Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 12 Oct 2014 11:52:09 +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/2014/Oct/12/t14131111888iqb53olihoh4e8.htm/, Retrieved Wed, 15 May 2024 21:57:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240539, Retrieved Wed, 15 May 2024 21:57:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-12 10:52:09] [2f27692a17e58baa8638275162e45e6c] [Current]
Feedback Forum

Post a new message
Dataseries X:
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133
125
118
116
118
116
111
108
102
102
129
136
137
126
119
117




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=240539&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=240539&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240539&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 Mean112.8888888888891.5200222842906174.2679170270019
Geometric Mean112.158691752977
Harmonic Mean111.425003848676
Quadratic Mean113.613134999631
Winsorized Mean ( 1 / 24 )112.9305555555561.5094027657547174.8180393714132
Winsorized Mean ( 2 / 24 )113.0416666666671.4724169047763176.7728666385014
Winsorized Mean ( 3 / 24 )113.0416666666671.4724169047763176.7728666385014
Winsorized Mean ( 4 / 24 )113.0416666666671.4493856963257377.9928123709469
Winsorized Mean ( 5 / 24 )113.1111111111111.4086080593720380.2999176091162
Winsorized Mean ( 6 / 24 )113.1111111111111.3765808319868482.1681578609928
Winsorized Mean ( 7 / 24 )113.3055555555561.343948194087784.3079785768602
Winsorized Mean ( 8 / 24 )113.0833333333331.2994145184531587.0263735916622
Winsorized Mean ( 9 / 24 )113.0833333333331.2553095372969990.0840230823315
Winsorized Mean ( 10 / 24 )113.0833333333331.2076552249752593.6387563227337
Winsorized Mean ( 11 / 24 )112.7777777777781.1527035347625597.8376263945519
Winsorized Mean ( 12 / 24 )112.7777777777781.09848063767849102.667060218849
Winsorized Mean ( 13 / 24 )112.7777777777781.04143842048151108.290394861403
Winsorized Mean ( 14 / 24 )112.5833333333331.0098788256848111.482021872268
Winsorized Mean ( 15 / 24 )112.5833333333331.0098788256848111.482021872268
Winsorized Mean ( 16 / 24 )112.1388888888890.941626792033643119.090588583085
Winsorized Mean ( 17 / 24 )112.1388888888890.871947067431285128.607450013273
Winsorized Mean ( 18 / 24 )112.3888888888890.835807490404026134.467434402341
Winsorized Mean ( 19 / 24 )112.3888888888890.761339821479068147.619874487255
Winsorized Mean ( 20 / 24 )112.3888888888890.761339821479068147.619874487255
Winsorized Mean ( 21 / 24 )112.6805555555560.722385845796359155.983891726639
Winsorized Mean ( 22 / 24 )112.3750.679580758868824165.359302089498
Winsorized Mean ( 23 / 24 )112.3750.594851903558734188.91256685523
Winsorized Mean ( 24 / 24 )112.3750.594851903558734188.91256685523
Trimmed Mean ( 1 / 24 )112.9571428571431.4670198682022376.9976912416101
Trimmed Mean ( 2 / 24 )112.9852941176471.4166160335169879.7571758644736
Trimmed Mean ( 3 / 24 )112.9545454545451.3802523025638481.8361579580274
Trimmed Mean ( 4 / 24 )112.9218751.3365483351278284.4876852053399
Trimmed Mean ( 5 / 24 )112.8870967741941.2925169732868687.3389666111096
Trimmed Mean ( 6 / 24 )112.8333333333331.2523800317313790.0951232648968
Trimmed Mean ( 7 / 24 )112.7758620689661.2127182207874292.9942835325256
Trimmed Mean ( 8 / 24 )112.6785714285711.1724951590344396.1015237976452
Trimmed Mean ( 9 / 24 )112.6111111111111.1343738800312699.2716009187444
Trimmed Mean ( 10 / 24 )112.5384615384621.09759834435763102.531551834952
Trimmed Mean ( 11 / 24 )112.461.06261517983142105.83323307864
Trimmed Mean ( 12 / 24 )112.4166666666671.03134961729616108.999571805131
Trimmed Mean ( 13 / 24 )112.3695652173911.00354862905176111.972217353899
Trimmed Mean ( 14 / 24 )112.3181818181820.98012637106045114.595612499089
Trimmed Mean ( 15 / 24 )112.2857142857140.956234943045715117.424818139433
Trimmed Mean ( 16 / 24 )112.250.92386451443144121.500499528419
Trimmed Mean ( 17 / 24 )112.2631578947370.897034953454323125.149145484723
Trimmed Mean ( 18 / 24 )112.2777777777780.877054152199653128.016927456742
Trimmed Mean ( 19 / 24 )112.2647058823530.857294196658662130.952368883295
Trimmed Mean ( 20 / 24 )112.250.847196515268961132.495823550884
Trimmed Mean ( 21 / 24 )112.2333333333330.830016387226863135.218213833479
Trimmed Mean ( 22 / 24 )112.1785714285710.81333719005814137.923819050439
Trimmed Mean ( 23 / 24 )112.1538461538460.79940806503179140.296115413079
Trimmed Mean ( 24 / 24 )112.1250.801521424668673139.890209480488
Median111
Midrange110.5
Midmean - Weighted Average at Xnp112.263157894737
Midmean - Weighted Average at X(n+1)p112.513513513514
Midmean - Empirical Distribution Function112.263157894737
Midmean - Empirical Distribution Function - Averaging112.513513513514
Midmean - Empirical Distribution Function - Interpolation112.513513513514
Midmean - Closest Observation112.263157894737
Midmean - True Basic - Statistics Graphics Toolkit112.513513513514
Midmean - MS Excel (old versions)112.263157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.888888888889 & 1.52002228429061 & 74.2679170270019 \tabularnewline
Geometric Mean & 112.158691752977 &  &  \tabularnewline
Harmonic Mean & 111.425003848676 &  &  \tabularnewline
Quadratic Mean & 113.613134999631 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 112.930555555556 & 1.50940276575471 & 74.8180393714132 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 113.041666666667 & 1.47241690477631 & 76.7728666385014 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 113.041666666667 & 1.47241690477631 & 76.7728666385014 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 113.041666666667 & 1.44938569632573 & 77.9928123709469 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 113.111111111111 & 1.40860805937203 & 80.2999176091162 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 113.111111111111 & 1.37658083198684 & 82.1681578609928 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 113.305555555556 & 1.3439481940877 & 84.3079785768602 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 113.083333333333 & 1.29941451845315 & 87.0263735916622 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 113.083333333333 & 1.25530953729699 & 90.0840230823315 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 113.083333333333 & 1.20765522497525 & 93.6387563227337 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 112.777777777778 & 1.15270353476255 & 97.8376263945519 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 112.777777777778 & 1.09848063767849 & 102.667060218849 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 112.777777777778 & 1.04143842048151 & 108.290394861403 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 112.583333333333 & 1.0098788256848 & 111.482021872268 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 112.583333333333 & 1.0098788256848 & 111.482021872268 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 112.138888888889 & 0.941626792033643 & 119.090588583085 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 112.138888888889 & 0.871947067431285 & 128.607450013273 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 112.388888888889 & 0.835807490404026 & 134.467434402341 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 112.388888888889 & 0.761339821479068 & 147.619874487255 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 112.388888888889 & 0.761339821479068 & 147.619874487255 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 112.680555555556 & 0.722385845796359 & 155.983891726639 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 112.375 & 0.679580758868824 & 165.359302089498 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 112.375 & 0.594851903558734 & 188.91256685523 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 112.375 & 0.594851903558734 & 188.91256685523 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 112.957142857143 & 1.46701986820223 & 76.9976912416101 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 112.985294117647 & 1.41661603351698 & 79.7571758644736 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 112.954545454545 & 1.38025230256384 & 81.8361579580274 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 112.921875 & 1.33654833512782 & 84.4876852053399 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 112.887096774194 & 1.29251697328686 & 87.3389666111096 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 112.833333333333 & 1.25238003173137 & 90.0951232648968 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 112.775862068966 & 1.21271822078742 & 92.9942835325256 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 112.678571428571 & 1.17249515903443 & 96.1015237976452 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 112.611111111111 & 1.13437388003126 & 99.2716009187444 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 112.538461538462 & 1.09759834435763 & 102.531551834952 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 112.46 & 1.06261517983142 & 105.83323307864 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 112.416666666667 & 1.03134961729616 & 108.999571805131 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 112.369565217391 & 1.00354862905176 & 111.972217353899 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 112.318181818182 & 0.98012637106045 & 114.595612499089 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 112.285714285714 & 0.956234943045715 & 117.424818139433 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 112.25 & 0.92386451443144 & 121.500499528419 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 112.263157894737 & 0.897034953454323 & 125.149145484723 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 112.277777777778 & 0.877054152199653 & 128.016927456742 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 112.264705882353 & 0.857294196658662 & 130.952368883295 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 112.25 & 0.847196515268961 & 132.495823550884 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 112.233333333333 & 0.830016387226863 & 135.218213833479 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 112.178571428571 & 0.81333719005814 & 137.923819050439 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 112.153846153846 & 0.79940806503179 & 140.296115413079 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 112.125 & 0.801521424668673 & 139.890209480488 \tabularnewline
Median & 111 &  &  \tabularnewline
Midrange & 110.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.263157894737 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.513513513514 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.263157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.513513513514 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.513513513514 &  &  \tabularnewline
Midmean - Closest Observation & 112.263157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.513513513514 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.263157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240539&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]112.888888888889[/C][C]1.52002228429061[/C][C]74.2679170270019[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.158691752977[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.425003848676[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.613134999631[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]112.930555555556[/C][C]1.50940276575471[/C][C]74.8180393714132[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]113.041666666667[/C][C]1.47241690477631[/C][C]76.7728666385014[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]113.041666666667[/C][C]1.47241690477631[/C][C]76.7728666385014[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]113.041666666667[/C][C]1.44938569632573[/C][C]77.9928123709469[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]113.111111111111[/C][C]1.40860805937203[/C][C]80.2999176091162[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]113.111111111111[/C][C]1.37658083198684[/C][C]82.1681578609928[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]113.305555555556[/C][C]1.3439481940877[/C][C]84.3079785768602[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]113.083333333333[/C][C]1.29941451845315[/C][C]87.0263735916622[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]113.083333333333[/C][C]1.25530953729699[/C][C]90.0840230823315[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]113.083333333333[/C][C]1.20765522497525[/C][C]93.6387563227337[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]112.777777777778[/C][C]1.15270353476255[/C][C]97.8376263945519[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]112.777777777778[/C][C]1.09848063767849[/C][C]102.667060218849[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]112.777777777778[/C][C]1.04143842048151[/C][C]108.290394861403[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]112.583333333333[/C][C]1.0098788256848[/C][C]111.482021872268[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]112.583333333333[/C][C]1.0098788256848[/C][C]111.482021872268[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]112.138888888889[/C][C]0.941626792033643[/C][C]119.090588583085[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]112.138888888889[/C][C]0.871947067431285[/C][C]128.607450013273[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]112.388888888889[/C][C]0.835807490404026[/C][C]134.467434402341[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]112.388888888889[/C][C]0.761339821479068[/C][C]147.619874487255[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]112.388888888889[/C][C]0.761339821479068[/C][C]147.619874487255[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]112.680555555556[/C][C]0.722385845796359[/C][C]155.983891726639[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]112.375[/C][C]0.679580758868824[/C][C]165.359302089498[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]112.375[/C][C]0.594851903558734[/C][C]188.91256685523[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]112.375[/C][C]0.594851903558734[/C][C]188.91256685523[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]112.957142857143[/C][C]1.46701986820223[/C][C]76.9976912416101[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]112.985294117647[/C][C]1.41661603351698[/C][C]79.7571758644736[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]112.954545454545[/C][C]1.38025230256384[/C][C]81.8361579580274[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]112.921875[/C][C]1.33654833512782[/C][C]84.4876852053399[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]112.887096774194[/C][C]1.29251697328686[/C][C]87.3389666111096[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]112.833333333333[/C][C]1.25238003173137[/C][C]90.0951232648968[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]112.775862068966[/C][C]1.21271822078742[/C][C]92.9942835325256[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]112.678571428571[/C][C]1.17249515903443[/C][C]96.1015237976452[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]112.611111111111[/C][C]1.13437388003126[/C][C]99.2716009187444[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]112.538461538462[/C][C]1.09759834435763[/C][C]102.531551834952[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]112.46[/C][C]1.06261517983142[/C][C]105.83323307864[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]112.416666666667[/C][C]1.03134961729616[/C][C]108.999571805131[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]112.369565217391[/C][C]1.00354862905176[/C][C]111.972217353899[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]112.318181818182[/C][C]0.98012637106045[/C][C]114.595612499089[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]112.285714285714[/C][C]0.956234943045715[/C][C]117.424818139433[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]112.25[/C][C]0.92386451443144[/C][C]121.500499528419[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]112.263157894737[/C][C]0.897034953454323[/C][C]125.149145484723[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]112.277777777778[/C][C]0.877054152199653[/C][C]128.016927456742[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]112.264705882353[/C][C]0.857294196658662[/C][C]130.952368883295[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]112.25[/C][C]0.847196515268961[/C][C]132.495823550884[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]112.233333333333[/C][C]0.830016387226863[/C][C]135.218213833479[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]112.178571428571[/C][C]0.81333719005814[/C][C]137.923819050439[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]112.153846153846[/C][C]0.79940806503179[/C][C]140.296115413079[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]112.125[/C][C]0.801521424668673[/C][C]139.890209480488[/C][/ROW]
[ROW][C]Median[/C][C]111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.513513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.513513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.513513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.513513513514[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.263157894737[/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=240539&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240539&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 Mean112.8888888888891.5200222842906174.2679170270019
Geometric Mean112.158691752977
Harmonic Mean111.425003848676
Quadratic Mean113.613134999631
Winsorized Mean ( 1 / 24 )112.9305555555561.5094027657547174.8180393714132
Winsorized Mean ( 2 / 24 )113.0416666666671.4724169047763176.7728666385014
Winsorized Mean ( 3 / 24 )113.0416666666671.4724169047763176.7728666385014
Winsorized Mean ( 4 / 24 )113.0416666666671.4493856963257377.9928123709469
Winsorized Mean ( 5 / 24 )113.1111111111111.4086080593720380.2999176091162
Winsorized Mean ( 6 / 24 )113.1111111111111.3765808319868482.1681578609928
Winsorized Mean ( 7 / 24 )113.3055555555561.343948194087784.3079785768602
Winsorized Mean ( 8 / 24 )113.0833333333331.2994145184531587.0263735916622
Winsorized Mean ( 9 / 24 )113.0833333333331.2553095372969990.0840230823315
Winsorized Mean ( 10 / 24 )113.0833333333331.2076552249752593.6387563227337
Winsorized Mean ( 11 / 24 )112.7777777777781.1527035347625597.8376263945519
Winsorized Mean ( 12 / 24 )112.7777777777781.09848063767849102.667060218849
Winsorized Mean ( 13 / 24 )112.7777777777781.04143842048151108.290394861403
Winsorized Mean ( 14 / 24 )112.5833333333331.0098788256848111.482021872268
Winsorized Mean ( 15 / 24 )112.5833333333331.0098788256848111.482021872268
Winsorized Mean ( 16 / 24 )112.1388888888890.941626792033643119.090588583085
Winsorized Mean ( 17 / 24 )112.1388888888890.871947067431285128.607450013273
Winsorized Mean ( 18 / 24 )112.3888888888890.835807490404026134.467434402341
Winsorized Mean ( 19 / 24 )112.3888888888890.761339821479068147.619874487255
Winsorized Mean ( 20 / 24 )112.3888888888890.761339821479068147.619874487255
Winsorized Mean ( 21 / 24 )112.6805555555560.722385845796359155.983891726639
Winsorized Mean ( 22 / 24 )112.3750.679580758868824165.359302089498
Winsorized Mean ( 23 / 24 )112.3750.594851903558734188.91256685523
Winsorized Mean ( 24 / 24 )112.3750.594851903558734188.91256685523
Trimmed Mean ( 1 / 24 )112.9571428571431.4670198682022376.9976912416101
Trimmed Mean ( 2 / 24 )112.9852941176471.4166160335169879.7571758644736
Trimmed Mean ( 3 / 24 )112.9545454545451.3802523025638481.8361579580274
Trimmed Mean ( 4 / 24 )112.9218751.3365483351278284.4876852053399
Trimmed Mean ( 5 / 24 )112.8870967741941.2925169732868687.3389666111096
Trimmed Mean ( 6 / 24 )112.8333333333331.2523800317313790.0951232648968
Trimmed Mean ( 7 / 24 )112.7758620689661.2127182207874292.9942835325256
Trimmed Mean ( 8 / 24 )112.6785714285711.1724951590344396.1015237976452
Trimmed Mean ( 9 / 24 )112.6111111111111.1343738800312699.2716009187444
Trimmed Mean ( 10 / 24 )112.5384615384621.09759834435763102.531551834952
Trimmed Mean ( 11 / 24 )112.461.06261517983142105.83323307864
Trimmed Mean ( 12 / 24 )112.4166666666671.03134961729616108.999571805131
Trimmed Mean ( 13 / 24 )112.3695652173911.00354862905176111.972217353899
Trimmed Mean ( 14 / 24 )112.3181818181820.98012637106045114.595612499089
Trimmed Mean ( 15 / 24 )112.2857142857140.956234943045715117.424818139433
Trimmed Mean ( 16 / 24 )112.250.92386451443144121.500499528419
Trimmed Mean ( 17 / 24 )112.2631578947370.897034953454323125.149145484723
Trimmed Mean ( 18 / 24 )112.2777777777780.877054152199653128.016927456742
Trimmed Mean ( 19 / 24 )112.2647058823530.857294196658662130.952368883295
Trimmed Mean ( 20 / 24 )112.250.847196515268961132.495823550884
Trimmed Mean ( 21 / 24 )112.2333333333330.830016387226863135.218213833479
Trimmed Mean ( 22 / 24 )112.1785714285710.81333719005814137.923819050439
Trimmed Mean ( 23 / 24 )112.1538461538460.79940806503179140.296115413079
Trimmed Mean ( 24 / 24 )112.1250.801521424668673139.890209480488
Median111
Midrange110.5
Midmean - Weighted Average at Xnp112.263157894737
Midmean - Weighted Average at X(n+1)p112.513513513514
Midmean - Empirical Distribution Function112.263157894737
Midmean - Empirical Distribution Function - Averaging112.513513513514
Midmean - Empirical Distribution Function - Interpolation112.513513513514
Midmean - Closest Observation112.263157894737
Midmean - True Basic - Statistics Graphics Toolkit112.513513513514
Midmean - MS Excel (old versions)112.263157894737
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')