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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 25 Nov 2007 10:17:34 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/25/t1196010570qihn51i5te5hqlt.htm/, Retrieved Sat, 04 May 2024 13:47:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6504, Retrieved Sat, 04 May 2024 13:47:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 3 Q3 ass...] [2007-11-25 17:17:34] [44cf2be50bc8700e14714598feda9df9] [Current]
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Dataseries X:
427,712333
134,3275108
489,9938335
-217,8448921
619,9908325
381,3151079
-847,3048921
49,51351079
-264,9848921
-893,4891675
389,2108325
-106,6009168
-227,0116341
-502,488592
-122,9424584
-105,4748201
-559,7117575
-320,8748201
643,9251799
326,9111408
-978,6088592
513,2082425
206,1082425
102,6882425
31,8485776
101,1485509
227,9728263
655,8285509
-328,8357246
686,8855087
106,9685509
792,1085509
-183,6114491
521,8427544
-625,6157246
200,7642754
520,3618088
-120,1375416
537,727482
631,7832066
184,4030832
-123,0567934
695,9232066
-105,3615416
869,4645838
840,6030832
-48,58396917
475,4030832
-394,1621583
-192,7993834
414,7248921
-105,9219383
250,1163412
-294,8593834
-199,7938335
-560,5393834
557,7406166
244,0363412
516,1363412
715,0163412
-645,3861254




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6504&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6504&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6504&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.159195316721359.20122693439881.65806015178523
Geometric MeanNaN
Harmonic Mean2657.38931949860
Quadratic Mean468.958786949895
Winsorized Mean ( 1 / 20 )99.081460744590158.69181844516861.68816477951104
Winsorized Mean ( 2 / 20 )99.005714616721357.94635645258111.70857532168981
Winsorized Mean ( 3 / 20 )105.14472561672154.72298766058071.92139958199800
Winsorized Mean ( 4 / 20 )105.18913651508254.19912683164721.94079024265131
Winsorized Mean ( 5 / 20 )109.78246793311552.90145024571512.07522605567901
Winsorized Mean ( 6 / 20 )106.80909102491852.33942426279662.04070053366711
Winsorized Mean ( 7 / 20 )112.00972318065650.74059424277412.20749726825690
Winsorized Mean ( 8 / 20 )124.62407864295147.7356570480482.61071254382256
Winsorized Mean ( 9 / 20 )132.52254645278745.74277970727252.89712490803696
Winsorized Mean ( 10 / 20 )123.62265933803343.77159794635442.82426653670589
Winsorized Mean ( 11 / 20 )124.70504168393442.39621042962682.94141953774221
Winsorized Mean ( 12 / 20 )127.45712634622940.93717915238223.11348092333842
Winsorized Mean ( 13 / 20 )135.23417652983639.62274216685373.41304435620223
Winsorized Mean ( 14 / 20 )136.36823950688539.14686128890483.48350378592256
Winsorized Mean ( 15 / 20 )140.08700013803338.36786253111733.65115466164993
Winsorized Mean ( 16 / 20 )135.83258468885237.11932803718713.65934923586903
Winsorized Mean ( 17 / 20 )134.32688186918036.09895074437883.72107441073193
Winsorized Mean ( 18 / 20 )138.12278841016431.34881136806304.40599762423141
Winsorized Mean ( 19 / 20 )134.11313247409830.72453021571444.36501816406958
Winsorized Mean ( 20 / 20 )126.66751188393429.33507461154854.31795431105085
Trimmed Mean ( 1 / 20 )103.33652863932256.88071115723741.81672357002825
Trimmed Mean ( 2 / 20 )107.89019778982554.64967540892931.97421479601682
Trimmed Mean ( 3 / 20 )112.81704754945552.38840407789952.15347364622331
Trimmed Mean ( 4 / 20 )115.76051697018951.15971131225532.26272811165098
Trimmed Mean ( 5 / 20 )118.92156700823549.80977927264362.38751443481198
Trimmed Mean ( 6 / 20 )121.19701616571448.54201689853612.49674455058272
Trimmed Mean ( 7 / 20 )124.30929784510647.0801428806042.64037639308693
Trimmed Mean ( 8 / 20 )126.69112024044445.66582401071862.77430929989805
Trimmed Mean ( 9 / 20 )127.05765959348844.66322662166132.84479356294125
Trimmed Mean ( 10 / 20 )126.15425011268343.83839733124572.87771127122767
Trimmed Mean ( 11 / 20 )126.55021687487243.19909996179082.92946420149504
Trimmed Mean ( 12 / 20 )126.82676647351442.6152985726092.97608536655968
Trimmed Mean ( 13 / 20 )126.73521420628642.10274060227743.01014167708196
Trimmed Mean ( 14 / 20 )125.52673704606141.6209854441393.01594822195007
Trimmed Mean ( 15 / 20 )124.00293140064540.9400777603473.0288885166884
Trimmed Mean ( 16 / 20 )121.74746429034540.04755521893183.04007232463446
Trimmed Mean ( 17 / 20 )119.75859312296338.99812096614433.07088111314209
Trimmed Mean ( 18 / 20 )117.667615208837.6167831236793.12806161074232
Trimmed Mean ( 19 / 20 )114.65368872260937.05376206538273.09425230615715
Trimmed Mean ( 20 / 20 )111.67868604381036.12307037570453.09161665612239
Median106.9685509
Midrange-54.5721377
Midmean - Weighted Average at Xnp111.029421030667
Midmean - Weighted Average at X(n+1)p124.002931400645
Midmean - Empirical Distribution Function124.002931400645
Midmean - Empirical Distribution Function - Averaging124.002931400645
Midmean - Empirical Distribution Function - Interpolation124.002931400645
Midmean - Closest Observation113.32018691625
Midmean - True Basic - Statistics Graphics Toolkit124.002931400645
Midmean - MS Excel (old versions)124.002931400645
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.1591953167213 & 59.2012269343988 & 1.65806015178523 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 2657.38931949860 &  &  \tabularnewline
Quadratic Mean & 468.958786949895 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.0814607445901 & 58.6918184451686 & 1.68816477951104 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 99.0057146167213 & 57.9463564525811 & 1.70857532168981 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 105.144725616721 & 54.7229876605807 & 1.92139958199800 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 105.189136515082 & 54.1991268316472 & 1.94079024265131 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 109.782467933115 & 52.9014502457151 & 2.07522605567901 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 106.809091024918 & 52.3394242627966 & 2.04070053366711 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 112.009723180656 & 50.7405942427741 & 2.20749726825690 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 124.624078642951 & 47.735657048048 & 2.61071254382256 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 132.522546452787 & 45.7427797072725 & 2.89712490803696 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 123.622659338033 & 43.7715979463544 & 2.82426653670589 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 124.705041683934 & 42.3962104296268 & 2.94141953774221 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 127.457126346229 & 40.9371791523822 & 3.11348092333842 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 135.234176529836 & 39.6227421668537 & 3.41304435620223 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 136.368239506885 & 39.1468612889048 & 3.48350378592256 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 140.087000138033 & 38.3678625311173 & 3.65115466164993 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 135.832584688852 & 37.1193280371871 & 3.65934923586903 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 134.326881869180 & 36.0989507443788 & 3.72107441073193 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 138.122788410164 & 31.3488113680630 & 4.40599762423141 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 134.113132474098 & 30.7245302157144 & 4.36501816406958 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 126.667511883934 & 29.3350746115485 & 4.31795431105085 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.336528639322 & 56.8807111572374 & 1.81672357002825 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 107.890197789825 & 54.6496754089293 & 1.97421479601682 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 112.817047549455 & 52.3884040778995 & 2.15347364622331 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 115.760516970189 & 51.1597113122553 & 2.26272811165098 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 118.921567008235 & 49.8097792726436 & 2.38751443481198 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 121.197016165714 & 48.5420168985361 & 2.49674455058272 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 124.309297845106 & 47.080142880604 & 2.64037639308693 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 126.691120240444 & 45.6658240107186 & 2.77430929989805 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 127.057659593488 & 44.6632266216613 & 2.84479356294125 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 126.154250112683 & 43.8383973312457 & 2.87771127122767 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 126.550216874872 & 43.1990999617908 & 2.92946420149504 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 126.826766473514 & 42.615298572609 & 2.97608536655968 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 126.735214206286 & 42.1027406022774 & 3.01014167708196 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 125.526737046061 & 41.620985444139 & 3.01594822195007 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 124.002931400645 & 40.940077760347 & 3.0288885166884 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 121.747464290345 & 40.0475552189318 & 3.04007232463446 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 119.758593122963 & 38.9981209661443 & 3.07088111314209 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 117.6676152088 & 37.616783123679 & 3.12806161074232 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.653688722609 & 37.0537620653827 & 3.09425230615715 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111.678686043810 & 36.1230703757045 & 3.09161665612239 \tabularnewline
Median & 106.9685509 &  &  \tabularnewline
Midrange & -54.5721377 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.029421030667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 124.002931400645 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 124.002931400645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 124.002931400645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 124.002931400645 &  &  \tabularnewline
Midmean - Closest Observation & 113.32018691625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 124.002931400645 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 124.002931400645 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6504&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]98.1591953167213[/C][C]59.2012269343988[/C][C]1.65806015178523[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2657.38931949860[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]468.958786949895[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.0814607445901[/C][C]58.6918184451686[/C][C]1.68816477951104[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]99.0057146167213[/C][C]57.9463564525811[/C][C]1.70857532168981[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]105.144725616721[/C][C]54.7229876605807[/C][C]1.92139958199800[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]105.189136515082[/C][C]54.1991268316472[/C][C]1.94079024265131[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]109.782467933115[/C][C]52.9014502457151[/C][C]2.07522605567901[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]106.809091024918[/C][C]52.3394242627966[/C][C]2.04070053366711[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]112.009723180656[/C][C]50.7405942427741[/C][C]2.20749726825690[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]124.624078642951[/C][C]47.735657048048[/C][C]2.61071254382256[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]132.522546452787[/C][C]45.7427797072725[/C][C]2.89712490803696[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]123.622659338033[/C][C]43.7715979463544[/C][C]2.82426653670589[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]124.705041683934[/C][C]42.3962104296268[/C][C]2.94141953774221[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]127.457126346229[/C][C]40.9371791523822[/C][C]3.11348092333842[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]135.234176529836[/C][C]39.6227421668537[/C][C]3.41304435620223[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]136.368239506885[/C][C]39.1468612889048[/C][C]3.48350378592256[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]140.087000138033[/C][C]38.3678625311173[/C][C]3.65115466164993[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]135.832584688852[/C][C]37.1193280371871[/C][C]3.65934923586903[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]134.326881869180[/C][C]36.0989507443788[/C][C]3.72107441073193[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]138.122788410164[/C][C]31.3488113680630[/C][C]4.40599762423141[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]134.113132474098[/C][C]30.7245302157144[/C][C]4.36501816406958[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]126.667511883934[/C][C]29.3350746115485[/C][C]4.31795431105085[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.336528639322[/C][C]56.8807111572374[/C][C]1.81672357002825[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]107.890197789825[/C][C]54.6496754089293[/C][C]1.97421479601682[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]112.817047549455[/C][C]52.3884040778995[/C][C]2.15347364622331[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]115.760516970189[/C][C]51.1597113122553[/C][C]2.26272811165098[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]118.921567008235[/C][C]49.8097792726436[/C][C]2.38751443481198[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]121.197016165714[/C][C]48.5420168985361[/C][C]2.49674455058272[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]124.309297845106[/C][C]47.080142880604[/C][C]2.64037639308693[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]126.691120240444[/C][C]45.6658240107186[/C][C]2.77430929989805[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]127.057659593488[/C][C]44.6632266216613[/C][C]2.84479356294125[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]126.154250112683[/C][C]43.8383973312457[/C][C]2.87771127122767[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]126.550216874872[/C][C]43.1990999617908[/C][C]2.92946420149504[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]126.826766473514[/C][C]42.615298572609[/C][C]2.97608536655968[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]126.735214206286[/C][C]42.1027406022774[/C][C]3.01014167708196[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]125.526737046061[/C][C]41.620985444139[/C][C]3.01594822195007[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]124.002931400645[/C][C]40.940077760347[/C][C]3.0288885166884[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]121.747464290345[/C][C]40.0475552189318[/C][C]3.04007232463446[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]119.758593122963[/C][C]38.9981209661443[/C][C]3.07088111314209[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]117.6676152088[/C][C]37.616783123679[/C][C]3.12806161074232[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.653688722609[/C][C]37.0537620653827[/C][C]3.09425230615715[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111.678686043810[/C][C]36.1230703757045[/C][C]3.09161665612239[/C][/ROW]
[ROW][C]Median[/C][C]106.9685509[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-54.5721377[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.029421030667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]124.002931400645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]124.002931400645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]124.002931400645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]124.002931400645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.32018691625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]124.002931400645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]124.002931400645[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6504&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6504&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 Mean98.159195316721359.20122693439881.65806015178523
Geometric MeanNaN
Harmonic Mean2657.38931949860
Quadratic Mean468.958786949895
Winsorized Mean ( 1 / 20 )99.081460744590158.69181844516861.68816477951104
Winsorized Mean ( 2 / 20 )99.005714616721357.94635645258111.70857532168981
Winsorized Mean ( 3 / 20 )105.14472561672154.72298766058071.92139958199800
Winsorized Mean ( 4 / 20 )105.18913651508254.19912683164721.94079024265131
Winsorized Mean ( 5 / 20 )109.78246793311552.90145024571512.07522605567901
Winsorized Mean ( 6 / 20 )106.80909102491852.33942426279662.04070053366711
Winsorized Mean ( 7 / 20 )112.00972318065650.74059424277412.20749726825690
Winsorized Mean ( 8 / 20 )124.62407864295147.7356570480482.61071254382256
Winsorized Mean ( 9 / 20 )132.52254645278745.74277970727252.89712490803696
Winsorized Mean ( 10 / 20 )123.62265933803343.77159794635442.82426653670589
Winsorized Mean ( 11 / 20 )124.70504168393442.39621042962682.94141953774221
Winsorized Mean ( 12 / 20 )127.45712634622940.93717915238223.11348092333842
Winsorized Mean ( 13 / 20 )135.23417652983639.62274216685373.41304435620223
Winsorized Mean ( 14 / 20 )136.36823950688539.14686128890483.48350378592256
Winsorized Mean ( 15 / 20 )140.08700013803338.36786253111733.65115466164993
Winsorized Mean ( 16 / 20 )135.83258468885237.11932803718713.65934923586903
Winsorized Mean ( 17 / 20 )134.32688186918036.09895074437883.72107441073193
Winsorized Mean ( 18 / 20 )138.12278841016431.34881136806304.40599762423141
Winsorized Mean ( 19 / 20 )134.11313247409830.72453021571444.36501816406958
Winsorized Mean ( 20 / 20 )126.66751188393429.33507461154854.31795431105085
Trimmed Mean ( 1 / 20 )103.33652863932256.88071115723741.81672357002825
Trimmed Mean ( 2 / 20 )107.89019778982554.64967540892931.97421479601682
Trimmed Mean ( 3 / 20 )112.81704754945552.38840407789952.15347364622331
Trimmed Mean ( 4 / 20 )115.76051697018951.15971131225532.26272811165098
Trimmed Mean ( 5 / 20 )118.92156700823549.80977927264362.38751443481198
Trimmed Mean ( 6 / 20 )121.19701616571448.54201689853612.49674455058272
Trimmed Mean ( 7 / 20 )124.30929784510647.0801428806042.64037639308693
Trimmed Mean ( 8 / 20 )126.69112024044445.66582401071862.77430929989805
Trimmed Mean ( 9 / 20 )127.05765959348844.66322662166132.84479356294125
Trimmed Mean ( 10 / 20 )126.15425011268343.83839733124572.87771127122767
Trimmed Mean ( 11 / 20 )126.55021687487243.19909996179082.92946420149504
Trimmed Mean ( 12 / 20 )126.82676647351442.6152985726092.97608536655968
Trimmed Mean ( 13 / 20 )126.73521420628642.10274060227743.01014167708196
Trimmed Mean ( 14 / 20 )125.52673704606141.6209854441393.01594822195007
Trimmed Mean ( 15 / 20 )124.00293140064540.9400777603473.0288885166884
Trimmed Mean ( 16 / 20 )121.74746429034540.04755521893183.04007232463446
Trimmed Mean ( 17 / 20 )119.75859312296338.99812096614433.07088111314209
Trimmed Mean ( 18 / 20 )117.667615208837.6167831236793.12806161074232
Trimmed Mean ( 19 / 20 )114.65368872260937.05376206538273.09425230615715
Trimmed Mean ( 20 / 20 )111.67868604381036.12307037570453.09161665612239
Median106.9685509
Midrange-54.5721377
Midmean - Weighted Average at Xnp111.029421030667
Midmean - Weighted Average at X(n+1)p124.002931400645
Midmean - Empirical Distribution Function124.002931400645
Midmean - Empirical Distribution Function - Averaging124.002931400645
Midmean - Empirical Distribution Function - Interpolation124.002931400645
Midmean - Closest Observation113.32018691625
Midmean - True Basic - Statistics Graphics Toolkit124.002931400645
Midmean - MS Excel (old versions)124.002931400645
Number of observations61



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')