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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 computationWed, 19 Oct 2011 10:05:24 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t1319033326xhve1m2n62an551.htm/, Retrieved Wed, 15 May 2024 06:53:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132786, Retrieved Wed, 15 May 2024 06:53:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten gemi...] [2011-10-19 14:05:24] [01f7a7111ea64623cbc95865e1cb8905] [Current]
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Dataseries X:
123,06
123,39
124,02
124,05
123,99
124,46
124,46
124,6
124,84
124,84
124,99
125,02
128,27
128,38
128,47
128,52
128,71
128,92
128,92
128,82
128,97
129,04
128,95
129,39
129,39
129,48
130,16
129,89
129,85
129,9
129,9
129,57
129,54
129,57
128,97
129,01
129,01
128,72
128,32
128,39
128,33
128,44
128,44
128,6
128,3
128,56
128,01
128,01
128,01
128,26
128,38
128,36
128,48
128,46
128,46
129,56
129,66
129,47
129,41
129,48
129,48
130,17
129,77
129,87
129,97
130,05
130,05
129,89
130,33
130,6
131,46
131,73




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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132786&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132786&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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean128.3722222222220.234652310152087547.074188781773
Geometric Mean128.356791417598
Harmonic Mean128.341154247034
Quadratic Mean128.387448060332
Winsorized Mean ( 1 / 24 )128.3730555555560.232501000291392552.139798945666
Winsorized Mean ( 2 / 24 )128.3658333333330.223762004512689573.671270119739
Winsorized Mean ( 3 / 24 )128.3558333333330.22192171338134578.383391952155
Winsorized Mean ( 4 / 24 )128.3486111111110.220389140968402582.372663857849
Winsorized Mean ( 5 / 24 )128.3763888888890.212701097478059603.553015997632
Winsorized Mean ( 6 / 24 )128.3672222222220.211646446690703606.517256629477
Winsorized Mean ( 7 / 24 )128.3808333333330.208135469419974616.813816939041
Winsorized Mean ( 8 / 24 )128.3986111111110.200394788910194640.728293432083
Winsorized Mean ( 9 / 24 )128.3898611111110.199444994108902643.735691059797
Winsorized Mean ( 10 / 24 )128.4106944444440.194249722951012661.059858895285
Winsorized Mean ( 11 / 24 )128.413750.192948807896553665.532746223792
Winsorized Mean ( 12 / 24 )128.9120833333330.08412928270774781532.30931233723
Winsorized Mean ( 13 / 24 )128.9084722222220.08354097598375661543.05681378784
Winsorized Mean ( 14 / 24 )128.9045833333330.0829134816667171554.68785946638
Winsorized Mean ( 15 / 24 )128.940.07282044288116161770.65663017763
Winsorized Mean ( 16 / 24 )128.9177777777780.06870197774288061876.47840736488
Winsorized Mean ( 17 / 24 )128.9036111111110.06460282700065871995.32461806659
Winsorized Mean ( 18 / 24 )128.9086111111110.06394971419054982015.78087944231
Winsorized Mean ( 19 / 24 )128.9086111111110.06322492128257312038.88923064018
Winsorized Mean ( 20 / 24 )128.9113888888890.06135637757139512101.02672275406
Winsorized Mean ( 21 / 24 )128.8997222222220.05812604761107562217.58966108787
Winsorized Mean ( 22 / 24 )128.8997222222220.05812604761107562217.58966108787
Winsorized Mean ( 23 / 24 )128.9029166666670.05772500966653512233.0514522442
Winsorized Mean ( 24 / 24 )128.916250.05519861616140922335.49786145053
Trimmed Mean ( 1 / 24 )128.4001428571430.223804159884624573.716515918811
Trimmed Mean ( 2 / 24 )128.4288235294120.213363005562695601.926389210308
Trimmed Mean ( 3 / 24 )128.4631818181820.206486442105696622.138579696309
Trimmed Mean ( 4 / 24 )128.50343750.198943541428445645.929174565437
Trimmed Mean ( 5 / 24 )128.5483870967740.190218804895923675.792212905074
Trimmed Mean ( 6 / 24 )128.5896666666670.18213299397773706.020715183486
Trimmed Mean ( 7 / 24 )128.6356896551720.172277739725416746.676209359363
Trimmed Mean ( 8 / 24 )128.68250.160873276335633799.899790264277
Trimmed Mean ( 9 / 24 )128.7298148148150.148563701344389866.495743239485
Trimmed Mean ( 10 / 24 )128.7821153846150.1324520279527972.292515072737
Trimmed Mean ( 11 / 24 )128.83560.1120361311982771149.94688429568
Trimmed Mean ( 12 / 24 )128.8931250.08133208142529981584.77593025064
Trimmed Mean ( 13 / 24 )128.8906521739130.07970137632929451617.16971663561
Trimmed Mean ( 14 / 24 )128.8884090909090.07767222776749421659.3885973855
Trimmed Mean ( 15 / 24 )128.8864285714290.07512268048297181715.67930940169
Trimmed Mean ( 16 / 24 )128.880.07400277195085441741.55638501744
Trimmed Mean ( 17 / 24 )128.8755263157890.07333713472579591757.30244708426
Trimmed Mean ( 18 / 24 )128.8722222222220.07318178183291091760.98776217917
Trimmed Mean ( 19 / 24 )128.8679411764710.07285589934818721768.80585277789
Trimmed Mean ( 20 / 24 )128.8631250.07230708134129521782.16465952699
Trimmed Mean ( 21 / 24 )128.8573333333330.07171292278954381796.84955404051
Trimmed Mean ( 22 / 24 )128.8521428571430.07143531714178431803.75965296547
Trimmed Mean ( 23 / 24 )128.8461538461540.07059979717355181825.02158652691
Trimmed Mean ( 24 / 24 )128.838750.06900775134995131867.01852298642
Median128.87
Midrange127.395
Midmean - Weighted Average at Xnp128.875526315789
Midmean - Weighted Average at X(n+1)p128.891081081081
Midmean - Empirical Distribution Function128.875526315789
Midmean - Empirical Distribution Function - Averaging128.891081081081
Midmean - Empirical Distribution Function - Interpolation128.891081081081
Midmean - Closest Observation128.875526315789
Midmean - True Basic - Statistics Graphics Toolkit128.891081081081
Midmean - MS Excel (old versions)128.875526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 128.372222222222 & 0.234652310152087 & 547.074188781773 \tabularnewline
Geometric Mean & 128.356791417598 &  &  \tabularnewline
Harmonic Mean & 128.341154247034 &  &  \tabularnewline
Quadratic Mean & 128.387448060332 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 128.373055555556 & 0.232501000291392 & 552.139798945666 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 128.365833333333 & 0.223762004512689 & 573.671270119739 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 128.355833333333 & 0.22192171338134 & 578.383391952155 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 128.348611111111 & 0.220389140968402 & 582.372663857849 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 128.376388888889 & 0.212701097478059 & 603.553015997632 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 128.367222222222 & 0.211646446690703 & 606.517256629477 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 128.380833333333 & 0.208135469419974 & 616.813816939041 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 128.398611111111 & 0.200394788910194 & 640.728293432083 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 128.389861111111 & 0.199444994108902 & 643.735691059797 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 128.410694444444 & 0.194249722951012 & 661.059858895285 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 128.41375 & 0.192948807896553 & 665.532746223792 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 128.912083333333 & 0.0841292827077478 & 1532.30931233723 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 128.908472222222 & 0.0835409759837566 & 1543.05681378784 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 128.904583333333 & 0.082913481666717 & 1554.68785946638 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 128.94 & 0.0728204428811616 & 1770.65663017763 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 128.917777777778 & 0.0687019777428806 & 1876.47840736488 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 128.903611111111 & 0.0646028270006587 & 1995.32461806659 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 128.908611111111 & 0.0639497141905498 & 2015.78087944231 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 128.908611111111 & 0.0632249212825731 & 2038.88923064018 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 128.911388888889 & 0.0613563775713951 & 2101.02672275406 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 128.899722222222 & 0.0581260476110756 & 2217.58966108787 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 128.899722222222 & 0.0581260476110756 & 2217.58966108787 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 128.902916666667 & 0.0577250096665351 & 2233.0514522442 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 128.91625 & 0.0551986161614092 & 2335.49786145053 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 128.400142857143 & 0.223804159884624 & 573.716515918811 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 128.428823529412 & 0.213363005562695 & 601.926389210308 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 128.463181818182 & 0.206486442105696 & 622.138579696309 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 128.5034375 & 0.198943541428445 & 645.929174565437 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 128.548387096774 & 0.190218804895923 & 675.792212905074 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 128.589666666667 & 0.18213299397773 & 706.020715183486 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 128.635689655172 & 0.172277739725416 & 746.676209359363 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 128.6825 & 0.160873276335633 & 799.899790264277 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 128.729814814815 & 0.148563701344389 & 866.495743239485 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 128.782115384615 & 0.1324520279527 & 972.292515072737 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 128.8356 & 0.112036131198277 & 1149.94688429568 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 128.893125 & 0.0813320814252998 & 1584.77593025064 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 128.890652173913 & 0.0797013763292945 & 1617.16971663561 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 128.888409090909 & 0.0776722277674942 & 1659.3885973855 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 128.886428571429 & 0.0751226804829718 & 1715.67930940169 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 128.88 & 0.0740027719508544 & 1741.55638501744 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 128.875526315789 & 0.0733371347257959 & 1757.30244708426 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 128.872222222222 & 0.0731817818329109 & 1760.98776217917 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 128.867941176471 & 0.0728558993481872 & 1768.80585277789 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 128.863125 & 0.0723070813412952 & 1782.16465952699 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 128.857333333333 & 0.0717129227895438 & 1796.84955404051 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 128.852142857143 & 0.0714353171417843 & 1803.75965296547 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 128.846153846154 & 0.0705997971735518 & 1825.02158652691 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 128.83875 & 0.0690077513499513 & 1867.01852298642 \tabularnewline
Median & 128.87 &  &  \tabularnewline
Midrange & 127.395 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 128.875526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 128.891081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 128.875526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 128.891081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 128.891081081081 &  &  \tabularnewline
Midmean - Closest Observation & 128.875526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 128.891081081081 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 128.875526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132786&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]128.372222222222[/C][C]0.234652310152087[/C][C]547.074188781773[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]128.356791417598[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]128.341154247034[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]128.387448060332[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]128.373055555556[/C][C]0.232501000291392[/C][C]552.139798945666[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]128.365833333333[/C][C]0.223762004512689[/C][C]573.671270119739[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]128.355833333333[/C][C]0.22192171338134[/C][C]578.383391952155[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]128.348611111111[/C][C]0.220389140968402[/C][C]582.372663857849[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]128.376388888889[/C][C]0.212701097478059[/C][C]603.553015997632[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]128.367222222222[/C][C]0.211646446690703[/C][C]606.517256629477[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]128.380833333333[/C][C]0.208135469419974[/C][C]616.813816939041[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]128.398611111111[/C][C]0.200394788910194[/C][C]640.728293432083[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]128.389861111111[/C][C]0.199444994108902[/C][C]643.735691059797[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]128.410694444444[/C][C]0.194249722951012[/C][C]661.059858895285[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]128.41375[/C][C]0.192948807896553[/C][C]665.532746223792[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]128.912083333333[/C][C]0.0841292827077478[/C][C]1532.30931233723[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]128.908472222222[/C][C]0.0835409759837566[/C][C]1543.05681378784[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]128.904583333333[/C][C]0.082913481666717[/C][C]1554.68785946638[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]128.94[/C][C]0.0728204428811616[/C][C]1770.65663017763[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]128.917777777778[/C][C]0.0687019777428806[/C][C]1876.47840736488[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]128.903611111111[/C][C]0.0646028270006587[/C][C]1995.32461806659[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]128.908611111111[/C][C]0.0639497141905498[/C][C]2015.78087944231[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]128.908611111111[/C][C]0.0632249212825731[/C][C]2038.88923064018[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]128.911388888889[/C][C]0.0613563775713951[/C][C]2101.02672275406[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]128.899722222222[/C][C]0.0581260476110756[/C][C]2217.58966108787[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]128.899722222222[/C][C]0.0581260476110756[/C][C]2217.58966108787[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]128.902916666667[/C][C]0.0577250096665351[/C][C]2233.0514522442[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]128.91625[/C][C]0.0551986161614092[/C][C]2335.49786145053[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]128.400142857143[/C][C]0.223804159884624[/C][C]573.716515918811[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]128.428823529412[/C][C]0.213363005562695[/C][C]601.926389210308[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]128.463181818182[/C][C]0.206486442105696[/C][C]622.138579696309[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]128.5034375[/C][C]0.198943541428445[/C][C]645.929174565437[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]128.548387096774[/C][C]0.190218804895923[/C][C]675.792212905074[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]128.589666666667[/C][C]0.18213299397773[/C][C]706.020715183486[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]128.635689655172[/C][C]0.172277739725416[/C][C]746.676209359363[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]128.6825[/C][C]0.160873276335633[/C][C]799.899790264277[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]128.729814814815[/C][C]0.148563701344389[/C][C]866.495743239485[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]128.782115384615[/C][C]0.1324520279527[/C][C]972.292515072737[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]128.8356[/C][C]0.112036131198277[/C][C]1149.94688429568[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]128.893125[/C][C]0.0813320814252998[/C][C]1584.77593025064[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]128.890652173913[/C][C]0.0797013763292945[/C][C]1617.16971663561[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]128.888409090909[/C][C]0.0776722277674942[/C][C]1659.3885973855[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]128.886428571429[/C][C]0.0751226804829718[/C][C]1715.67930940169[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]128.88[/C][C]0.0740027719508544[/C][C]1741.55638501744[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]128.875526315789[/C][C]0.0733371347257959[/C][C]1757.30244708426[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]128.872222222222[/C][C]0.0731817818329109[/C][C]1760.98776217917[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]128.867941176471[/C][C]0.0728558993481872[/C][C]1768.80585277789[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]128.863125[/C][C]0.0723070813412952[/C][C]1782.16465952699[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]128.857333333333[/C][C]0.0717129227895438[/C][C]1796.84955404051[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]128.852142857143[/C][C]0.0714353171417843[/C][C]1803.75965296547[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]128.846153846154[/C][C]0.0705997971735518[/C][C]1825.02158652691[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]128.83875[/C][C]0.0690077513499513[/C][C]1867.01852298642[/C][/ROW]
[ROW][C]Median[/C][C]128.87[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]127.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]128.875526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]128.891081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]128.875526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]128.891081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]128.891081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]128.875526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]128.891081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]128.875526315789[/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=132786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132786&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 Mean128.3722222222220.234652310152087547.074188781773
Geometric Mean128.356791417598
Harmonic Mean128.341154247034
Quadratic Mean128.387448060332
Winsorized Mean ( 1 / 24 )128.3730555555560.232501000291392552.139798945666
Winsorized Mean ( 2 / 24 )128.3658333333330.223762004512689573.671270119739
Winsorized Mean ( 3 / 24 )128.3558333333330.22192171338134578.383391952155
Winsorized Mean ( 4 / 24 )128.3486111111110.220389140968402582.372663857849
Winsorized Mean ( 5 / 24 )128.3763888888890.212701097478059603.553015997632
Winsorized Mean ( 6 / 24 )128.3672222222220.211646446690703606.517256629477
Winsorized Mean ( 7 / 24 )128.3808333333330.208135469419974616.813816939041
Winsorized Mean ( 8 / 24 )128.3986111111110.200394788910194640.728293432083
Winsorized Mean ( 9 / 24 )128.3898611111110.199444994108902643.735691059797
Winsorized Mean ( 10 / 24 )128.4106944444440.194249722951012661.059858895285
Winsorized Mean ( 11 / 24 )128.413750.192948807896553665.532746223792
Winsorized Mean ( 12 / 24 )128.9120833333330.08412928270774781532.30931233723
Winsorized Mean ( 13 / 24 )128.9084722222220.08354097598375661543.05681378784
Winsorized Mean ( 14 / 24 )128.9045833333330.0829134816667171554.68785946638
Winsorized Mean ( 15 / 24 )128.940.07282044288116161770.65663017763
Winsorized Mean ( 16 / 24 )128.9177777777780.06870197774288061876.47840736488
Winsorized Mean ( 17 / 24 )128.9036111111110.06460282700065871995.32461806659
Winsorized Mean ( 18 / 24 )128.9086111111110.06394971419054982015.78087944231
Winsorized Mean ( 19 / 24 )128.9086111111110.06322492128257312038.88923064018
Winsorized Mean ( 20 / 24 )128.9113888888890.06135637757139512101.02672275406
Winsorized Mean ( 21 / 24 )128.8997222222220.05812604761107562217.58966108787
Winsorized Mean ( 22 / 24 )128.8997222222220.05812604761107562217.58966108787
Winsorized Mean ( 23 / 24 )128.9029166666670.05772500966653512233.0514522442
Winsorized Mean ( 24 / 24 )128.916250.05519861616140922335.49786145053
Trimmed Mean ( 1 / 24 )128.4001428571430.223804159884624573.716515918811
Trimmed Mean ( 2 / 24 )128.4288235294120.213363005562695601.926389210308
Trimmed Mean ( 3 / 24 )128.4631818181820.206486442105696622.138579696309
Trimmed Mean ( 4 / 24 )128.50343750.198943541428445645.929174565437
Trimmed Mean ( 5 / 24 )128.5483870967740.190218804895923675.792212905074
Trimmed Mean ( 6 / 24 )128.5896666666670.18213299397773706.020715183486
Trimmed Mean ( 7 / 24 )128.6356896551720.172277739725416746.676209359363
Trimmed Mean ( 8 / 24 )128.68250.160873276335633799.899790264277
Trimmed Mean ( 9 / 24 )128.7298148148150.148563701344389866.495743239485
Trimmed Mean ( 10 / 24 )128.7821153846150.1324520279527972.292515072737
Trimmed Mean ( 11 / 24 )128.83560.1120361311982771149.94688429568
Trimmed Mean ( 12 / 24 )128.8931250.08133208142529981584.77593025064
Trimmed Mean ( 13 / 24 )128.8906521739130.07970137632929451617.16971663561
Trimmed Mean ( 14 / 24 )128.8884090909090.07767222776749421659.3885973855
Trimmed Mean ( 15 / 24 )128.8864285714290.07512268048297181715.67930940169
Trimmed Mean ( 16 / 24 )128.880.07400277195085441741.55638501744
Trimmed Mean ( 17 / 24 )128.8755263157890.07333713472579591757.30244708426
Trimmed Mean ( 18 / 24 )128.8722222222220.07318178183291091760.98776217917
Trimmed Mean ( 19 / 24 )128.8679411764710.07285589934818721768.80585277789
Trimmed Mean ( 20 / 24 )128.8631250.07230708134129521782.16465952699
Trimmed Mean ( 21 / 24 )128.8573333333330.07171292278954381796.84955404051
Trimmed Mean ( 22 / 24 )128.8521428571430.07143531714178431803.75965296547
Trimmed Mean ( 23 / 24 )128.8461538461540.07059979717355181825.02158652691
Trimmed Mean ( 24 / 24 )128.838750.06900775134995131867.01852298642
Median128.87
Midrange127.395
Midmean - Weighted Average at Xnp128.875526315789
Midmean - Weighted Average at X(n+1)p128.891081081081
Midmean - Empirical Distribution Function128.875526315789
Midmean - Empirical Distribution Function - Averaging128.891081081081
Midmean - Empirical Distribution Function - Interpolation128.891081081081
Midmean - Closest Observation128.875526315789
Midmean - True Basic - Statistics Graphics Toolkit128.891081081081
Midmean - MS Excel (old versions)128.875526315789
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')