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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, 07 Nov 2008 08:35:47 -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/2008/Nov/07/t1226072227ni3zypbv8j5o2jw.htm/, Retrieved Sun, 19 May 2024 01:40:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22526, Retrieved Sun, 19 May 2024 01:40:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Waerlop Jeroen - ...] [2008-11-07 15:35:47] [d393909564acd650d077e72b144b40b8] [Current]
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Dataseries X:
1,83
1,89
1,9
2,01
2,04
2,04
2,03
2,04
1,87
1,85
1,82
1,79
1,88
2,01
1,9
1,96
1,94
1,92
1,79
1,77
1,74
1,75
1,86
1,84
1,77
1,98
1,94
1,85
1,84
1,82
1,83
1,91
1,85
1,81
1,83
1,79
1,8
1,82
1,88
2,01
1,97
1,92
1,98
2,02
1,9
1,94
1,96
1,84
1,87
1,84
2,07
2,08
2,14
2,15
2,05
2,05
1,95
2,02
2,02
1,88
1,96
1,93
2,03
2,1
1,95
2,07
2,09
2,01
1,92
1,99
2,11
2




Summary of computational 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 computational 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=22526&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]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=22526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22526&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.930694444444440.0120904364566544159.687737607009
Geometric Mean1.92801440940248
Harmonic Mean1.92534383598924
Quadratic Mean1.93338038735843
Winsorized Mean ( 1 / 24 )1.930694444444440.0120255439995653160.549447452376
Winsorized Mean ( 2 / 24 )1.930416666666670.0117209293096181164.698260323316
Winsorized Mean ( 3 / 24 )1.930.0116330837913965165.906137582141
Winsorized Mean ( 4 / 24 )1.930555555555560.0113157985189916170.607098766865
Winsorized Mean ( 5 / 24 )1.929861111111110.0111812025347660172.598707975332
Winsorized Mean ( 6 / 24 )1.929027777777780.0110273520413873174.931186611061
Winsorized Mean ( 7 / 24 )1.930.0108590341581653177.732197163112
Winsorized Mean ( 8 / 24 )1.928888888888890.0102883991135958187.481926740178
Winsorized Mean ( 9 / 24 )1.930138888888890.0100905389912735191.282040588526
Winsorized Mean ( 10 / 24 )1.928750.00986397608759525195.534740035061
Winsorized Mean ( 11 / 24 )1.928750.00986397608759525195.534740035061
Winsorized Mean ( 12 / 24 )1.930416666666670.00961186811224533200.836782623698
Winsorized Mean ( 13 / 24 )1.928611111111110.00932860702673737206.741596637460
Winsorized Mean ( 14 / 24 )1.928611111111110.00932860702673737206.741596637460
Winsorized Mean ( 15 / 24 )1.928611111111110.0087104921972016221.412414757769
Winsorized Mean ( 16 / 24 )1.928611111111110.0087104921972016221.412414757769
Winsorized Mean ( 17 / 24 )1.928611111111110.0087104921972016221.412414757769
Winsorized Mean ( 18 / 24 )1.926111111111110.00834870777898326230.707692986912
Winsorized Mean ( 19 / 24 )1.928750.00797329634571475241.901205771263
Winsorized Mean ( 20 / 24 )1.928750.00797329634571475241.901205771263
Winsorized Mean ( 21 / 24 )1.928750.00797329634571475241.901205771263
Winsorized Mean ( 22 / 24 )1.928750.00711777047217193270.976706475821
Winsorized Mean ( 23 / 24 )1.928750.00624217036961646308.987080741680
Winsorized Mean ( 24 / 24 )1.925416666666670.00579020779072572332.529804845802
Trimmed Mean ( 1 / 24 )1.930285714285710.0117142857142857164.780487804878
Trimmed Mean ( 2 / 24 )1.929852941176470.0113440346590948170.120508194081
Trimmed Mean ( 3 / 24 )1.929545454545450.0110970119630156173.879730956071
Trimmed Mean ( 4 / 24 )1.9293750.0108399132947683177.988047278125
Trimmed Mean ( 5 / 24 )1.929032258064520.0106447606610188181.218941364145
Trimmed Mean ( 6 / 24 )1.928833333333330.0104478572578593184.615207284000
Trimmed Mean ( 7 / 24 )1.928793103448280.0102482128824563188.207751494910
Trimmed Mean ( 8 / 24 )1.928571428571430.010043504625264192.021759388669
Trimmed Mean ( 9 / 24 )1.928518518518520.00992426741257352194.323514103942
Trimmed Mean ( 10 / 24 )1.928269230769230.0098124230745893196.513054534182
Trimmed Mean ( 11 / 24 )1.92820.0097129831059426198.517796125918
Trimmed Mean ( 12 / 24 )1.9281250.00957730885260342201.322211664488
Trimmed Mean ( 13 / 24 )1.927826086956520.00944811942782992204.043365632955
Trimmed Mean ( 14 / 24 )1.927727272727270.00933215834197123206.568213063569
Trimmed Mean ( 15 / 24 )1.927619047619050.00916875928269014210.237720086973
Trimmed Mean ( 16 / 24 )1.92750.0090776564240913212.334539880204
Trimmed Mean ( 17 / 24 )1.927368421052630.00893857822750383215.623600532147
Trimmed Mean ( 18 / 24 )1.927222222222220.00873427031606788220.650627068049
Trimmed Mean ( 19 / 24 )1.927352941176470.0085312555632066225.916680950072
Trimmed Mean ( 20 / 24 )1.92718750.00833079178313027231.333053348245
Trimmed Mean ( 21 / 24 )1.9270.00802510428907778240.121490087382
Trimmed Mean ( 22 / 24 )1.926785714285710.00756022681395592254.858189006834
Trimmed Mean ( 23 / 24 )1.926538461538460.00716706801316448268.804266681967
Trimmed Mean ( 24 / 24 )1.926250.00688446318410763279.796688352787
Median1.925
Midrange1.945
Midmean - Weighted Average at Xnp1.92051282051282
Midmean - Weighted Average at X(n+1)p1.92051282051282
Midmean - Empirical Distribution Function1.92051282051282
Midmean - Empirical Distribution Function - Averaging1.92051282051282
Midmean - Empirical Distribution Function - Interpolation1.92051282051282
Midmean - Closest Observation1.92051282051282
Midmean - True Basic - Statistics Graphics Toolkit1.92051282051282
Midmean - MS Excel (old versions)1.92761904761905
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.93069444444444 & 0.0120904364566544 & 159.687737607009 \tabularnewline
Geometric Mean & 1.92801440940248 &  &  \tabularnewline
Harmonic Mean & 1.92534383598924 &  &  \tabularnewline
Quadratic Mean & 1.93338038735843 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.93069444444444 & 0.0120255439995653 & 160.549447452376 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.93041666666667 & 0.0117209293096181 & 164.698260323316 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.93 & 0.0116330837913965 & 165.906137582141 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.93055555555556 & 0.0113157985189916 & 170.607098766865 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.92986111111111 & 0.0111812025347660 & 172.598707975332 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.92902777777778 & 0.0110273520413873 & 174.931186611061 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.93 & 0.0108590341581653 & 177.732197163112 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.92888888888889 & 0.0102883991135958 & 187.481926740178 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.93013888888889 & 0.0100905389912735 & 191.282040588526 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.92875 & 0.00986397608759525 & 195.534740035061 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.92875 & 0.00986397608759525 & 195.534740035061 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.93041666666667 & 0.00961186811224533 & 200.836782623698 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.92861111111111 & 0.00932860702673737 & 206.741596637460 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.92861111111111 & 0.00932860702673737 & 206.741596637460 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.92861111111111 & 0.0087104921972016 & 221.412414757769 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.92861111111111 & 0.0087104921972016 & 221.412414757769 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.92861111111111 & 0.0087104921972016 & 221.412414757769 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.92611111111111 & 0.00834870777898326 & 230.707692986912 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.92875 & 0.00797329634571475 & 241.901205771263 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.92875 & 0.00797329634571475 & 241.901205771263 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.92875 & 0.00797329634571475 & 241.901205771263 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.92875 & 0.00711777047217193 & 270.976706475821 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.92875 & 0.00624217036961646 & 308.987080741680 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.92541666666667 & 0.00579020779072572 & 332.529804845802 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.93028571428571 & 0.0117142857142857 & 164.780487804878 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.92985294117647 & 0.0113440346590948 & 170.120508194081 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.92954545454545 & 0.0110970119630156 & 173.879730956071 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.929375 & 0.0108399132947683 & 177.988047278125 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.92903225806452 & 0.0106447606610188 & 181.218941364145 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.92883333333333 & 0.0104478572578593 & 184.615207284000 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.92879310344828 & 0.0102482128824563 & 188.207751494910 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.92857142857143 & 0.010043504625264 & 192.021759388669 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.92851851851852 & 0.00992426741257352 & 194.323514103942 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.92826923076923 & 0.0098124230745893 & 196.513054534182 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.9282 & 0.0097129831059426 & 198.517796125918 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.928125 & 0.00957730885260342 & 201.322211664488 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.92782608695652 & 0.00944811942782992 & 204.043365632955 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.92772727272727 & 0.00933215834197123 & 206.568213063569 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.92761904761905 & 0.00916875928269014 & 210.237720086973 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.9275 & 0.0090776564240913 & 212.334539880204 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.92736842105263 & 0.00893857822750383 & 215.623600532147 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.92722222222222 & 0.00873427031606788 & 220.650627068049 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.92735294117647 & 0.0085312555632066 & 225.916680950072 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.9271875 & 0.00833079178313027 & 231.333053348245 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.927 & 0.00802510428907778 & 240.121490087382 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.92678571428571 & 0.00756022681395592 & 254.858189006834 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.92653846153846 & 0.00716706801316448 & 268.804266681967 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.92625 & 0.00688446318410763 & 279.796688352787 \tabularnewline
Median & 1.925 &  &  \tabularnewline
Midrange & 1.945 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.92051282051282 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.92051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.92051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.92051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.92051282051282 &  &  \tabularnewline
Midmean - Closest Observation & 1.92051282051282 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.92051282051282 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.92761904761905 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22526&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]1.93069444444444[/C][C]0.0120904364566544[/C][C]159.687737607009[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.92801440940248[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.92534383598924[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.93338038735843[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.93069444444444[/C][C]0.0120255439995653[/C][C]160.549447452376[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.93041666666667[/C][C]0.0117209293096181[/C][C]164.698260323316[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.93[/C][C]0.0116330837913965[/C][C]165.906137582141[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.93055555555556[/C][C]0.0113157985189916[/C][C]170.607098766865[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.92986111111111[/C][C]0.0111812025347660[/C][C]172.598707975332[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.92902777777778[/C][C]0.0110273520413873[/C][C]174.931186611061[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.93[/C][C]0.0108590341581653[/C][C]177.732197163112[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.92888888888889[/C][C]0.0102883991135958[/C][C]187.481926740178[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.93013888888889[/C][C]0.0100905389912735[/C][C]191.282040588526[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.92875[/C][C]0.00986397608759525[/C][C]195.534740035061[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.92875[/C][C]0.00986397608759525[/C][C]195.534740035061[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.93041666666667[/C][C]0.00961186811224533[/C][C]200.836782623698[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.92861111111111[/C][C]0.00932860702673737[/C][C]206.741596637460[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.92861111111111[/C][C]0.00932860702673737[/C][C]206.741596637460[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.92861111111111[/C][C]0.0087104921972016[/C][C]221.412414757769[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.92861111111111[/C][C]0.0087104921972016[/C][C]221.412414757769[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.92861111111111[/C][C]0.0087104921972016[/C][C]221.412414757769[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.92611111111111[/C][C]0.00834870777898326[/C][C]230.707692986912[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.92875[/C][C]0.00797329634571475[/C][C]241.901205771263[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.92875[/C][C]0.00797329634571475[/C][C]241.901205771263[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.92875[/C][C]0.00797329634571475[/C][C]241.901205771263[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.92875[/C][C]0.00711777047217193[/C][C]270.976706475821[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.92875[/C][C]0.00624217036961646[/C][C]308.987080741680[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.92541666666667[/C][C]0.00579020779072572[/C][C]332.529804845802[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.93028571428571[/C][C]0.0117142857142857[/C][C]164.780487804878[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.92985294117647[/C][C]0.0113440346590948[/C][C]170.120508194081[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.92954545454545[/C][C]0.0110970119630156[/C][C]173.879730956071[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.929375[/C][C]0.0108399132947683[/C][C]177.988047278125[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.92903225806452[/C][C]0.0106447606610188[/C][C]181.218941364145[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.92883333333333[/C][C]0.0104478572578593[/C][C]184.615207284000[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.92879310344828[/C][C]0.0102482128824563[/C][C]188.207751494910[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.92857142857143[/C][C]0.010043504625264[/C][C]192.021759388669[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.92851851851852[/C][C]0.00992426741257352[/C][C]194.323514103942[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.92826923076923[/C][C]0.0098124230745893[/C][C]196.513054534182[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.9282[/C][C]0.0097129831059426[/C][C]198.517796125918[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.928125[/C][C]0.00957730885260342[/C][C]201.322211664488[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.92782608695652[/C][C]0.00944811942782992[/C][C]204.043365632955[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.92772727272727[/C][C]0.00933215834197123[/C][C]206.568213063569[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.92761904761905[/C][C]0.00916875928269014[/C][C]210.237720086973[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.9275[/C][C]0.0090776564240913[/C][C]212.334539880204[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.92736842105263[/C][C]0.00893857822750383[/C][C]215.623600532147[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.92722222222222[/C][C]0.00873427031606788[/C][C]220.650627068049[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.92735294117647[/C][C]0.0085312555632066[/C][C]225.916680950072[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.9271875[/C][C]0.00833079178313027[/C][C]231.333053348245[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.927[/C][C]0.00802510428907778[/C][C]240.121490087382[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.92678571428571[/C][C]0.00756022681395592[/C][C]254.858189006834[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.92653846153846[/C][C]0.00716706801316448[/C][C]268.804266681967[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.92625[/C][C]0.00688446318410763[/C][C]279.796688352787[/C][/ROW]
[ROW][C]Median[/C][C]1.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.92051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.92051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.92051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.92051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.92051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.92051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.92051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.92761904761905[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22526&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 Mean1.930694444444440.0120904364566544159.687737607009
Geometric Mean1.92801440940248
Harmonic Mean1.92534383598924
Quadratic Mean1.93338038735843
Winsorized Mean ( 1 / 24 )1.930694444444440.0120255439995653160.549447452376
Winsorized Mean ( 2 / 24 )1.930416666666670.0117209293096181164.698260323316
Winsorized Mean ( 3 / 24 )1.930.0116330837913965165.906137582141
Winsorized Mean ( 4 / 24 )1.930555555555560.0113157985189916170.607098766865
Winsorized Mean ( 5 / 24 )1.929861111111110.0111812025347660172.598707975332
Winsorized Mean ( 6 / 24 )1.929027777777780.0110273520413873174.931186611061
Winsorized Mean ( 7 / 24 )1.930.0108590341581653177.732197163112
Winsorized Mean ( 8 / 24 )1.928888888888890.0102883991135958187.481926740178
Winsorized Mean ( 9 / 24 )1.930138888888890.0100905389912735191.282040588526
Winsorized Mean ( 10 / 24 )1.928750.00986397608759525195.534740035061
Winsorized Mean ( 11 / 24 )1.928750.00986397608759525195.534740035061
Winsorized Mean ( 12 / 24 )1.930416666666670.00961186811224533200.836782623698
Winsorized Mean ( 13 / 24 )1.928611111111110.00932860702673737206.741596637460
Winsorized Mean ( 14 / 24 )1.928611111111110.00932860702673737206.741596637460
Winsorized Mean ( 15 / 24 )1.928611111111110.0087104921972016221.412414757769
Winsorized Mean ( 16 / 24 )1.928611111111110.0087104921972016221.412414757769
Winsorized Mean ( 17 / 24 )1.928611111111110.0087104921972016221.412414757769
Winsorized Mean ( 18 / 24 )1.926111111111110.00834870777898326230.707692986912
Winsorized Mean ( 19 / 24 )1.928750.00797329634571475241.901205771263
Winsorized Mean ( 20 / 24 )1.928750.00797329634571475241.901205771263
Winsorized Mean ( 21 / 24 )1.928750.00797329634571475241.901205771263
Winsorized Mean ( 22 / 24 )1.928750.00711777047217193270.976706475821
Winsorized Mean ( 23 / 24 )1.928750.00624217036961646308.987080741680
Winsorized Mean ( 24 / 24 )1.925416666666670.00579020779072572332.529804845802
Trimmed Mean ( 1 / 24 )1.930285714285710.0117142857142857164.780487804878
Trimmed Mean ( 2 / 24 )1.929852941176470.0113440346590948170.120508194081
Trimmed Mean ( 3 / 24 )1.929545454545450.0110970119630156173.879730956071
Trimmed Mean ( 4 / 24 )1.9293750.0108399132947683177.988047278125
Trimmed Mean ( 5 / 24 )1.929032258064520.0106447606610188181.218941364145
Trimmed Mean ( 6 / 24 )1.928833333333330.0104478572578593184.615207284000
Trimmed Mean ( 7 / 24 )1.928793103448280.0102482128824563188.207751494910
Trimmed Mean ( 8 / 24 )1.928571428571430.010043504625264192.021759388669
Trimmed Mean ( 9 / 24 )1.928518518518520.00992426741257352194.323514103942
Trimmed Mean ( 10 / 24 )1.928269230769230.0098124230745893196.513054534182
Trimmed Mean ( 11 / 24 )1.92820.0097129831059426198.517796125918
Trimmed Mean ( 12 / 24 )1.9281250.00957730885260342201.322211664488
Trimmed Mean ( 13 / 24 )1.927826086956520.00944811942782992204.043365632955
Trimmed Mean ( 14 / 24 )1.927727272727270.00933215834197123206.568213063569
Trimmed Mean ( 15 / 24 )1.927619047619050.00916875928269014210.237720086973
Trimmed Mean ( 16 / 24 )1.92750.0090776564240913212.334539880204
Trimmed Mean ( 17 / 24 )1.927368421052630.00893857822750383215.623600532147
Trimmed Mean ( 18 / 24 )1.927222222222220.00873427031606788220.650627068049
Trimmed Mean ( 19 / 24 )1.927352941176470.0085312555632066225.916680950072
Trimmed Mean ( 20 / 24 )1.92718750.00833079178313027231.333053348245
Trimmed Mean ( 21 / 24 )1.9270.00802510428907778240.121490087382
Trimmed Mean ( 22 / 24 )1.926785714285710.00756022681395592254.858189006834
Trimmed Mean ( 23 / 24 )1.926538461538460.00716706801316448268.804266681967
Trimmed Mean ( 24 / 24 )1.926250.00688446318410763279.796688352787
Median1.925
Midrange1.945
Midmean - Weighted Average at Xnp1.92051282051282
Midmean - Weighted Average at X(n+1)p1.92051282051282
Midmean - Empirical Distribution Function1.92051282051282
Midmean - Empirical Distribution Function - Averaging1.92051282051282
Midmean - Empirical Distribution Function - Interpolation1.92051282051282
Midmean - Closest Observation1.92051282051282
Midmean - True Basic - Statistics Graphics Toolkit1.92051282051282
Midmean - MS Excel (old versions)1.92761904761905
Number of observations72



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')