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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 17:47:48 -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/21/t1256082646xb7fetk2jtg33pi.htm/, Retrieved Thu, 02 May 2024 07:32:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49232, Retrieved Thu, 02 May 2024 07:32:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
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]
-   PD      [Univariate Data Series] [WS3V2 - Y[t]+X[t]] [2009-10-20 17:13:57] [90e6802d28d0afa9b030a19cd25ed2b0]
- RMPD          [Central Tendency] [WorkShop3 (SHW)] [2009-10-20 23:47:48] [2d9a0b3c2f25bb8f387fafb994d0d852] [Current]
Feedback Forum

Post a new message
Dataseries X:
581000
597000
587000
536000
524000
537000
536000
533000
528000
516000
502000
506000
518000
534000
528000
478000
469000
490000
493000
508000
517000
514000
510000
527000
542000
565000
555000
499000
511000
526000
532000
549000
561000
557000
566000
588000
620000
626000
620000
573000
573000
574000
580000
590000
593000
597000
595000
612000
628000
629000
621000
569000
567000
573000
584000
589000
591000
595000
594000
611000




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=49232&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=49232&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49232&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 Mean557066.6666666675394.43460155308103.266923748836
Geometric Mean555512.873623636
Harmonic Mean553948.234585395
Quadratic Mean558605.555527929
Winsorized Mean ( 1 / 20 )5572005351.10738842773104.127979416933
Winsorized Mean ( 2 / 20 )557533.3333333335242.34532985369106.351889899038
Winsorized Mean ( 3 / 20 )557433.3333333335156.27896898785108.107675454719
Winsorized Mean ( 4 / 20 )557766.6666666675060.61376476044110.217197477245
Winsorized Mean ( 5 / 20 )558016.6666666675012.32896162908111.32881958436
Winsorized Mean ( 6 / 20 )557616.6666666674776.59617281143116.739336232911
Winsorized Mean ( 7 / 20 )557733.3333333334711.91941330057118.366483891679
Winsorized Mean ( 8 / 20 )556133.3333333334334.81938882233128.294464763023
Winsorized Mean ( 9 / 20 )556283.3333333334307.92802626421129.130136330466
Winsorized Mean ( 10 / 20 )5564504167.36208885921133.525714381187
Winsorized Mean ( 11 / 20 )556816.6666666674104.80575912560135.649942857535
Winsorized Mean ( 12 / 20 )556816.6666666674039.87831015102137.830059204395
Winsorized Mean ( 13 / 20 )556816.6666666673970.19201934027140.249303800473
Winsorized Mean ( 14 / 20 )5577503673.05234911266151.849183454938
Winsorized Mean ( 15 / 20 )5580003557.75591049246156.840439321415
Winsorized Mean ( 16 / 20 )5580003476.79961936554160.492424381313
Winsorized Mean ( 17 / 20 )5580003391.49817735550164.529057902988
Winsorized Mean ( 18 / 20 )5577003346.74983577752166.639285087299
Winsorized Mean ( 19 / 20 )558016.6666666673019.00680217238184.834517850419
Winsorized Mean ( 20 / 20 )5573502826.41145180868197.193511809238
Trimmed Mean ( 1 / 20 )557344.8275862075219.8810070586106.773473731017
Trimmed Mean ( 2 / 20 )5575005057.78299565816110.226160449862
Trimmed Mean ( 3 / 20 )557481.4814814814929.32161244004113.094970325039
Trimmed Mean ( 4 / 20 )5575004809.6888765272115.911863389080
Trimmed Mean ( 5 / 20 )5574204695.64192216831118.710073987626
Trimmed Mean ( 6 / 20 )557270.8333333334565.88292279349122.051056226467
Trimmed Mean ( 7 / 20 )557195.6521739134472.5269327821124.581843898996
Trimmed Mean ( 8 / 20 )557090.9090909094367.59862393118127.550848202595
Trimmed Mean ( 9 / 20 )557261.9047619054329.63205511133128.708836609807
Trimmed Mean ( 10 / 20 )5574254278.7320641661130.278080431437
Trimmed Mean ( 11 / 20 )557578.9473684214238.7213877265131.544137102978
Trimmed Mean ( 12 / 20 )557694.4444444444191.03719489095133.068359575595
Trimmed Mean ( 13 / 20 )557823.5294117654132.06033561651134.998882906809
Trimmed Mean ( 14 / 20 )557968.754057.67005064721137.50964051673
Trimmed Mean ( 15 / 20 )5580004024.06553727395138.665733654529
Trimmed Mean ( 16 / 20 )5580003990.72999912622139.824042248455
Trimmed Mean ( 17 / 20 )5580003945.39653851851141.430650772946
Trimmed Mean ( 18 / 20 )5580003881.86045340506143.745507263286
Trimmed Mean ( 19 / 20 )558045.4545454553773.04019982145147.903394872883
Trimmed Mean ( 20 / 20 )5580503708.08150140374150.495613375473
Median563000
Midrange549000
Midmean - Weighted Average at Xnp556903.225806452
Midmean - Weighted Average at X(n+1)p558000
Midmean - Empirical Distribution Function556903.225806452
Midmean - Empirical Distribution Function - Averaging558000
Midmean - Empirical Distribution Function - Interpolation558000
Midmean - Closest Observation556903.225806452
Midmean - True Basic - Statistics Graphics Toolkit558000
Midmean - MS Excel (old versions)557968.75
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 557066.666666667 & 5394.43460155308 & 103.266923748836 \tabularnewline
Geometric Mean & 555512.873623636 &  &  \tabularnewline
Harmonic Mean & 553948.234585395 &  &  \tabularnewline
Quadratic Mean & 558605.555527929 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 557200 & 5351.10738842773 & 104.127979416933 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 557533.333333333 & 5242.34532985369 & 106.351889899038 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 557433.333333333 & 5156.27896898785 & 108.107675454719 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 557766.666666667 & 5060.61376476044 & 110.217197477245 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 558016.666666667 & 5012.32896162908 & 111.32881958436 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 557616.666666667 & 4776.59617281143 & 116.739336232911 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 557733.333333333 & 4711.91941330057 & 118.366483891679 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 556133.333333333 & 4334.81938882233 & 128.294464763023 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 556283.333333333 & 4307.92802626421 & 129.130136330466 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 556450 & 4167.36208885921 & 133.525714381187 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 556816.666666667 & 4104.80575912560 & 135.649942857535 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 556816.666666667 & 4039.87831015102 & 137.830059204395 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 556816.666666667 & 3970.19201934027 & 140.249303800473 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 557750 & 3673.05234911266 & 151.849183454938 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 558000 & 3557.75591049246 & 156.840439321415 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 558000 & 3476.79961936554 & 160.492424381313 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 558000 & 3391.49817735550 & 164.529057902988 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 557700 & 3346.74983577752 & 166.639285087299 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 558016.666666667 & 3019.00680217238 & 184.834517850419 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 557350 & 2826.41145180868 & 197.193511809238 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 557344.827586207 & 5219.8810070586 & 106.773473731017 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 557500 & 5057.78299565816 & 110.226160449862 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 557481.481481481 & 4929.32161244004 & 113.094970325039 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 557500 & 4809.6888765272 & 115.911863389080 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 557420 & 4695.64192216831 & 118.710073987626 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 557270.833333333 & 4565.88292279349 & 122.051056226467 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 557195.652173913 & 4472.5269327821 & 124.581843898996 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 557090.909090909 & 4367.59862393118 & 127.550848202595 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 557261.904761905 & 4329.63205511133 & 128.708836609807 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 557425 & 4278.7320641661 & 130.278080431437 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 557578.947368421 & 4238.7213877265 & 131.544137102978 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 557694.444444444 & 4191.03719489095 & 133.068359575595 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 557823.529411765 & 4132.06033561651 & 134.998882906809 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 557968.75 & 4057.67005064721 & 137.50964051673 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 558000 & 4024.06553727395 & 138.665733654529 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 558000 & 3990.72999912622 & 139.824042248455 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 558000 & 3945.39653851851 & 141.430650772946 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 558000 & 3881.86045340506 & 143.745507263286 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 558045.454545455 & 3773.04019982145 & 147.903394872883 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 558050 & 3708.08150140374 & 150.495613375473 \tabularnewline
Median & 563000 &  &  \tabularnewline
Midrange & 549000 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 556903.225806452 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 558000 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 556903.225806452 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 558000 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 558000 &  &  \tabularnewline
Midmean - Closest Observation & 556903.225806452 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 558000 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 557968.75 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49232&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]557066.666666667[/C][C]5394.43460155308[/C][C]103.266923748836[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]555512.873623636[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]553948.234585395[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]558605.555527929[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]557200[/C][C]5351.10738842773[/C][C]104.127979416933[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]557533.333333333[/C][C]5242.34532985369[/C][C]106.351889899038[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]557433.333333333[/C][C]5156.27896898785[/C][C]108.107675454719[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]557766.666666667[/C][C]5060.61376476044[/C][C]110.217197477245[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]558016.666666667[/C][C]5012.32896162908[/C][C]111.32881958436[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]557616.666666667[/C][C]4776.59617281143[/C][C]116.739336232911[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]557733.333333333[/C][C]4711.91941330057[/C][C]118.366483891679[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]556133.333333333[/C][C]4334.81938882233[/C][C]128.294464763023[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]556283.333333333[/C][C]4307.92802626421[/C][C]129.130136330466[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]556450[/C][C]4167.36208885921[/C][C]133.525714381187[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]556816.666666667[/C][C]4104.80575912560[/C][C]135.649942857535[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]556816.666666667[/C][C]4039.87831015102[/C][C]137.830059204395[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]556816.666666667[/C][C]3970.19201934027[/C][C]140.249303800473[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]557750[/C][C]3673.05234911266[/C][C]151.849183454938[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]558000[/C][C]3557.75591049246[/C][C]156.840439321415[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]558000[/C][C]3476.79961936554[/C][C]160.492424381313[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]558000[/C][C]3391.49817735550[/C][C]164.529057902988[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]557700[/C][C]3346.74983577752[/C][C]166.639285087299[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]558016.666666667[/C][C]3019.00680217238[/C][C]184.834517850419[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]557350[/C][C]2826.41145180868[/C][C]197.193511809238[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]557344.827586207[/C][C]5219.8810070586[/C][C]106.773473731017[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]557500[/C][C]5057.78299565816[/C][C]110.226160449862[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]557481.481481481[/C][C]4929.32161244004[/C][C]113.094970325039[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]557500[/C][C]4809.6888765272[/C][C]115.911863389080[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]557420[/C][C]4695.64192216831[/C][C]118.710073987626[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]557270.833333333[/C][C]4565.88292279349[/C][C]122.051056226467[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]557195.652173913[/C][C]4472.5269327821[/C][C]124.581843898996[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]557090.909090909[/C][C]4367.59862393118[/C][C]127.550848202595[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]557261.904761905[/C][C]4329.63205511133[/C][C]128.708836609807[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]557425[/C][C]4278.7320641661[/C][C]130.278080431437[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]557578.947368421[/C][C]4238.7213877265[/C][C]131.544137102978[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]557694.444444444[/C][C]4191.03719489095[/C][C]133.068359575595[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]557823.529411765[/C][C]4132.06033561651[/C][C]134.998882906809[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]557968.75[/C][C]4057.67005064721[/C][C]137.50964051673[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]558000[/C][C]4024.06553727395[/C][C]138.665733654529[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]558000[/C][C]3990.72999912622[/C][C]139.824042248455[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]558000[/C][C]3945.39653851851[/C][C]141.430650772946[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]558000[/C][C]3881.86045340506[/C][C]143.745507263286[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]558045.454545455[/C][C]3773.04019982145[/C][C]147.903394872883[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]558050[/C][C]3708.08150140374[/C][C]150.495613375473[/C][/ROW]
[ROW][C]Median[/C][C]563000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]549000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]556903.225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]558000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]556903.225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]558000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]558000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]556903.225806452[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]558000[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]557968.75[/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=49232&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49232&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 Mean557066.6666666675394.43460155308103.266923748836
Geometric Mean555512.873623636
Harmonic Mean553948.234585395
Quadratic Mean558605.555527929
Winsorized Mean ( 1 / 20 )5572005351.10738842773104.127979416933
Winsorized Mean ( 2 / 20 )557533.3333333335242.34532985369106.351889899038
Winsorized Mean ( 3 / 20 )557433.3333333335156.27896898785108.107675454719
Winsorized Mean ( 4 / 20 )557766.6666666675060.61376476044110.217197477245
Winsorized Mean ( 5 / 20 )558016.6666666675012.32896162908111.32881958436
Winsorized Mean ( 6 / 20 )557616.6666666674776.59617281143116.739336232911
Winsorized Mean ( 7 / 20 )557733.3333333334711.91941330057118.366483891679
Winsorized Mean ( 8 / 20 )556133.3333333334334.81938882233128.294464763023
Winsorized Mean ( 9 / 20 )556283.3333333334307.92802626421129.130136330466
Winsorized Mean ( 10 / 20 )5564504167.36208885921133.525714381187
Winsorized Mean ( 11 / 20 )556816.6666666674104.80575912560135.649942857535
Winsorized Mean ( 12 / 20 )556816.6666666674039.87831015102137.830059204395
Winsorized Mean ( 13 / 20 )556816.6666666673970.19201934027140.249303800473
Winsorized Mean ( 14 / 20 )5577503673.05234911266151.849183454938
Winsorized Mean ( 15 / 20 )5580003557.75591049246156.840439321415
Winsorized Mean ( 16 / 20 )5580003476.79961936554160.492424381313
Winsorized Mean ( 17 / 20 )5580003391.49817735550164.529057902988
Winsorized Mean ( 18 / 20 )5577003346.74983577752166.639285087299
Winsorized Mean ( 19 / 20 )558016.6666666673019.00680217238184.834517850419
Winsorized Mean ( 20 / 20 )5573502826.41145180868197.193511809238
Trimmed Mean ( 1 / 20 )557344.8275862075219.8810070586106.773473731017
Trimmed Mean ( 2 / 20 )5575005057.78299565816110.226160449862
Trimmed Mean ( 3 / 20 )557481.4814814814929.32161244004113.094970325039
Trimmed Mean ( 4 / 20 )5575004809.6888765272115.911863389080
Trimmed Mean ( 5 / 20 )5574204695.64192216831118.710073987626
Trimmed Mean ( 6 / 20 )557270.8333333334565.88292279349122.051056226467
Trimmed Mean ( 7 / 20 )557195.6521739134472.5269327821124.581843898996
Trimmed Mean ( 8 / 20 )557090.9090909094367.59862393118127.550848202595
Trimmed Mean ( 9 / 20 )557261.9047619054329.63205511133128.708836609807
Trimmed Mean ( 10 / 20 )5574254278.7320641661130.278080431437
Trimmed Mean ( 11 / 20 )557578.9473684214238.7213877265131.544137102978
Trimmed Mean ( 12 / 20 )557694.4444444444191.03719489095133.068359575595
Trimmed Mean ( 13 / 20 )557823.5294117654132.06033561651134.998882906809
Trimmed Mean ( 14 / 20 )557968.754057.67005064721137.50964051673
Trimmed Mean ( 15 / 20 )5580004024.06553727395138.665733654529
Trimmed Mean ( 16 / 20 )5580003990.72999912622139.824042248455
Trimmed Mean ( 17 / 20 )5580003945.39653851851141.430650772946
Trimmed Mean ( 18 / 20 )5580003881.86045340506143.745507263286
Trimmed Mean ( 19 / 20 )558045.4545454553773.04019982145147.903394872883
Trimmed Mean ( 20 / 20 )5580503708.08150140374150.495613375473
Median563000
Midrange549000
Midmean - Weighted Average at Xnp556903.225806452
Midmean - Weighted Average at X(n+1)p558000
Midmean - Empirical Distribution Function556903.225806452
Midmean - Empirical Distribution Function - Averaging558000
Midmean - Empirical Distribution Function - Interpolation558000
Midmean - Closest Observation556903.225806452
Midmean - True Basic - Statistics Graphics Toolkit558000
Midmean - MS Excel (old versions)557968.75
Number of observations60



Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')