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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, 09 Oct 2015 19:21:15 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444414925bod59y4n1fjlxic.htm/, Retrieved Tue, 14 May 2024 17:53:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282020, Retrieved Tue, 14 May 2024 17:53:40 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Datareeks - studi...] [2015-10-09 17:11:44] [b78554c675fd79077ee7678381a14583]
- RMPD    [Central Tendency] [Central Tendency ...] [2015-10-09 18:21:15] [3f1a7081c5450f075552d8bc3f139f2c] [Current]
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Dataseries X:
26.133
25.979
25.541
25.308
25.663
25.78
25.328
24.806
24.651
24.531
24.633
25.174
24.449
24.277
24.393
24.301
24.381
24.286
24.335
24.273
24.556
24.841
25.464
25.514
25.531
25.042
24.676
24.809
25.313
25.64
25.447
25.021
24.752
24.939
25.365
25.214
25.563
25.475
25.659
25.841
25.888
25.759
25.944
25.818
25.789
25.662
26.927
27.521
27.485
27.444
27.395
27.45
27.437
27.45
27.458
27.816
27.599
27.588
27.667
27.64





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=282020&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=282020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282020&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'Gertrude Mary Cox' @ cox.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean25.710350.143359210300441179.342156992343
Geometric Mean25.6871510650997
Harmonic Mean25.664341899375
Quadratic Mean25.7339203591291
Winsorized Mean ( 1 / 20 )25.70793333333330.142749909449478180.090715521132
Winsorized Mean ( 2 / 20 )25.70733333333330.14249094067083180.413808852032
Winsorized Mean ( 3 / 20 )25.70603333333330.141897199533341181.159553661897
Winsorized Mean ( 4 / 20 )25.70756666666670.141354887294209181.86542509252
Winsorized Mean ( 5 / 20 )25.70581666666670.139485569169686184.290151444951
Winsorized Mean ( 6 / 20 )25.70341666666670.138503293504797185.579822805992
Winsorized Mean ( 7 / 20 )25.70680.136785077819637187.935704754992
Winsorized Mean ( 8 / 20 )25.71666666666670.134886469664981190.654160721528
Winsorized Mean ( 9 / 20 )25.72041666666670.134331641824597191.469532548787
Winsorized Mean ( 10 / 20 )25.732250.132265954950558194.549307942614
Winsorized Mean ( 11 / 20 )25.73426666666670.131521633344727195.665656000602
Winsorized Mean ( 12 / 20 )25.73086666666670.128986013928167199.48571076083
Winsorized Mean ( 13 / 20 )25.64593333333330.105032085134597244.172371713543
Winsorized Mean ( 14 / 20 )25.47326666666670.0678527729332186375.419685378779
Winsorized Mean ( 15 / 20 )25.43551666666670.0616636241042057412.488189531044
Winsorized Mean ( 16 / 20 )25.43471666666670.0588164726324098432.442061352916
Winsorized Mean ( 17 / 20 )25.44661666666670.0518209111406785491.049194360682
Winsorized Mean ( 18 / 20 )25.45711666666670.0457678191760112556.223065135902
Winsorized Mean ( 19 / 20 )25.45648333333330.0436669631141013582.968943061504
Winsorized Mean ( 20 / 20 )25.49081666666670.0354025557798288720.027582900964
Trimmed Mean ( 1 / 20 )25.69882758620690.141556209323443181.545039310055
Trimmed Mean ( 2 / 20 )25.68907142857140.139973944368375183.527523958063
Trimmed Mean ( 3 / 20 )25.67892592592590.13807759911208185.974597552801
Trimmed Mean ( 4 / 20 )25.66850.135892981194241188.887606809585
Trimmed Mean ( 5 / 20 )25.656780.133255400901381192.538387385799
Trimmed Mean ( 6 / 20 )25.64452083333330.130456287989011196.575582738438
Trimmed Mean ( 7 / 20 )25.63171739130430.127087974638148201.684836541651
Trimmed Mean ( 8 / 20 )25.61709090909090.123141060325286208.030455815643
Trimmed Mean ( 9 / 20 )25.59930952380950.118393551712999216.222160357732
Trimmed Mean ( 10 / 20 )25.5791250.112111106677192228.15870575296
Trimmed Mean ( 11 / 20 )25.55494736842110.104017314097717245.679746589246
Trimmed Mean ( 12 / 20 )25.52777777777780.0926957055486418275.393316515425
Trimmed Mean ( 13 / 20 )25.49791176470590.0766044702489089332.851486105918
Trimmed Mean ( 14 / 20 )25.47656250.063268723122921402.672303825432
Trimmed Mean ( 15 / 20 )25.47703333333330.0595995927497722427.469923163707
Trimmed Mean ( 16 / 20 )25.48296428571430.056239201953413453.117459007041
Trimmed Mean ( 17 / 20 )25.48992307692310.0521120367928393489.136956558675
Trimmed Mean ( 18 / 20 )25.49629166666670.0485706373087165524.932203475351
Trimmed Mean ( 19 / 20 )25.50222727272730.0455064303442504560.409310943665
Trimmed Mean ( 20 / 20 )25.509450.0411723255930103619.577583548758
Median25.5225
Midrange26.0445
Midmean - Weighted Average at Xnp25.4553870967742
Midmean - Weighted Average at X(n+1)p25.4770333333333
Midmean - Empirical Distribution Function25.4553870967742
Midmean - Empirical Distribution Function - Averaging25.4770333333333
Midmean - Empirical Distribution Function - Interpolation25.4770333333333
Midmean - Closest Observation25.4553870967742
Midmean - True Basic - Statistics Graphics Toolkit25.4770333333333
Midmean - MS Excel (old versions)25.4765625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 25.71035 & 0.143359210300441 & 179.342156992343 \tabularnewline
Geometric Mean & 25.6871510650997 &  &  \tabularnewline
Harmonic Mean & 25.664341899375 &  &  \tabularnewline
Quadratic Mean & 25.7339203591291 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 25.7079333333333 & 0.142749909449478 & 180.090715521132 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 25.7073333333333 & 0.14249094067083 & 180.413808852032 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 25.7060333333333 & 0.141897199533341 & 181.159553661897 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 25.7075666666667 & 0.141354887294209 & 181.86542509252 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 25.7058166666667 & 0.139485569169686 & 184.290151444951 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 25.7034166666667 & 0.138503293504797 & 185.579822805992 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 25.7068 & 0.136785077819637 & 187.935704754992 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 25.7166666666667 & 0.134886469664981 & 190.654160721528 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 25.7204166666667 & 0.134331641824597 & 191.469532548787 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 25.73225 & 0.132265954950558 & 194.549307942614 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 25.7342666666667 & 0.131521633344727 & 195.665656000602 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 25.7308666666667 & 0.128986013928167 & 199.48571076083 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 25.6459333333333 & 0.105032085134597 & 244.172371713543 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 25.4732666666667 & 0.0678527729332186 & 375.419685378779 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 25.4355166666667 & 0.0616636241042057 & 412.488189531044 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 25.4347166666667 & 0.0588164726324098 & 432.442061352916 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 25.4466166666667 & 0.0518209111406785 & 491.049194360682 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 25.4571166666667 & 0.0457678191760112 & 556.223065135902 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 25.4564833333333 & 0.0436669631141013 & 582.968943061504 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 25.4908166666667 & 0.0354025557798288 & 720.027582900964 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 25.6988275862069 & 0.141556209323443 & 181.545039310055 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 25.6890714285714 & 0.139973944368375 & 183.527523958063 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 25.6789259259259 & 0.13807759911208 & 185.974597552801 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 25.6685 & 0.135892981194241 & 188.887606809585 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 25.65678 & 0.133255400901381 & 192.538387385799 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 25.6445208333333 & 0.130456287989011 & 196.575582738438 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 25.6317173913043 & 0.127087974638148 & 201.684836541651 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 25.6170909090909 & 0.123141060325286 & 208.030455815643 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 25.5993095238095 & 0.118393551712999 & 216.222160357732 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 25.579125 & 0.112111106677192 & 228.15870575296 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 25.5549473684211 & 0.104017314097717 & 245.679746589246 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 25.5277777777778 & 0.0926957055486418 & 275.393316515425 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 25.4979117647059 & 0.0766044702489089 & 332.851486105918 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 25.4765625 & 0.063268723122921 & 402.672303825432 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 25.4770333333333 & 0.0595995927497722 & 427.469923163707 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 25.4829642857143 & 0.056239201953413 & 453.117459007041 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 25.4899230769231 & 0.0521120367928393 & 489.136956558675 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 25.4962916666667 & 0.0485706373087165 & 524.932203475351 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 25.5022272727273 & 0.0455064303442504 & 560.409310943665 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 25.50945 & 0.0411723255930103 & 619.577583548758 \tabularnewline
Median & 25.5225 &  &  \tabularnewline
Midrange & 26.0445 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 25.4553870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 25.4770333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 25.4553870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 25.4770333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 25.4770333333333 &  &  \tabularnewline
Midmean - Closest Observation & 25.4553870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 25.4770333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 25.4765625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282020&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]25.71035[/C][C]0.143359210300441[/C][C]179.342156992343[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]25.6871510650997[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]25.664341899375[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]25.7339203591291[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]25.7079333333333[/C][C]0.142749909449478[/C][C]180.090715521132[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]25.7073333333333[/C][C]0.14249094067083[/C][C]180.413808852032[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]25.7060333333333[/C][C]0.141897199533341[/C][C]181.159553661897[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]25.7075666666667[/C][C]0.141354887294209[/C][C]181.86542509252[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]25.7058166666667[/C][C]0.139485569169686[/C][C]184.290151444951[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]25.7034166666667[/C][C]0.138503293504797[/C][C]185.579822805992[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]25.7068[/C][C]0.136785077819637[/C][C]187.935704754992[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]25.7166666666667[/C][C]0.134886469664981[/C][C]190.654160721528[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]25.7204166666667[/C][C]0.134331641824597[/C][C]191.469532548787[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]25.73225[/C][C]0.132265954950558[/C][C]194.549307942614[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]25.7342666666667[/C][C]0.131521633344727[/C][C]195.665656000602[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]25.7308666666667[/C][C]0.128986013928167[/C][C]199.48571076083[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]25.6459333333333[/C][C]0.105032085134597[/C][C]244.172371713543[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]25.4732666666667[/C][C]0.0678527729332186[/C][C]375.419685378779[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]25.4355166666667[/C][C]0.0616636241042057[/C][C]412.488189531044[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]25.4347166666667[/C][C]0.0588164726324098[/C][C]432.442061352916[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]25.4466166666667[/C][C]0.0518209111406785[/C][C]491.049194360682[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]25.4571166666667[/C][C]0.0457678191760112[/C][C]556.223065135902[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]25.4564833333333[/C][C]0.0436669631141013[/C][C]582.968943061504[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]25.4908166666667[/C][C]0.0354025557798288[/C][C]720.027582900964[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]25.6988275862069[/C][C]0.141556209323443[/C][C]181.545039310055[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]25.6890714285714[/C][C]0.139973944368375[/C][C]183.527523958063[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]25.6789259259259[/C][C]0.13807759911208[/C][C]185.974597552801[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]25.6685[/C][C]0.135892981194241[/C][C]188.887606809585[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]25.65678[/C][C]0.133255400901381[/C][C]192.538387385799[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]25.6445208333333[/C][C]0.130456287989011[/C][C]196.575582738438[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]25.6317173913043[/C][C]0.127087974638148[/C][C]201.684836541651[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]25.6170909090909[/C][C]0.123141060325286[/C][C]208.030455815643[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]25.5993095238095[/C][C]0.118393551712999[/C][C]216.222160357732[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]25.579125[/C][C]0.112111106677192[/C][C]228.15870575296[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]25.5549473684211[/C][C]0.104017314097717[/C][C]245.679746589246[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]25.5277777777778[/C][C]0.0926957055486418[/C][C]275.393316515425[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]25.4979117647059[/C][C]0.0766044702489089[/C][C]332.851486105918[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]25.4765625[/C][C]0.063268723122921[/C][C]402.672303825432[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]25.4770333333333[/C][C]0.0595995927497722[/C][C]427.469923163707[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]25.4829642857143[/C][C]0.056239201953413[/C][C]453.117459007041[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]25.4899230769231[/C][C]0.0521120367928393[/C][C]489.136956558675[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]25.4962916666667[/C][C]0.0485706373087165[/C][C]524.932203475351[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]25.5022272727273[/C][C]0.0455064303442504[/C][C]560.409310943665[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]25.50945[/C][C]0.0411723255930103[/C][C]619.577583548758[/C][/ROW]
[ROW][C]Median[/C][C]25.5225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]26.0445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]25.4553870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]25.4770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]25.4553870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]25.4770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]25.4770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]25.4553870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]25.4770333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]25.4765625[/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=282020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282020&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 Mean25.710350.143359210300441179.342156992343
Geometric Mean25.6871510650997
Harmonic Mean25.664341899375
Quadratic Mean25.7339203591291
Winsorized Mean ( 1 / 20 )25.70793333333330.142749909449478180.090715521132
Winsorized Mean ( 2 / 20 )25.70733333333330.14249094067083180.413808852032
Winsorized Mean ( 3 / 20 )25.70603333333330.141897199533341181.159553661897
Winsorized Mean ( 4 / 20 )25.70756666666670.141354887294209181.86542509252
Winsorized Mean ( 5 / 20 )25.70581666666670.139485569169686184.290151444951
Winsorized Mean ( 6 / 20 )25.70341666666670.138503293504797185.579822805992
Winsorized Mean ( 7 / 20 )25.70680.136785077819637187.935704754992
Winsorized Mean ( 8 / 20 )25.71666666666670.134886469664981190.654160721528
Winsorized Mean ( 9 / 20 )25.72041666666670.134331641824597191.469532548787
Winsorized Mean ( 10 / 20 )25.732250.132265954950558194.549307942614
Winsorized Mean ( 11 / 20 )25.73426666666670.131521633344727195.665656000602
Winsorized Mean ( 12 / 20 )25.73086666666670.128986013928167199.48571076083
Winsorized Mean ( 13 / 20 )25.64593333333330.105032085134597244.172371713543
Winsorized Mean ( 14 / 20 )25.47326666666670.0678527729332186375.419685378779
Winsorized Mean ( 15 / 20 )25.43551666666670.0616636241042057412.488189531044
Winsorized Mean ( 16 / 20 )25.43471666666670.0588164726324098432.442061352916
Winsorized Mean ( 17 / 20 )25.44661666666670.0518209111406785491.049194360682
Winsorized Mean ( 18 / 20 )25.45711666666670.0457678191760112556.223065135902
Winsorized Mean ( 19 / 20 )25.45648333333330.0436669631141013582.968943061504
Winsorized Mean ( 20 / 20 )25.49081666666670.0354025557798288720.027582900964
Trimmed Mean ( 1 / 20 )25.69882758620690.141556209323443181.545039310055
Trimmed Mean ( 2 / 20 )25.68907142857140.139973944368375183.527523958063
Trimmed Mean ( 3 / 20 )25.67892592592590.13807759911208185.974597552801
Trimmed Mean ( 4 / 20 )25.66850.135892981194241188.887606809585
Trimmed Mean ( 5 / 20 )25.656780.133255400901381192.538387385799
Trimmed Mean ( 6 / 20 )25.64452083333330.130456287989011196.575582738438
Trimmed Mean ( 7 / 20 )25.63171739130430.127087974638148201.684836541651
Trimmed Mean ( 8 / 20 )25.61709090909090.123141060325286208.030455815643
Trimmed Mean ( 9 / 20 )25.59930952380950.118393551712999216.222160357732
Trimmed Mean ( 10 / 20 )25.5791250.112111106677192228.15870575296
Trimmed Mean ( 11 / 20 )25.55494736842110.104017314097717245.679746589246
Trimmed Mean ( 12 / 20 )25.52777777777780.0926957055486418275.393316515425
Trimmed Mean ( 13 / 20 )25.49791176470590.0766044702489089332.851486105918
Trimmed Mean ( 14 / 20 )25.47656250.063268723122921402.672303825432
Trimmed Mean ( 15 / 20 )25.47703333333330.0595995927497722427.469923163707
Trimmed Mean ( 16 / 20 )25.48296428571430.056239201953413453.117459007041
Trimmed Mean ( 17 / 20 )25.48992307692310.0521120367928393489.136956558675
Trimmed Mean ( 18 / 20 )25.49629166666670.0485706373087165524.932203475351
Trimmed Mean ( 19 / 20 )25.50222727272730.0455064303442504560.409310943665
Trimmed Mean ( 20 / 20 )25.509450.0411723255930103619.577583548758
Median25.5225
Midrange26.0445
Midmean - Weighted Average at Xnp25.4553870967742
Midmean - Weighted Average at X(n+1)p25.4770333333333
Midmean - Empirical Distribution Function25.4553870967742
Midmean - Empirical Distribution Function - Averaging25.4770333333333
Midmean - Empirical Distribution Function - Interpolation25.4770333333333
Midmean - Closest Observation25.4553870967742
Midmean - True Basic - Statistics Graphics Toolkit25.4770333333333
Midmean - MS Excel (old versions)25.4765625
Number of observations60



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