666666667 &  &  \tabularnewline
Midmean - Closest Observation & 27380.96875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 27380.96875 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 27380.96875 &  &  \tabularnewline
Number of observations & 62 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48952&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]24759.8870967742[/C][C]1971.30150457727[/C][C]12.5601725759773[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]41304816.0558504[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]29156.471253975[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]24757.1935483871[/C][C]1969.82650263163[/C][C]12.5682102029352[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]24773.8387096774[/C][C]1950.08786866172[/C][C]12.7039602203561[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]24827.7903225806[/C][C]1915.31060343607[/C][C]12.9628010611123[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]24890.5[/C][C]1877.49327797938[/C][C]13.2573044558583[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]24970.5[/C][C]1820.84035313868[/C][C]13.7137228735935[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]25147.4032258065[/C][C]1704.27368037225[/C][C]14.7554958545823[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]25241.5645161290[/C][C]1649.04527410085[/C][C]15.3067747214473[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]25675.5[/C][C]1543.60915676449[/C][C]16.6334203755422[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]25658.3709677419[/C][C]1529.02127394575[/C][C]16.7809116883827[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]26350.7903225806[/C][C]1368.04200467910[/C][C]19.2616821942990[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]27512.7096774194[/C][C]1146.29072970631[/C][C]24.0015111039660[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]27477.2903225806[/C][C]1134.21875082170[/C][C]24.2257415535357[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]27606.8709677419[/C][C]1059.08212619131[/C][C]26.0667896143448[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]27480.4193548387[/C][C]983.959560653147[/C][C]27.9284032126253[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]27455.7419354839[/C][C]964.129766817522[/C][C]28.477226697514[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]27352[/C][C]911.789340343155[/C][C]29.9981572384976[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]27313.6129032258[/C][C]882.19747125826[/C][C]30.9608832411058[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]27454.1290322581[/C][C]848.927378559956[/C][C]32.3397851519747[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]27266.8870967742[/C][C]802.65737985564[/C][C]33.9707673299886[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]27033.3387096774[/C][C]727.208158971448[/C][C]37.1741410986271[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]24999.8666666667[/C][C]1909.94036385537[/C][C]13.0893441176364[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]25259.2758620690[/C][C]1836.01813403397[/C][C]13.7576396408303[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]25528[/C][C]1757.55132418455[/C][C]14.5247536437346[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]25795.9814814815[/C][C]1676.78060211363[/C][C]15.3842318124177[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]26065.8846153846[/C][C]1590.54386636773[/C][C]16.3880325255728[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]26337.54[/C][C]1501.63835729173[/C][C]17.5392030125689[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]26593.75[/C][C]1427.42349986295[/C][C]18.6305956168953[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]26854.1086956522[/C][C]1348.61101607703[/C][C]19.9124197974951[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]27061.7045454545[/C][C]1279.27057480912[/C][C]21.1540115737380[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]27291.8809523810[/C][C]1190.87816893383[/C][C]22.9174416530071[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]27437.75[/C][C]1124.37414656971[/C][C]24.4026866712547[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]27426.6315789474[/C][C]1099.48275464794[/C][C]24.9450311639764[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]27419.3611111111[/C][C]1067.49848381200[/C][C]25.6856206607409[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]27393.0588235294[/C][C]1042.66355743969[/C][C]26.2721935835125[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]27380.96875[/C][C]1026.52420846921[/C][C]26.6734759142519[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]27370.6666666667[/C][C]1006.08161426367[/C][C]27.2052150428161[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]27373.25[/C][C]988.785238403762[/C][C]27.6837162781574[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]27381.6153846154[/C][C]968.313034376993[/C][C]28.2776482526981[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]27371.2083333333[/C][C]943.96956123236[/C][C]28.9958590376580[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]27386.6818181818[/C][C]918.168375721324[/C][C]29.8275158918064[/C][/ROW]
[ROW][C]Median[/C][C]26108.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17560.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]27083.2903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]27380.96875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]27380.96875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]27380.96875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]27370.6666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]27380.96875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]27380.96875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]27380.96875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]62[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48952&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 Mean24759.88709677421971.3015045772712.5601725759773
Geometric MeanNaN
Harmonic Mean41304816.0558504
Quadratic Mean29156.471253975
Winsorized Mean ( 1 / 20 )24757.19354838711969.8265026316312.5682102029352
Winsorized Mean ( 2 / 20 )24773.83870967741950.0878686617212.7039602203561
Winsorized Mean ( 3 / 20 )24827.79032258061915.3106034360712.9628010611123
Winsorized Mean ( 4 / 20 )24890.51877.4932779793813.2573044558583
Winsorized Mean ( 5 / 20 )24970.51820.8403531386813.7137228735935
Winsorized Mean ( 6 / 20 )25147.40322580651704.2736803722514.7554958545823
Winsorized Mean ( 7 / 20 )25241.56451612901649.0452741008515.3067747214473
Winsorized Mean ( 8 / 20 )25675.51543.6091567644916.6334203755422
Winsorized Mean ( 9 / 20 )25658.37096774191529.0212739457516.7809116883827
Winsorized Mean ( 10 / 20 )26350.79032258061368.0420046791019.2616821942990
Winsorized Mean ( 11 / 20 )27512.70967741941146.2907297063124.0015111039660
Winsorized Mean ( 12 / 20 )27477.29032258061134.2187508217024.2257415535357
Winsorized Mean ( 13 / 20 )27606.87096774191059.0821261913126.0667896143448
Winsorized Mean ( 14 / 20 )27480.4193548387983.95956065314727.9284032126253
Winsorized Mean ( 15 / 20 )27455.7419354839964.12976681752228.477226697514
Winsorized Mean ( 16 / 20 )27352911.78934034315529.9981572384976
Winsorized Mean ( 17 / 20 )27313.6129032258882.1974712582630.9608832411058
Winsorized Mean ( 18 / 20 )27454.1290322581848.92737855995632.3397851519747
Winsorized Mean ( 19 / 20 )27266.8870967742802.6573798556433.9707673299886
Winsorized Mean ( 20 / 20 )27033.3387096774727.20815897144837.1741410986271
Trimmed Mean ( 1 / 20 )24999.86666666671909.9403638553713.0893441176364
Trimmed Mean ( 2 / 20 )25259.27586206901836.0181340339713.7576396408303
Trimmed Mean ( 3 / 20 )255281757.5513241845514.5247536437346
Trimmed Mean ( 4 / 20 )25795.98148148151676.7806021136315.3842318124177
Trimmed Mean ( 5 / 20 )26065.88461538461590.5438663677316.3880325255728
Trimmed Mean ( 6 / 20 )26337.541501.6383572917317.5392030125689
Trimmed Mean ( 7 / 20 )26593.751427.4234998629518.6305956168953
Trimmed Mean ( 8 / 20 )26854.10869565221348.6110160770319.9124197974951
Trimmed Mean ( 9 / 20 )27061.70454545451279.2705748091221.1540115737380
Trimmed Mean ( 10 / 20 )27291.88095238101190.8781689338322.9174416530071
Trimmed Mean ( 11 / 20 )27437.751124.3741465697124.4026866712547
Trimmed Mean ( 12 / 20 )27426.63157894741099.4827546479424.9450311639764
Trimmed Mean ( 13 / 20 )27419.36111111111067.4984838120025.6856206607409
Trimmed Mean ( 14 / 20 )27393.05882352941042.6635574396926.2721935835125
Trimmed Mean ( 15 / 20 )27380.968751026.5242084692126.6734759142519
Trimmed Mean ( 16 / 20 )27370.66666666671006.0816142636727.2052150428161
Trimmed Mean ( 17 / 20 )27373.25988.78523840376227.6837162781574
Trimmed Mean ( 18 / 20 )27381.6153846154968.31303437699328.2776482526981
Trimmed Mean ( 19 / 20 )27371.2083333333943.9695612323628.9958590376580
Trimmed Mean ( 20 / 20 )27386.6818181818918.16837572132429.8275158918064
Median26108.5
Midrange17560.5
Midmean - Weighted Average at Xnp27083.2903225806
Midmean - Weighted Average at X(n+1)p27380.96875
Midmean - Empirical Distribution Function27380.96875
Midmean - Empirical Distribution Function - Averaging27380.96875
Midmean - Empirical Distribution Function - Interpolation27370.6666666667
Midmean - Closest Observation27380.96875
Midmean - True Basic - Statistics Graphics Toolkit27380.96875
Midmean - MS Excel (old versions)27380.96875
Number of observations62



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')