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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 22:33:18 +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/2016/Oct/13/t1476394486gtr6obpb42gl0nc.htm/, Retrieved Tue, 30 Apr 2024 12:10:58 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 12:10:58 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
122,9
122,82
120,26
118,82
126,69
125,79
123,96
128,7
127,74
127,55
126,16
124,74
122,32
120,92
117,09
115,77
117,88
117,77
122,61
127,31
124,62
119,07
116,92
115,07
113,84
112,89
111,86
111,58
107,72
106,49
108,53
108,62
107,92
106,43
117,66
115,11
113,98
112,16
109,72
117,99
112,57
113,66
118,18
115,66
114,72
110,46
108,38
106,52
107,01
105,89
103,76
103,71
101,07
100,4
102,24
99,18
98,14
96,22
94,38
94,62
94,71
94,97
93,69
106,42
105,73
105,18
104,8
102,77
100,29
99,3
96,63
95,5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

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

As an alternative you can also use a QR Code:  
QR Code


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

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






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.4269444444441.1669077322858895.4890788375939
Geometric Mean110.988731027178
Harmonic Mean110.546953814757
Quadratic Mean111.859924806777
Winsorized Mean ( 1 / 24 )111.4231944444441.162183805693295.8739864543067
Winsorized Mean ( 2 / 24 )111.4245833333331.1597764499377596.0741902797856
Winsorized Mean ( 3 / 24 )111.4183333333331.1570660815432796.2938375868089
Winsorized Mean ( 4 / 24 )111.3983333333331.147576765837497.0726635895636
Winsorized Mean ( 5 / 24 )111.3983333333331.1333999220979298.286872234061
Winsorized Mean ( 6 / 24 )111.42751.1160918173858699.8372161360237
Winsorized Mean ( 7 / 24 )111.3652777777781.09039898751094102.132594631248
Winsorized Mean ( 8 / 24 )111.5197222222221.05714733317842105.491182470211
Winsorized Mean ( 9 / 24 )111.5672222222221.02017614128241109.360744392607
Winsorized Mean ( 10 / 24 )111.4366666666670.992741497445923112.251444060076
Winsorized Mean ( 11 / 24 )111.5756944444440.965261866291213115.591114018776
Winsorized Mean ( 12 / 24 )111.5590277777780.956527184702664116.629228695111
Winsorized Mean ( 13 / 24 )111.6276388888890.928389667398712120.237916048401
Winsorized Mean ( 14 / 24 )111.5829166666670.84932108202474131.378955530762
Winsorized Mean ( 15 / 24 )111.5558333333330.811303934864201137.501901000894
Winsorized Mean ( 16 / 24 )111.5002777777780.74083217737364150.506796523152
Winsorized Mean ( 17 / 24 )111.4530555555560.730643424474652152.540968442565
Winsorized Mean ( 18 / 24 )111.5530555555560.670375296020979166.403887818779
Winsorized Mean ( 19 / 24 )111.6031944444440.64930987880696171.879711193527
Winsorized Mean ( 20 / 24 )111.7254166666670.624086247146299179.022398230282
Winsorized Mean ( 21 / 24 )111.740.613344910841944182.181343685747
Winsorized Mean ( 22 / 24 )111.8683333333330.587218183998208190.505567405376
Winsorized Mean ( 23 / 24 )111.6894444444440.561818806413406198.799761007394
Winsorized Mean ( 24 / 24 )111.6527777777780.551534536685931202.440228763694
Trimmed Mean ( 1 / 24 )111.4335714285711.1464153337341997.2017454316503
Trimmed Mean ( 2 / 24 )111.4445588235291.1274356997062298.8478179754009
Trimmed Mean ( 3 / 24 )111.4554545454551.10610975782476100.763467419941
Trimmed Mean ( 4 / 24 )111.4693751.08160745937727103.058992459406
Trimmed Mean ( 5 / 24 )111.491.05544489881103105.633179075094
Trimmed Mean ( 6 / 24 )111.5121.02814812953737108.459079773045
Trimmed Mean ( 7 / 24 )111.5294827586210.999753339888342111.556999420554
Trimmed Mean ( 8 / 24 )111.5596428571430.971644407601746114.815298667235
Trimmed Mean ( 9 / 24 )111.5662962962960.945241467724423118.029413759091
Trimmed Mean ( 10 / 24 )111.5661538461540.921119644364536121.120154725526
Trimmed Mean ( 11 / 24 )111.58480.896976246585591124.401064604281
Trimmed Mean ( 12 / 24 )111.5860416666670.872497776805441127.89263724571
Trimmed Mean ( 13 / 24 )111.5895652173910.842910070590896132.386086144593
Trimmed Mean ( 14 / 24 )111.5847727272730.811168439782641137.560545078865
Trimmed Mean ( 15 / 24 )111.5850.78843773326335141.526711993031
Trimmed Mean ( 16 / 24 )111.58850.766900818479557145.505777684829
Trimmed Mean ( 17 / 24 )111.5989473684210.754052945671155147.998821580215
Trimmed Mean ( 18 / 24 )111.6161111111110.737780054739267151.286430683676
Trimmed Mean ( 19 / 24 )111.6235294117650.729012087900699153.116157145215
Trimmed Mean ( 20 / 24 )111.62593750.71999479996092155.037144026677
Trimmed Mean ( 21 / 24 )111.6140.71145449204631156.881432681621
Trimmed Mean ( 22 / 24 )111.5985714285710.699299103805748159.58632124827
Trimmed Mean ( 23 / 24 )111.5646153846150.686249613875577162.571480010833
Trimmed Mean ( 24 / 24 )111.5483333333330.671912602868647166.016134921553
Median112.01
Midrange111.195
Midmean - Weighted Average at Xnp111.403783783784
Midmean - Weighted Average at X(n+1)p111.616111111111
Midmean - Empirical Distribution Function111.403783783784
Midmean - Empirical Distribution Function - Averaging111.616111111111
Midmean - Empirical Distribution Function - Interpolation111.616111111111
Midmean - Closest Observation111.403783783784
Midmean - True Basic - Statistics Graphics Toolkit111.616111111111
Midmean - MS Excel (old versions)111.598947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.426944444444 & 1.16690773228588 & 95.4890788375939 \tabularnewline
Geometric Mean & 110.988731027178 &  &  \tabularnewline
Harmonic Mean & 110.546953814757 &  &  \tabularnewline
Quadratic Mean & 111.859924806777 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 111.423194444444 & 1.1621838056932 & 95.8739864543067 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 111.424583333333 & 1.15977644993775 & 96.0741902797856 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 111.418333333333 & 1.15706608154327 & 96.2938375868089 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 111.398333333333 & 1.1475767658374 & 97.0726635895636 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 111.398333333333 & 1.13339992209792 & 98.286872234061 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 111.4275 & 1.11609181738586 & 99.8372161360237 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 111.365277777778 & 1.09039898751094 & 102.132594631248 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 111.519722222222 & 1.05714733317842 & 105.491182470211 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 111.567222222222 & 1.02017614128241 & 109.360744392607 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 111.436666666667 & 0.992741497445923 & 112.251444060076 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 111.575694444444 & 0.965261866291213 & 115.591114018776 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 111.559027777778 & 0.956527184702664 & 116.629228695111 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 111.627638888889 & 0.928389667398712 & 120.237916048401 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 111.582916666667 & 0.84932108202474 & 131.378955530762 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 111.555833333333 & 0.811303934864201 & 137.501901000894 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 111.500277777778 & 0.74083217737364 & 150.506796523152 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 111.453055555556 & 0.730643424474652 & 152.540968442565 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 111.553055555556 & 0.670375296020979 & 166.403887818779 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 111.603194444444 & 0.64930987880696 & 171.879711193527 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 111.725416666667 & 0.624086247146299 & 179.022398230282 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 111.74 & 0.613344910841944 & 182.181343685747 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 111.868333333333 & 0.587218183998208 & 190.505567405376 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 111.689444444444 & 0.561818806413406 & 198.799761007394 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 111.652777777778 & 0.551534536685931 & 202.440228763694 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 111.433571428571 & 1.14641533373419 & 97.2017454316503 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 111.444558823529 & 1.12743569970622 & 98.8478179754009 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 111.455454545455 & 1.10610975782476 & 100.763467419941 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 111.469375 & 1.08160745937727 & 103.058992459406 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 111.49 & 1.05544489881103 & 105.633179075094 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 111.512 & 1.02814812953737 & 108.459079773045 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 111.529482758621 & 0.999753339888342 & 111.556999420554 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 111.559642857143 & 0.971644407601746 & 114.815298667235 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 111.566296296296 & 0.945241467724423 & 118.029413759091 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 111.566153846154 & 0.921119644364536 & 121.120154725526 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 111.5848 & 0.896976246585591 & 124.401064604281 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 111.586041666667 & 0.872497776805441 & 127.89263724571 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 111.589565217391 & 0.842910070590896 & 132.386086144593 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 111.584772727273 & 0.811168439782641 & 137.560545078865 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 111.585 & 0.78843773326335 & 141.526711993031 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 111.5885 & 0.766900818479557 & 145.505777684829 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 111.598947368421 & 0.754052945671155 & 147.998821580215 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 111.616111111111 & 0.737780054739267 & 151.286430683676 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 111.623529411765 & 0.729012087900699 & 153.116157145215 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 111.6259375 & 0.71999479996092 & 155.037144026677 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 111.614 & 0.71145449204631 & 156.881432681621 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 111.598571428571 & 0.699299103805748 & 159.58632124827 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 111.564615384615 & 0.686249613875577 & 162.571480010833 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 111.548333333333 & 0.671912602868647 & 166.016134921553 \tabularnewline
Median & 112.01 &  &  \tabularnewline
Midrange & 111.195 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.403783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.616111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.403783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.616111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.616111111111 &  &  \tabularnewline
Midmean - Closest Observation & 111.403783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.616111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.598947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]111.426944444444[/C][C]1.16690773228588[/C][C]95.4890788375939[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.988731027178[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.546953814757[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.859924806777[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]111.423194444444[/C][C]1.1621838056932[/C][C]95.8739864543067[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]111.424583333333[/C][C]1.15977644993775[/C][C]96.0741902797856[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]111.418333333333[/C][C]1.15706608154327[/C][C]96.2938375868089[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]111.398333333333[/C][C]1.1475767658374[/C][C]97.0726635895636[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]111.398333333333[/C][C]1.13339992209792[/C][C]98.286872234061[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]111.4275[/C][C]1.11609181738586[/C][C]99.8372161360237[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]111.365277777778[/C][C]1.09039898751094[/C][C]102.132594631248[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]111.519722222222[/C][C]1.05714733317842[/C][C]105.491182470211[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]111.567222222222[/C][C]1.02017614128241[/C][C]109.360744392607[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]111.436666666667[/C][C]0.992741497445923[/C][C]112.251444060076[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]111.575694444444[/C][C]0.965261866291213[/C][C]115.591114018776[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]111.559027777778[/C][C]0.956527184702664[/C][C]116.629228695111[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]111.627638888889[/C][C]0.928389667398712[/C][C]120.237916048401[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]111.582916666667[/C][C]0.84932108202474[/C][C]131.378955530762[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]111.555833333333[/C][C]0.811303934864201[/C][C]137.501901000894[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]111.500277777778[/C][C]0.74083217737364[/C][C]150.506796523152[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]111.453055555556[/C][C]0.730643424474652[/C][C]152.540968442565[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]111.553055555556[/C][C]0.670375296020979[/C][C]166.403887818779[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]111.603194444444[/C][C]0.64930987880696[/C][C]171.879711193527[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]111.725416666667[/C][C]0.624086247146299[/C][C]179.022398230282[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]111.74[/C][C]0.613344910841944[/C][C]182.181343685747[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]111.868333333333[/C][C]0.587218183998208[/C][C]190.505567405376[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]111.689444444444[/C][C]0.561818806413406[/C][C]198.799761007394[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]111.652777777778[/C][C]0.551534536685931[/C][C]202.440228763694[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]111.433571428571[/C][C]1.14641533373419[/C][C]97.2017454316503[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]111.444558823529[/C][C]1.12743569970622[/C][C]98.8478179754009[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]111.455454545455[/C][C]1.10610975782476[/C][C]100.763467419941[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]111.469375[/C][C]1.08160745937727[/C][C]103.058992459406[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]111.49[/C][C]1.05544489881103[/C][C]105.633179075094[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]111.512[/C][C]1.02814812953737[/C][C]108.459079773045[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]111.529482758621[/C][C]0.999753339888342[/C][C]111.556999420554[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]111.559642857143[/C][C]0.971644407601746[/C][C]114.815298667235[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]111.566296296296[/C][C]0.945241467724423[/C][C]118.029413759091[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]111.566153846154[/C][C]0.921119644364536[/C][C]121.120154725526[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]111.5848[/C][C]0.896976246585591[/C][C]124.401064604281[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]111.586041666667[/C][C]0.872497776805441[/C][C]127.89263724571[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]111.589565217391[/C][C]0.842910070590896[/C][C]132.386086144593[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]111.584772727273[/C][C]0.811168439782641[/C][C]137.560545078865[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]111.585[/C][C]0.78843773326335[/C][C]141.526711993031[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]111.5885[/C][C]0.766900818479557[/C][C]145.505777684829[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]111.598947368421[/C][C]0.754052945671155[/C][C]147.998821580215[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]111.616111111111[/C][C]0.737780054739267[/C][C]151.286430683676[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]111.623529411765[/C][C]0.729012087900699[/C][C]153.116157145215[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]111.6259375[/C][C]0.71999479996092[/C][C]155.037144026677[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]111.614[/C][C]0.71145449204631[/C][C]156.881432681621[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]111.598571428571[/C][C]0.699299103805748[/C][C]159.58632124827[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]111.564615384615[/C][C]0.686249613875577[/C][C]162.571480010833[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]111.548333333333[/C][C]0.671912602868647[/C][C]166.016134921553[/C][/ROW]
[ROW][C]Median[/C][C]112.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.195[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.403783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.616111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.403783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.616111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.616111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.403783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.616111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.598947368421[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.4269444444441.1669077322858895.4890788375939
Geometric Mean110.988731027178
Harmonic Mean110.546953814757
Quadratic Mean111.859924806777
Winsorized Mean ( 1 / 24 )111.4231944444441.162183805693295.8739864543067
Winsorized Mean ( 2 / 24 )111.4245833333331.1597764499377596.0741902797856
Winsorized Mean ( 3 / 24 )111.4183333333331.1570660815432796.2938375868089
Winsorized Mean ( 4 / 24 )111.3983333333331.147576765837497.0726635895636
Winsorized Mean ( 5 / 24 )111.3983333333331.1333999220979298.286872234061
Winsorized Mean ( 6 / 24 )111.42751.1160918173858699.8372161360237
Winsorized Mean ( 7 / 24 )111.3652777777781.09039898751094102.132594631248
Winsorized Mean ( 8 / 24 )111.5197222222221.05714733317842105.491182470211
Winsorized Mean ( 9 / 24 )111.5672222222221.02017614128241109.360744392607
Winsorized Mean ( 10 / 24 )111.4366666666670.992741497445923112.251444060076
Winsorized Mean ( 11 / 24 )111.5756944444440.965261866291213115.591114018776
Winsorized Mean ( 12 / 24 )111.5590277777780.956527184702664116.629228695111
Winsorized Mean ( 13 / 24 )111.6276388888890.928389667398712120.237916048401
Winsorized Mean ( 14 / 24 )111.5829166666670.84932108202474131.378955530762
Winsorized Mean ( 15 / 24 )111.5558333333330.811303934864201137.501901000894
Winsorized Mean ( 16 / 24 )111.5002777777780.74083217737364150.506796523152
Winsorized Mean ( 17 / 24 )111.4530555555560.730643424474652152.540968442565
Winsorized Mean ( 18 / 24 )111.5530555555560.670375296020979166.403887818779
Winsorized Mean ( 19 / 24 )111.6031944444440.64930987880696171.879711193527
Winsorized Mean ( 20 / 24 )111.7254166666670.624086247146299179.022398230282
Winsorized Mean ( 21 / 24 )111.740.613344910841944182.181343685747
Winsorized Mean ( 22 / 24 )111.8683333333330.587218183998208190.505567405376
Winsorized Mean ( 23 / 24 )111.6894444444440.561818806413406198.799761007394
Winsorized Mean ( 24 / 24 )111.6527777777780.551534536685931202.440228763694
Trimmed Mean ( 1 / 24 )111.4335714285711.1464153337341997.2017454316503
Trimmed Mean ( 2 / 24 )111.4445588235291.1274356997062298.8478179754009
Trimmed Mean ( 3 / 24 )111.4554545454551.10610975782476100.763467419941
Trimmed Mean ( 4 / 24 )111.4693751.08160745937727103.058992459406
Trimmed Mean ( 5 / 24 )111.491.05544489881103105.633179075094
Trimmed Mean ( 6 / 24 )111.5121.02814812953737108.459079773045
Trimmed Mean ( 7 / 24 )111.5294827586210.999753339888342111.556999420554
Trimmed Mean ( 8 / 24 )111.5596428571430.971644407601746114.815298667235
Trimmed Mean ( 9 / 24 )111.5662962962960.945241467724423118.029413759091
Trimmed Mean ( 10 / 24 )111.5661538461540.921119644364536121.120154725526
Trimmed Mean ( 11 / 24 )111.58480.896976246585591124.401064604281
Trimmed Mean ( 12 / 24 )111.5860416666670.872497776805441127.89263724571
Trimmed Mean ( 13 / 24 )111.5895652173910.842910070590896132.386086144593
Trimmed Mean ( 14 / 24 )111.5847727272730.811168439782641137.560545078865
Trimmed Mean ( 15 / 24 )111.5850.78843773326335141.526711993031
Trimmed Mean ( 16 / 24 )111.58850.766900818479557145.505777684829
Trimmed Mean ( 17 / 24 )111.5989473684210.754052945671155147.998821580215
Trimmed Mean ( 18 / 24 )111.6161111111110.737780054739267151.286430683676
Trimmed Mean ( 19 / 24 )111.6235294117650.729012087900699153.116157145215
Trimmed Mean ( 20 / 24 )111.62593750.71999479996092155.037144026677
Trimmed Mean ( 21 / 24 )111.6140.71145449204631156.881432681621
Trimmed Mean ( 22 / 24 )111.5985714285710.699299103805748159.58632124827
Trimmed Mean ( 23 / 24 )111.5646153846150.686249613875577162.571480010833
Trimmed Mean ( 24 / 24 )111.5483333333330.671912602868647166.016134921553
Median112.01
Midrange111.195
Midmean - Weighted Average at Xnp111.403783783784
Midmean - Weighted Average at X(n+1)p111.616111111111
Midmean - Empirical Distribution Function111.403783783784
Midmean - Empirical Distribution Function - Averaging111.616111111111
Midmean - Empirical Distribution Function - Interpolation111.616111111111
Midmean - Closest Observation111.403783783784
Midmean - True Basic - Statistics Graphics Toolkit111.616111111111
Midmean - MS Excel (old versions)111.598947368421
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')