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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 22 Oct 2012 10:21:37 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/22/t1350915795396c09a6819b9p1.htm/, Retrieved Sat, 04 May 2024 00:41:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=181533, Retrieved Sat, 04 May 2024 00:41:47 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [centrum maten tom...] [2012-10-22 14:21:37] [81048bae71988e8f0b979655b8024c85] [Current]

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2,08
2,09
2,36
2,99
2,75
1,58
1,69
1,3
1,97
1,84
1,96
1,86
2,75
2,62
2,41
3,61
2,03
1,45
1,4
1,3
1,58
2,1
2,27
2,54
2,55
2,05
2,32
2,6
2,1
1,61
1,55
1,12
1,39
2,18
1,94
2,27
2,41
2,2
2,58
2,9
2,12
1,34
1,07
0,86
1
1,54
1,29
1,44
2,6
2,77
3,31
3,2
2,07
1,42
1,43
1,28
1,59
1,68
2,01
2,52
2,74
3,06
2,69
2,32
1,67
1,04
0,98
0,86
0,97
1,3
1,82
1,99

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181533&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=181533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181533&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.97611111111111	0.0756959250260793	26.1059113873077
Geometric Mean	1.86857525069832
Harmonic Mean	1.75788372361889
Quadratic Mean	2.07649611391669
Winsorized Mean ( 1 / 24 )	1.97194444444444	0.0745349795754749	26.4566309090839
Winsorized Mean ( 2 / 24 )	1.97194444444444	0.0731714065028973	26.9496588720946
Winsorized Mean ( 3 / 24 )	1.96652777777778	0.0717749917547992	27.3985092815603
Winsorized Mean ( 4 / 24 )	1.96375	0.0707462008966881	27.7576742653319
Winsorized Mean ( 5 / 24 )	1.96027777777778	0.0689800985741864	28.4180193751035
Winsorized Mean ( 6 / 24 )	1.95194444444444	0.0665326231324141	29.3381555174769
Winsorized Mean ( 7 / 24 )	1.95486111111111	0.0653059469571021	29.9338912028213
Winsorized Mean ( 8 / 24 )	1.97263888888889	0.0623088604815182	31.6590429297612
Winsorized Mean ( 9 / 24 )	1.97263888888889	0.0618949565296	31.8707532809319
Winsorized Mean ( 10 / 24 )	1.96708333333333	0.0604881801138853	32.5201275626043
Winsorized Mean ( 11 / 24 )	1.95638888888889	0.0587364693424114	33.3079075196686
Winsorized Mean ( 12 / 24 )	1.95305555555556	0.0582103461677883	33.5516911362453
Winsorized Mean ( 13 / 24 )	1.96027777777778	0.0570869433498231	34.3384609991359
Winsorized Mean ( 14 / 24 )	1.96611111111111	0.0550130001550052	35.7390272403137
Winsorized Mean ( 15 / 24 )	1.96194444444444	0.0537329653790193	36.5128637625965
Winsorized Mean ( 16 / 24 )	1.96416666666667	0.0527405251115817	37.2420764205728
Winsorized Mean ( 17 / 24 )	1.96180555555556	0.0516754976509009	37.9639412243058
Winsorized Mean ( 18 / 24 )	1.93680555555556	0.0472721561225974	40.9713817692718
Winsorized Mean ( 19 / 24 )	1.93944444444444	0.0468828363878041	41.3678990836178
Winsorized Mean ( 20 / 24 )	1.95055555555556	0.041339508516116	47.1838109733487
Winsorized Mean ( 21 / 24 )	1.94180555555556	0.0393264528023966	49.3765752358224
Winsorized Mean ( 22 / 24 )	1.95097222222222	0.0380537671066907	51.2688327742247
Winsorized Mean ( 23 / 24 )	1.935	0.0359125393857497	53.8809015763397
Winsorized Mean ( 24 / 24 )	1.93833333333333	0.0354498256814483	54.6782190341688
Trimmed Mean ( 1 / 24 )	1.96871428571429	0.0724775745794385	27.1630817827174
Trimmed Mean ( 2 / 24 )	1.96529411764706	0.0700289889141163	28.0640081789172
Trimmed Mean ( 3 / 24 )	1.96166666666667	0.0679827838254576	28.8553447841022
Trimmed Mean ( 4 / 24 )	1.95984375	0.0661750819988503	29.6160381037994
Trimmed Mean ( 5 / 24 )	1.95870967741935	0.0643769651919671	30.4256292849257
Trimmed Mean ( 6 / 24 )	1.95833333333333	0.0627613931254184	31.2028340323792
Trimmed Mean ( 7 / 24 )	1.95965517241379	0.061480014860915	31.8746697906154
Trimmed Mean ( 8 / 24 )	1.96053571428571	0.0602114346277	32.5608537050831
Trimmed Mean ( 9 / 24 )	1.95851851851852	0.0593456088209714	33.0019113027689
Trimmed Mean ( 10 / 24 )	1.95634615384615	0.0583257022671722	33.5417505113737
Trimmed Mean ( 11 / 24 )	1.9548	0.0573305773740403	34.0969878472766
Trimmed Mean ( 12 / 24 )	1.95458333333333	0.0564202178921496	34.643314158581
Trimmed Mean ( 13 / 24 )	1.95478260869565	0.055326644549832	35.3316674922334
Trimmed Mean ( 14 / 24 )	1.95409090909091	0.0541221683797755	36.1051851318861
Trimmed Mean ( 15 / 24 )	1.95261904761905	0.0529721285422887	36.8612532921012
Trimmed Mean ( 16 / 24 )	1.9515	0.0517000099191579	37.7466078449794
Trimmed Mean ( 17 / 24 )	1.95	0.0501831637989898	38.8576536906039
Trimmed Mean ( 18 / 24 )	1.94861111111111	0.0483491809450787	40.3028773812031
Trimmed Mean ( 19 / 24 )	1.95	0.0469554345547414	41.5287392927151
Trimmed Mean ( 20 / 24 )	1.95125	0.0450375067707908	43.325000425323
Trimmed Mean ( 21 / 24 )	1.95133333333333	0.043890494175017	44.4591333502017
Trimmed Mean ( 22 / 24 )	1.9525	0.0427080187754579	45.717409891231
Trimmed Mean ( 23 / 24 )	1.95269230769231	0.0412331371306276	47.3573548747002
Trimmed Mean ( 24 / 24 )	1.955	0.0395948686471922	49.3750848732424
Median	2
Midrange	2.235
Midmean - Weighted Average at Xnp	1.93459459459459
Midmean - Weighted Average at X(n+1)p	1.94861111111111
Midmean - Empirical Distribution Function	1.93459459459459
Midmean - Empirical Distribution Function - Averaging	1.94861111111111
Midmean - Empirical Distribution Function - Interpolation	1.94861111111111
Midmean - Closest Observation	1.93459459459459
Midmean - True Basic - Statistics Graphics Toolkit	1.94861111111111
Midmean - MS Excel (old versions)	1.95
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.97611111111111 & 0.0756959250260793 & 26.1059113873077 \tabularnewline
Geometric Mean & 1.86857525069832 &  &  \tabularnewline
Harmonic Mean & 1.75788372361889 &  &  \tabularnewline
Quadratic Mean & 2.07649611391669 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.97194444444444 & 0.0745349795754749 & 26.4566309090839 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.97194444444444 & 0.0731714065028973 & 26.9496588720946 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.96652777777778 & 0.0717749917547992 & 27.3985092815603 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.96375 & 0.0707462008966881 & 27.7576742653319 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.96027777777778 & 0.0689800985741864 & 28.4180193751035 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.95194444444444 & 0.0665326231324141 & 29.3381555174769 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.95486111111111 & 0.0653059469571021 & 29.9338912028213 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.97263888888889 & 0.0623088604815182 & 31.6590429297612 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.97263888888889 & 0.0618949565296 & 31.8707532809319 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.96708333333333 & 0.0604881801138853 & 32.5201275626043 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.95638888888889 & 0.0587364693424114 & 33.3079075196686 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.95305555555556 & 0.0582103461677883 & 33.5516911362453 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.96027777777778 & 0.0570869433498231 & 34.3384609991359 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.96611111111111 & 0.0550130001550052 & 35.7390272403137 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.96194444444444 & 0.0537329653790193 & 36.5128637625965 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.96416666666667 & 0.0527405251115817 & 37.2420764205728 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.96180555555556 & 0.0516754976509009 & 37.9639412243058 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.93680555555556 & 0.0472721561225974 & 40.9713817692718 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.93944444444444 & 0.0468828363878041 & 41.3678990836178 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.95055555555556 & 0.041339508516116 & 47.1838109733487 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.94180555555556 & 0.0393264528023966 & 49.3765752358224 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.95097222222222 & 0.0380537671066907 & 51.2688327742247 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.935 & 0.0359125393857497 & 53.8809015763397 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.93833333333333 & 0.0354498256814483 & 54.6782190341688 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.96871428571429 & 0.0724775745794385 & 27.1630817827174 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.96529411764706 & 0.0700289889141163 & 28.0640081789172 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.96166666666667 & 0.0679827838254576 & 28.8553447841022 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.95984375 & 0.0661750819988503 & 29.6160381037994 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.95870967741935 & 0.0643769651919671 & 30.4256292849257 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.95833333333333 & 0.0627613931254184 & 31.2028340323792 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.95965517241379 & 0.061480014860915 & 31.8746697906154 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.96053571428571 & 0.0602114346277 & 32.5608537050831 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.95851851851852 & 0.0593456088209714 & 33.0019113027689 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.95634615384615 & 0.0583257022671722 & 33.5417505113737 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.9548 & 0.0573305773740403 & 34.0969878472766 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.95458333333333 & 0.0564202178921496 & 34.643314158581 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.95478260869565 & 0.055326644549832 & 35.3316674922334 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.95409090909091 & 0.0541221683797755 & 36.1051851318861 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.95261904761905 & 0.0529721285422887 & 36.8612532921012 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.9515 & 0.0517000099191579 & 37.7466078449794 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.95 & 0.0501831637989898 & 38.8576536906039 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.94861111111111 & 0.0483491809450787 & 40.3028773812031 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.95 & 0.0469554345547414 & 41.5287392927151 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.95125 & 0.0450375067707908 & 43.325000425323 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.95133333333333 & 0.043890494175017 & 44.4591333502017 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.9525 & 0.0427080187754579 & 45.717409891231 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.95269230769231 & 0.0412331371306276 & 47.3573548747002 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.955 & 0.0395948686471922 & 49.3750848732424 \tabularnewline
Median & 2 &  &  \tabularnewline
Midrange & 2.235 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.93459459459459 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.94861111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.93459459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.94861111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.94861111111111 &  &  \tabularnewline
Midmean - Closest Observation & 1.93459459459459 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.94861111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.95 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181533&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.97611111111111[/C][C]0.0756959250260793[/C][C]26.1059113873077[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.86857525069832[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.75788372361889[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.07649611391669[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.97194444444444[/C][C]0.0745349795754749[/C][C]26.4566309090839[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.97194444444444[/C][C]0.0731714065028973[/C][C]26.9496588720946[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.96652777777778[/C][C]0.0717749917547992[/C][C]27.3985092815603[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.96375[/C][C]0.0707462008966881[/C][C]27.7576742653319[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.96027777777778[/C][C]0.0689800985741864[/C][C]28.4180193751035[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.95194444444444[/C][C]0.0665326231324141[/C][C]29.3381555174769[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.95486111111111[/C][C]0.0653059469571021[/C][C]29.9338912028213[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.97263888888889[/C][C]0.0623088604815182[/C][C]31.6590429297612[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.97263888888889[/C][C]0.0618949565296[/C][C]31.8707532809319[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.96708333333333[/C][C]0.0604881801138853[/C][C]32.5201275626043[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.95638888888889[/C][C]0.0587364693424114[/C][C]33.3079075196686[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.95305555555556[/C][C]0.0582103461677883[/C][C]33.5516911362453[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.96027777777778[/C][C]0.0570869433498231[/C][C]34.3384609991359[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.96611111111111[/C][C]0.0550130001550052[/C][C]35.7390272403137[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.96194444444444[/C][C]0.0537329653790193[/C][C]36.5128637625965[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.96416666666667[/C][C]0.0527405251115817[/C][C]37.2420764205728[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.96180555555556[/C][C]0.0516754976509009[/C][C]37.9639412243058[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.93680555555556[/C][C]0.0472721561225974[/C][C]40.9713817692718[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.93944444444444[/C][C]0.0468828363878041[/C][C]41.3678990836178[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.95055555555556[/C][C]0.041339508516116[/C][C]47.1838109733487[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.94180555555556[/C][C]0.0393264528023966[/C][C]49.3765752358224[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.95097222222222[/C][C]0.0380537671066907[/C][C]51.2688327742247[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.935[/C][C]0.0359125393857497[/C][C]53.8809015763397[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.93833333333333[/C][C]0.0354498256814483[/C][C]54.6782190341688[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.96871428571429[/C][C]0.0724775745794385[/C][C]27.1630817827174[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.96529411764706[/C][C]0.0700289889141163[/C][C]28.0640081789172[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.96166666666667[/C][C]0.0679827838254576[/C][C]28.8553447841022[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.95984375[/C][C]0.0661750819988503[/C][C]29.6160381037994[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.95870967741935[/C][C]0.0643769651919671[/C][C]30.4256292849257[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.95833333333333[/C][C]0.0627613931254184[/C][C]31.2028340323792[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.95965517241379[/C][C]0.061480014860915[/C][C]31.8746697906154[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.96053571428571[/C][C]0.0602114346277[/C][C]32.5608537050831[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.95851851851852[/C][C]0.0593456088209714[/C][C]33.0019113027689[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.95634615384615[/C][C]0.0583257022671722[/C][C]33.5417505113737[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.9548[/C][C]0.0573305773740403[/C][C]34.0969878472766[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.95458333333333[/C][C]0.0564202178921496[/C][C]34.643314158581[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.95478260869565[/C][C]0.055326644549832[/C][C]35.3316674922334[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.95409090909091[/C][C]0.0541221683797755[/C][C]36.1051851318861[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.95261904761905[/C][C]0.0529721285422887[/C][C]36.8612532921012[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.9515[/C][C]0.0517000099191579[/C][C]37.7466078449794[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.95[/C][C]0.0501831637989898[/C][C]38.8576536906039[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.94861111111111[/C][C]0.0483491809450787[/C][C]40.3028773812031[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.95[/C][C]0.0469554345547414[/C][C]41.5287392927151[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.95125[/C][C]0.0450375067707908[/C][C]43.325000425323[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.95133333333333[/C][C]0.043890494175017[/C][C]44.4591333502017[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.9525[/C][C]0.0427080187754579[/C][C]45.717409891231[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.95269230769231[/C][C]0.0412331371306276[/C][C]47.3573548747002[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.955[/C][C]0.0395948686471922[/C][C]49.3750848732424[/C][/ROW]
[ROW][C]Median[/C][C]2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.93459459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.94861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.93459459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.94861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.94861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.93459459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.94861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.95[/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=181533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181533&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.97611111111111	0.0756959250260793	26.1059113873077
Geometric Mean	1.86857525069832
Harmonic Mean	1.75788372361889
Quadratic Mean	2.07649611391669
Winsorized Mean ( 1 / 24 )	1.97194444444444	0.0745349795754749	26.4566309090839
Winsorized Mean ( 2 / 24 )	1.97194444444444	0.0731714065028973	26.9496588720946
Winsorized Mean ( 3 / 24 )	1.96652777777778	0.0717749917547992	27.3985092815603
Winsorized Mean ( 4 / 24 )	1.96375	0.0707462008966881	27.7576742653319
Winsorized Mean ( 5 / 24 )	1.96027777777778	0.0689800985741864	28.4180193751035
Winsorized Mean ( 6 / 24 )	1.95194444444444	0.0665326231324141	29.3381555174769
Winsorized Mean ( 7 / 24 )	1.95486111111111	0.0653059469571021	29.9338912028213
Winsorized Mean ( 8 / 24 )	1.97263888888889	0.0623088604815182	31.6590429297612
Winsorized Mean ( 9 / 24 )	1.97263888888889	0.0618949565296	31.8707532809319
Winsorized Mean ( 10 / 24 )	1.96708333333333	0.0604881801138853	32.5201275626043
Winsorized Mean ( 11 / 24 )	1.95638888888889	0.0587364693424114	33.3079075196686
Winsorized Mean ( 12 / 24 )	1.95305555555556	0.0582103461677883	33.5516911362453
Winsorized Mean ( 13 / 24 )	1.96027777777778	0.0570869433498231	34.3384609991359
Winsorized Mean ( 14 / 24 )	1.96611111111111	0.0550130001550052	35.7390272403137
Winsorized Mean ( 15 / 24 )	1.96194444444444	0.0537329653790193	36.5128637625965
Winsorized Mean ( 16 / 24 )	1.96416666666667	0.0527405251115817	37.2420764205728
Winsorized Mean ( 17 / 24 )	1.96180555555556	0.0516754976509009	37.9639412243058
Winsorized Mean ( 18 / 24 )	1.93680555555556	0.0472721561225974	40.9713817692718
Winsorized Mean ( 19 / 24 )	1.93944444444444	0.0468828363878041	41.3678990836178
Winsorized Mean ( 20 / 24 )	1.95055555555556	0.041339508516116	47.1838109733487
Winsorized Mean ( 21 / 24 )	1.94180555555556	0.0393264528023966	49.3765752358224
Winsorized Mean ( 22 / 24 )	1.95097222222222	0.0380537671066907	51.2688327742247
Winsorized Mean ( 23 / 24 )	1.935	0.0359125393857497	53.8809015763397
Winsorized Mean ( 24 / 24 )	1.93833333333333	0.0354498256814483	54.6782190341688
Trimmed Mean ( 1 / 24 )	1.96871428571429	0.0724775745794385	27.1630817827174
Trimmed Mean ( 2 / 24 )	1.96529411764706	0.0700289889141163	28.0640081789172
Trimmed Mean ( 3 / 24 )	1.96166666666667	0.0679827838254576	28.8553447841022
Trimmed Mean ( 4 / 24 )	1.95984375	0.0661750819988503	29.6160381037994
Trimmed Mean ( 5 / 24 )	1.95870967741935	0.0643769651919671	30.4256292849257
Trimmed Mean ( 6 / 24 )	1.95833333333333	0.0627613931254184	31.2028340323792
Trimmed Mean ( 7 / 24 )	1.95965517241379	0.061480014860915	31.8746697906154
Trimmed Mean ( 8 / 24 )	1.96053571428571	0.0602114346277	32.5608537050831
Trimmed Mean ( 9 / 24 )	1.95851851851852	0.0593456088209714	33.0019113027689
Trimmed Mean ( 10 / 24 )	1.95634615384615	0.0583257022671722	33.5417505113737
Trimmed Mean ( 11 / 24 )	1.9548	0.0573305773740403	34.0969878472766
Trimmed Mean ( 12 / 24 )	1.95458333333333	0.0564202178921496	34.643314158581
Trimmed Mean ( 13 / 24 )	1.95478260869565	0.055326644549832	35.3316674922334
Trimmed Mean ( 14 / 24 )	1.95409090909091	0.0541221683797755	36.1051851318861
Trimmed Mean ( 15 / 24 )	1.95261904761905	0.0529721285422887	36.8612532921012
Trimmed Mean ( 16 / 24 )	1.9515	0.0517000099191579	37.7466078449794
Trimmed Mean ( 17 / 24 )	1.95	0.0501831637989898	38.8576536906039
Trimmed Mean ( 18 / 24 )	1.94861111111111	0.0483491809450787	40.3028773812031
Trimmed Mean ( 19 / 24 )	1.95	0.0469554345547414	41.5287392927151
Trimmed Mean ( 20 / 24 )	1.95125	0.0450375067707908	43.325000425323
Trimmed Mean ( 21 / 24 )	1.95133333333333	0.043890494175017	44.4591333502017
Trimmed Mean ( 22 / 24 )	1.9525	0.0427080187754579	45.717409891231
Trimmed Mean ( 23 / 24 )	1.95269230769231	0.0412331371306276	47.3573548747002
Trimmed Mean ( 24 / 24 )	1.955	0.0395948686471922	49.3750848732424
Median	2
Midrange	2.235
Midmean - Weighted Average at Xnp	1.93459459459459
Midmean - Weighted Average at X(n+1)p	1.94861111111111
Midmean - Empirical Distribution Function	1.93459459459459
Midmean - Empirical Distribution Function - Averaging	1.94861111111111
Midmean - Empirical Distribution Function - Interpolation	1.94861111111111
Midmean - Closest Observation	1.93459459459459
Midmean - True Basic - Statistics Graphics Toolkit	1.94861111111111
Midmean - MS Excel (old versions)	1.95
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code