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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 computationFri, 12 Mar 2010 11:40:55 -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/2010/Mar/12/t1268419544pgskh3rlud53doy.htm/, Retrieved Fri, 21 Jan 2022 10:26:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74359, Retrieved Fri, 21 Jan 2022 10:26:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Datareeks - goudk...] [2010-02-07 19:30:00] [eff9c8e59483abf95ad26d00265fce8e]
- RMP     [Central Tendency] [KDGP1W52] [2010-03-12 18:40:55] [615289131d9f16e370470ddcc9ade44c] [Current]
- RM        [Mean versus Median] [Vergelijking - Go...] [2010-03-12 19:06:25] [eff9c8e59483abf95ad26d00265fce8e]
-           [Central Tendency] [Robuustheid -Goud...] [2010-03-12 19:08:59] [eff9c8e59483abf95ad26d00265fce8e]
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Dataseries X:
25204
24977
24320
22680
22052
21467
21383
21777
21928
21814
22937
23595
20830
19650
19195
19644
18483
18079
19178
18391
18441
18584
20108
20148
19394
17745
17696
17032
16438
15683
15594
15713
15937
16171
15928
16348
15579
15305
15648
14954
15137
15839
16050
15168
17064
16005
14886
14931
14544
13812
13031
12574
11964
11451
11346
11353
10702
10646
10556
10463
10407
10625
10872
10805
10653
10574
10431
10383
10296
10872
10635
10297
10570




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74359&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74359&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74359&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16040.7123287671506.85302181478131.6476604427326
Geometric Mean15461.2113430948
Harmonic Mean14892.8804739624
Quadratic Mean16607.2650062044
Winsorized Mean ( 1 / 24 )16037.6164383562506.0790146186131.6899455916828
Winsorized Mean ( 2 / 24 )16021.9726027397501.43217375375931.9524223641216
Winsorized Mean ( 3 / 24 )15993.1643835616494.67250709395532.330813122234
Winsorized Mean ( 4 / 24 )15958.4246575342487.02833558665832.7669326227421
Winsorized Mean ( 5 / 24 )15943.0136986301483.22696849367332.9928061513787
Winsorized Mean ( 6 / 24 )15899.0410958904472.35425600419933.6591464854909
Winsorized Mean ( 7 / 24 )15888.4931506849470.00663315184233.8048274853856
Winsorized Mean ( 8 / 24 )15876.4383561644467.72145471777433.9442165759625
Winsorized Mean ( 9 / 24 )15878.1643835616465.93094198526534.0783643084682
Winsorized Mean ( 10 / 24 )15837.0684931507458.35906375628434.5516642855600
Winsorized Mean ( 11 / 24 )15826.0684931507455.94668618447734.7103487593886
Winsorized Mean ( 12 / 24 )15736.3150684932440.7679012806635.7020441433484
Winsorized Mean ( 13 / 24 )15623.5890410959420.52308869571737.1527496612697
Winsorized Mean ( 14 / 24 )15635.6712328767416.17970679331937.5695185941433
Winsorized Mean ( 15 / 24 )15555.3287671233400.23573297980238.8654172662497
Winsorized Mean ( 16 / 24 )15554.0136986301400.04893512177538.8802777187633
Winsorized Mean ( 17 / 24 )15606.1780821918374.11206613775241.7152492388348
Winsorized Mean ( 18 / 24 )15558.8356164384367.01142779628342.3933273954472
Winsorized Mean ( 19 / 24 )15579.9178082192362.35360228277042.9964479725554
Winsorized Mean ( 20 / 24 )15557.7260273973318.20158600799648.8926727945546
Winsorized Mean ( 21 / 24 )15704.1506849315287.26664652672454.6675044764397
Winsorized Mean ( 22 / 24 )15829.2191780822265.01756155486559.728944320564
Winsorized Mean ( 23 / 24 )16059.5342465753227.83388705844070.4879087738866
Winsorized Mean ( 24 / 24 )16197.6164383562181.29244333801689.3452376730125
Trimmed Mean ( 1 / 24 )15992.5633802817498.11196115737532.1063628809929
Trimmed Mean ( 2 / 24 )15944.8985507246488.5338854834232.6382652760036
Trimmed Mean ( 3 / 24 )15902.9104477612479.95144661119733.1344150747898
Trimmed Mean ( 4 / 24 )15869.1230769231472.60917008446733.5776876146666
Trimmed Mean ( 5 / 24 )15843.2539682540466.38267415810633.9705028640987
Trimmed Mean ( 6 / 24 )15819.3770491803459.82949629547734.4027018201875
Trimmed Mean ( 7 / 24 )15802.9491525424454.63948275249634.7592977558120
Trimmed Mean ( 8 / 24 )15787.2982456140448.61362950149735.1913031780978
Trimmed Mean ( 9 / 24 )15772.5090909091441.48956912359135.7256664573511
Trimmed Mean ( 10 / 24 )15756.3396226415432.83548440798736.4026060483288
Trimmed Mean ( 11 / 24 )15744.7843137255423.56125034648637.1723907719268
Trimmed Mean ( 12 / 24 )15733.7755102041412.23193852971638.1672889449586
Trimmed Mean ( 13 / 24 )15733.4468085106401.14413936191739.2214300663526
Trimmed Mean ( 14 / 24 )15747.1555555556391.24867438450440.2484572767647
Trimmed Mean ( 15 / 24 )15760.6744186047379.16371771225741.5669371365465
Trimmed Mean ( 16 / 24 )15785.0487804878366.75028546918843.040317638182
Trimmed Mean ( 17 / 24 )15812.0769230769349.98691200633445.1790520749266
Trimmed Mean ( 18 / 24 )15835.9729729730334.15920098260247.3905040663461
Trimmed Mean ( 19 / 24 )15868.0857142857313.98506192436150.5377090777279
Trimmed Mean ( 20 / 24 )15901.6363636364286.72450026041955.4596358148454
Trimmed Mean ( 21 / 24 )15942.1290322581262.46119525544260.7408993041517
Trimmed Mean ( 22 / 24 )15970.6551724138238.6330905616266.9255681801173
Trimmed Mean ( 23 / 24 )15988.0370370370211.78799592492575.4907612549699
Trimmed Mean ( 24 / 24 )15978.96186.97677645454685.459597191657
Median15839
Midrange17750
Midmean - Weighted Average at Xnp15742.6666666667
Midmean - Weighted Average at X(n+1)p15835.9729729730
Midmean - Empirical Distribution Function15835.9729729730
Midmean - Empirical Distribution Function - Averaging15835.9729729730
Midmean - Empirical Distribution Function - Interpolation15835.9729729730
Midmean - Closest Observation15717.8157894737
Midmean - True Basic - Statistics Graphics Toolkit15835.9729729730
Midmean - MS Excel (old versions)15835.9729729730
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16040.7123287671 & 506.853021814781 & 31.6476604427326 \tabularnewline
Geometric Mean & 15461.2113430948 &  &  \tabularnewline
Harmonic Mean & 14892.8804739624 &  &  \tabularnewline
Quadratic Mean & 16607.2650062044 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16037.6164383562 & 506.07901461861 & 31.6899455916828 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16021.9726027397 & 501.432173753759 & 31.9524223641216 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 15993.1643835616 & 494.672507093955 & 32.330813122234 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 15958.4246575342 & 487.028335586658 & 32.7669326227421 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 15943.0136986301 & 483.226968493673 & 32.9928061513787 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 15899.0410958904 & 472.354256004199 & 33.6591464854909 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 15888.4931506849 & 470.006633151842 & 33.8048274853856 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 15876.4383561644 & 467.721454717774 & 33.9442165759625 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 15878.1643835616 & 465.930941985265 & 34.0783643084682 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 15837.0684931507 & 458.359063756284 & 34.5516642855600 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 15826.0684931507 & 455.946686184477 & 34.7103487593886 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 15736.3150684932 & 440.76790128066 & 35.7020441433484 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 15623.5890410959 & 420.523088695717 & 37.1527496612697 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 15635.6712328767 & 416.179706793319 & 37.5695185941433 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 15555.3287671233 & 400.235732979802 & 38.8654172662497 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 15554.0136986301 & 400.048935121775 & 38.8802777187633 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 15606.1780821918 & 374.112066137752 & 41.7152492388348 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 15558.8356164384 & 367.011427796283 & 42.3933273954472 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 15579.9178082192 & 362.353602282770 & 42.9964479725554 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 15557.7260273973 & 318.201586007996 & 48.8926727945546 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 15704.1506849315 & 287.266646526724 & 54.6675044764397 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 15829.2191780822 & 265.017561554865 & 59.728944320564 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16059.5342465753 & 227.833887058440 & 70.4879087738866 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16197.6164383562 & 181.292443338016 & 89.3452376730125 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 15992.5633802817 & 498.111961157375 & 32.1063628809929 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 15944.8985507246 & 488.53388548342 & 32.6382652760036 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 15902.9104477612 & 479.951446611197 & 33.1344150747898 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 15869.1230769231 & 472.609170084467 & 33.5776876146666 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 15843.2539682540 & 466.382674158106 & 33.9705028640987 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 15819.3770491803 & 459.829496295477 & 34.4027018201875 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 15802.9491525424 & 454.639482752496 & 34.7592977558120 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 15787.2982456140 & 448.613629501497 & 35.1913031780978 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 15772.5090909091 & 441.489569123591 & 35.7256664573511 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 15756.3396226415 & 432.835484407987 & 36.4026060483288 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 15744.7843137255 & 423.561250346486 & 37.1723907719268 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 15733.7755102041 & 412.231938529716 & 38.1672889449586 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 15733.4468085106 & 401.144139361917 & 39.2214300663526 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 15747.1555555556 & 391.248674384504 & 40.2484572767647 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 15760.6744186047 & 379.163717712257 & 41.5669371365465 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 15785.0487804878 & 366.750285469188 & 43.040317638182 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 15812.0769230769 & 349.986912006334 & 45.1790520749266 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 15835.9729729730 & 334.159200982602 & 47.3905040663461 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 15868.0857142857 & 313.985061924361 & 50.5377090777279 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 15901.6363636364 & 286.724500260419 & 55.4596358148454 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 15942.1290322581 & 262.461195255442 & 60.7408993041517 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 15970.6551724138 & 238.63309056162 & 66.9255681801173 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 15988.0370370370 & 211.787995924925 & 75.4907612549699 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 15978.96 & 186.976776454546 & 85.459597191657 \tabularnewline
Median & 15839 &  &  \tabularnewline
Midrange & 17750 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15742.6666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15835.9729729730 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15835.9729729730 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15835.9729729730 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15835.9729729730 &  &  \tabularnewline
Midmean - Closest Observation & 15717.8157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15835.9729729730 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15835.9729729730 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74359&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]16040.7123287671[/C][C]506.853021814781[/C][C]31.6476604427326[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15461.2113430948[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14892.8804739624[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16607.2650062044[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16037.6164383562[/C][C]506.07901461861[/C][C]31.6899455916828[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16021.9726027397[/C][C]501.432173753759[/C][C]31.9524223641216[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]15993.1643835616[/C][C]494.672507093955[/C][C]32.330813122234[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]15958.4246575342[/C][C]487.028335586658[/C][C]32.7669326227421[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]15943.0136986301[/C][C]483.226968493673[/C][C]32.9928061513787[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]15899.0410958904[/C][C]472.354256004199[/C][C]33.6591464854909[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]15888.4931506849[/C][C]470.006633151842[/C][C]33.8048274853856[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]15876.4383561644[/C][C]467.721454717774[/C][C]33.9442165759625[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]15878.1643835616[/C][C]465.930941985265[/C][C]34.0783643084682[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]15837.0684931507[/C][C]458.359063756284[/C][C]34.5516642855600[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]15826.0684931507[/C][C]455.946686184477[/C][C]34.7103487593886[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]15736.3150684932[/C][C]440.76790128066[/C][C]35.7020441433484[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]15623.5890410959[/C][C]420.523088695717[/C][C]37.1527496612697[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]15635.6712328767[/C][C]416.179706793319[/C][C]37.5695185941433[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]15555.3287671233[/C][C]400.235732979802[/C][C]38.8654172662497[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]15554.0136986301[/C][C]400.048935121775[/C][C]38.8802777187633[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]15606.1780821918[/C][C]374.112066137752[/C][C]41.7152492388348[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]15558.8356164384[/C][C]367.011427796283[/C][C]42.3933273954472[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]15579.9178082192[/C][C]362.353602282770[/C][C]42.9964479725554[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]15557.7260273973[/C][C]318.201586007996[/C][C]48.8926727945546[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]15704.1506849315[/C][C]287.266646526724[/C][C]54.6675044764397[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]15829.2191780822[/C][C]265.017561554865[/C][C]59.728944320564[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16059.5342465753[/C][C]227.833887058440[/C][C]70.4879087738866[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16197.6164383562[/C][C]181.292443338016[/C][C]89.3452376730125[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]15992.5633802817[/C][C]498.111961157375[/C][C]32.1063628809929[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]15944.8985507246[/C][C]488.53388548342[/C][C]32.6382652760036[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]15902.9104477612[/C][C]479.951446611197[/C][C]33.1344150747898[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]15869.1230769231[/C][C]472.609170084467[/C][C]33.5776876146666[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]15843.2539682540[/C][C]466.382674158106[/C][C]33.9705028640987[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]15819.3770491803[/C][C]459.829496295477[/C][C]34.4027018201875[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]15802.9491525424[/C][C]454.639482752496[/C][C]34.7592977558120[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]15787.2982456140[/C][C]448.613629501497[/C][C]35.1913031780978[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]15772.5090909091[/C][C]441.489569123591[/C][C]35.7256664573511[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]15756.3396226415[/C][C]432.835484407987[/C][C]36.4026060483288[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]15744.7843137255[/C][C]423.561250346486[/C][C]37.1723907719268[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]15733.7755102041[/C][C]412.231938529716[/C][C]38.1672889449586[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]15733.4468085106[/C][C]401.144139361917[/C][C]39.2214300663526[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]15747.1555555556[/C][C]391.248674384504[/C][C]40.2484572767647[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]15760.6744186047[/C][C]379.163717712257[/C][C]41.5669371365465[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]15785.0487804878[/C][C]366.750285469188[/C][C]43.040317638182[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]15812.0769230769[/C][C]349.986912006334[/C][C]45.1790520749266[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]15835.9729729730[/C][C]334.159200982602[/C][C]47.3905040663461[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]15868.0857142857[/C][C]313.985061924361[/C][C]50.5377090777279[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]15901.6363636364[/C][C]286.724500260419[/C][C]55.4596358148454[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]15942.1290322581[/C][C]262.461195255442[/C][C]60.7408993041517[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]15970.6551724138[/C][C]238.63309056162[/C][C]66.9255681801173[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]15988.0370370370[/C][C]211.787995924925[/C][C]75.4907612549699[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]15978.96[/C][C]186.976776454546[/C][C]85.459597191657[/C][/ROW]
[ROW][C]Median[/C][C]15839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17750[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15742.6666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15835.9729729730[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15835.9729729730[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15835.9729729730[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15835.9729729730[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15717.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15835.9729729730[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15835.9729729730[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74359&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74359&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 Mean16040.7123287671506.85302181478131.6476604427326
Geometric Mean15461.2113430948
Harmonic Mean14892.8804739624
Quadratic Mean16607.2650062044
Winsorized Mean ( 1 / 24 )16037.6164383562506.0790146186131.6899455916828
Winsorized Mean ( 2 / 24 )16021.9726027397501.43217375375931.9524223641216
Winsorized Mean ( 3 / 24 )15993.1643835616494.67250709395532.330813122234
Winsorized Mean ( 4 / 24 )15958.4246575342487.02833558665832.7669326227421
Winsorized Mean ( 5 / 24 )15943.0136986301483.22696849367332.9928061513787
Winsorized Mean ( 6 / 24 )15899.0410958904472.35425600419933.6591464854909
Winsorized Mean ( 7 / 24 )15888.4931506849470.00663315184233.8048274853856
Winsorized Mean ( 8 / 24 )15876.4383561644467.72145471777433.9442165759625
Winsorized Mean ( 9 / 24 )15878.1643835616465.93094198526534.0783643084682
Winsorized Mean ( 10 / 24 )15837.0684931507458.35906375628434.5516642855600
Winsorized Mean ( 11 / 24 )15826.0684931507455.94668618447734.7103487593886
Winsorized Mean ( 12 / 24 )15736.3150684932440.7679012806635.7020441433484
Winsorized Mean ( 13 / 24 )15623.5890410959420.52308869571737.1527496612697
Winsorized Mean ( 14 / 24 )15635.6712328767416.17970679331937.5695185941433
Winsorized Mean ( 15 / 24 )15555.3287671233400.23573297980238.8654172662497
Winsorized Mean ( 16 / 24 )15554.0136986301400.04893512177538.8802777187633
Winsorized Mean ( 17 / 24 )15606.1780821918374.11206613775241.7152492388348
Winsorized Mean ( 18 / 24 )15558.8356164384367.01142779628342.3933273954472
Winsorized Mean ( 19 / 24 )15579.9178082192362.35360228277042.9964479725554
Winsorized Mean ( 20 / 24 )15557.7260273973318.20158600799648.8926727945546
Winsorized Mean ( 21 / 24 )15704.1506849315287.26664652672454.6675044764397
Winsorized Mean ( 22 / 24 )15829.2191780822265.01756155486559.728944320564
Winsorized Mean ( 23 / 24 )16059.5342465753227.83388705844070.4879087738866
Winsorized Mean ( 24 / 24 )16197.6164383562181.29244333801689.3452376730125
Trimmed Mean ( 1 / 24 )15992.5633802817498.11196115737532.1063628809929
Trimmed Mean ( 2 / 24 )15944.8985507246488.5338854834232.6382652760036
Trimmed Mean ( 3 / 24 )15902.9104477612479.95144661119733.1344150747898
Trimmed Mean ( 4 / 24 )15869.1230769231472.60917008446733.5776876146666
Trimmed Mean ( 5 / 24 )15843.2539682540466.38267415810633.9705028640987
Trimmed Mean ( 6 / 24 )15819.3770491803459.82949629547734.4027018201875
Trimmed Mean ( 7 / 24 )15802.9491525424454.63948275249634.7592977558120
Trimmed Mean ( 8 / 24 )15787.2982456140448.61362950149735.1913031780978
Trimmed Mean ( 9 / 24 )15772.5090909091441.48956912359135.7256664573511
Trimmed Mean ( 10 / 24 )15756.3396226415432.83548440798736.4026060483288
Trimmed Mean ( 11 / 24 )15744.7843137255423.56125034648637.1723907719268
Trimmed Mean ( 12 / 24 )15733.7755102041412.23193852971638.1672889449586
Trimmed Mean ( 13 / 24 )15733.4468085106401.14413936191739.2214300663526
Trimmed Mean ( 14 / 24 )15747.1555555556391.24867438450440.2484572767647
Trimmed Mean ( 15 / 24 )15760.6744186047379.16371771225741.5669371365465
Trimmed Mean ( 16 / 24 )15785.0487804878366.75028546918843.040317638182
Trimmed Mean ( 17 / 24 )15812.0769230769349.98691200633445.1790520749266
Trimmed Mean ( 18 / 24 )15835.9729729730334.15920098260247.3905040663461
Trimmed Mean ( 19 / 24 )15868.0857142857313.98506192436150.5377090777279
Trimmed Mean ( 20 / 24 )15901.6363636364286.72450026041955.4596358148454
Trimmed Mean ( 21 / 24 )15942.1290322581262.46119525544260.7408993041517
Trimmed Mean ( 22 / 24 )15970.6551724138238.6330905616266.9255681801173
Trimmed Mean ( 23 / 24 )15988.0370370370211.78799592492575.4907612549699
Trimmed Mean ( 24 / 24 )15978.96186.97677645454685.459597191657
Median15839
Midrange17750
Midmean - Weighted Average at Xnp15742.6666666667
Midmean - Weighted Average at X(n+1)p15835.9729729730
Midmean - Empirical Distribution Function15835.9729729730
Midmean - Empirical Distribution Function - Averaging15835.9729729730
Midmean - Empirical Distribution Function - Interpolation15835.9729729730
Midmean - Closest Observation15717.8157894737
Midmean - True Basic - Statistics Graphics Toolkit15835.9729729730
Midmean - MS Excel (old versions)15835.9729729730
Number of observations73



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')