Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 16 Nov 2014 09:14:33 +0000

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/2014/Nov/16/t1416129384du1t1fex334sx60.htm/, Retrieved Sun, 19 May 2024 17:43:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=255040, Retrieved Sun, 19 May 2024 17:43:50 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

114

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

-       [Central Tendency] [] [2014-11-16 09:14:33] [4b199ad8119df16cb977784959786033] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

1,11
1,11
1,2
1,21
1,31
1,37
1,37
1,26
1,23
1,17
1,06
0,95
0,92
0,92
0,9
0,93
0,93
0,97
0,96
0,99
0,98
0,96
1
0,99
1,03
1,02
1,07
1,13
1,15
1,16
1,14
1,15
1,15
1,16
1,17
1,22
1,26
1,29
1,36
1,38
1,37
1,37
1,37
1,36
1,38
1,4
1,44
1,42
1,45
1,45
1,49
1,48
1,44
1,39
1,41
1,48
1,51
1,49
1,46
1,43
1,42
1,43
1,42
1,39
1,36
1,36
1,39
1,39
1,43
1,38
1,36
1,38

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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=255040&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=255040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255040&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	1.24916666666667	0.0219052858756916	57.0258098321772
Geometric Mean	1.2346859908837
Harmonic Mean	1.21946552036284
Quadratic Mean	1.26272962708218
Winsorized Mean ( 1 / 24 )	1.24916666666667	0.0217996550632428	57.3021299209881
Winsorized Mean ( 2 / 24 )	1.24916666666667	0.0217996550632428	57.3021299209881
Winsorized Mean ( 3 / 24 )	1.24916666666667	0.0216483761728985	57.7025573045287
Winsorized Mean ( 4 / 24 )	1.24916666666667	0.0216483761728985	57.7025573045287
Winsorized Mean ( 5 / 24 )	1.24916666666667	0.0211640418320005	59.0230673603139
Winsorized Mean ( 6 / 24 )	1.24916666666667	0.0208849126755366	59.8119171515556
Winsorized Mean ( 7 / 24 )	1.24916666666667	0.0208849126755366	59.8119171515555
Winsorized Mean ( 8 / 24 )	1.24916666666667	0.0205220881804553	60.8693742899096
Winsorized Mean ( 9 / 24 )	1.25041666666667	0.0202849781950976	61.6424949852231
Winsorized Mean ( 10 / 24 )	1.25041666666667	0.0198462768944901	63.0051003175221
Winsorized Mean ( 11 / 24 )	1.25041666666667	0.0198462768944901	63.0051003175221
Winsorized Mean ( 12 / 24 )	1.25208333333333	0.0195408339162085	64.0752251773027
Winsorized Mean ( 13 / 24 )	1.25388888888889	0.018664901362239	67.1789721549579
Winsorized Mean ( 14 / 24 )	1.25583333333333	0.0183245284020643	68.5329142326994
Winsorized Mean ( 15 / 24 )	1.26208333333333	0.0172661408687866	73.0958552304473
Winsorized Mean ( 16 / 24 )	1.26208333333333	0.016619578434002	75.9395515563282
Winsorized Mean ( 17 / 24 )	1.26916666666667	0.0148397148271196	85.5250037788636
Winsorized Mean ( 18 / 24 )	1.26666666666667	0.0145350474933453	87.1456847489901
Winsorized Mean ( 19 / 24 )	1.27194444444444	0.0137502865084518	92.5031230194825
Winsorized Mean ( 20 / 24 )	1.27472222222222	0.0133508866588828	95.4784693175496
Winsorized Mean ( 21 / 24 )	1.27763888888889	0.0129409593695206	98.7282976792333
Winsorized Mean ( 22 / 24 )	1.27458333333333	0.0125736290036878	101.36956744624
Winsorized Mean ( 23 / 24 )	1.27458333333333	0.0125736290036878	101.36956744624
Winsorized Mean ( 24 / 24 )	1.27791666666667	0.0121124386395373	105.504490441363
Trimmed Mean ( 1 / 24 )	1.25042857142857	0.0216450145492177	57.7698189384568
Trimmed Mean ( 2 / 24 )	1.25176470588235	0.0214498017170165	58.3578684034784
Trimmed Mean ( 3 / 24 )	1.25318181818182	0.0212062346144375	59.0949709350397
Trimmed Mean ( 4 / 24 )	1.2546875	0.0209709369350189	59.8298256242822
Trimmed Mean ( 5 / 24 )	1.25629032258065	0.0206763402353937	60.7598012161811
Trimmed Mean ( 6 / 24 )	1.258	0.0204563749681159	61.4967217779674
Trimmed Mean ( 7 / 24 )	1.2598275862069	0.0202487426201166	62.2175712261408
Trimmed Mean ( 8 / 24 )	1.26178571428571	0.0199774339297943	63.1605499845449
Trimmed Mean ( 9 / 24 )	1.26388888888889	0.0197121434665687	64.1172732449118
Trimmed Mean ( 10 / 24 )	1.26596153846154	0.0194208367508823	65.1857360576405
Trimmed Mean ( 11 / 24 )	1.2682	0.0191336651705088	66.2810804254433
Trimmed Mean ( 12 / 24 )	1.270625	0.0187494828533883	67.7685358009955
Trimmed Mean ( 13 / 24 )	1.27304347826087	0.0183125562510023	69.5175190624296
Trimmed Mean ( 14 / 24 )	1.27545454545455	0.0179306113389014	71.1327975018555
Trimmed Mean ( 15 / 24 )	1.27785714285714	0.0174924430814478	73.0519537440953
Trimmed Mean ( 16 / 24 )	1.27975	0.0171549779723196	74.5993379918612
Trimmed Mean ( 17 / 24 )	1.28184210526316	0.0168241480549521	76.1906101323123
Trimmed Mean ( 18 / 24 )	1.28333333333333	0.0167711013731908	76.5205161412231
Trimmed Mean ( 19 / 24 )	1.28529411764706	0.016698198127293	76.9720246369731
Trimmed Mean ( 20 / 24 )	1.286875	0.0167310165657255	76.9155296060278
Trimmed Mean ( 21 / 24 )	1.28833333333333	0.0167954792311909	76.707149322704
Trimmed Mean ( 22 / 24 )	1.28964285714286	0.0168990321163712	76.3145988635348
Trimmed Mean ( 23 / 24 )	1.29153846153846	0.017013047551284	75.9145860049625
Trimmed Mean ( 24 / 24 )	1.29375	0.0170337739952642	75.952046819436
Median	1.335
Midrange	1.205
Midmean - Weighted Average at Xnp	1.27864864864865
Midmean - Weighted Average at X(n+1)p	1.27864864864865
Midmean - Empirical Distribution Function	1.27864864864865
Midmean - Empirical Distribution Function - Averaging	1.27864864864865
Midmean - Empirical Distribution Function - Interpolation	1.27864864864865
Midmean - Closest Observation	1.27864864864865
Midmean - True Basic - Statistics Graphics Toolkit	1.27864864864865
Midmean - MS Excel (old versions)	1.28184210526316
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.24916666666667 & 0.0219052858756916 & 57.0258098321772 \tabularnewline
Geometric Mean & 1.2346859908837 &  &  \tabularnewline
Harmonic Mean & 1.21946552036284 &  &  \tabularnewline
Quadratic Mean & 1.26272962708218 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.24916666666667 & 0.0217996550632428 & 57.3021299209881 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.24916666666667 & 0.0217996550632428 & 57.3021299209881 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.24916666666667 & 0.0216483761728985 & 57.7025573045287 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.24916666666667 & 0.0216483761728985 & 57.7025573045287 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.24916666666667 & 0.0211640418320005 & 59.0230673603139 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.24916666666667 & 0.0208849126755366 & 59.8119171515556 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.24916666666667 & 0.0208849126755366 & 59.8119171515555 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.24916666666667 & 0.0205220881804553 & 60.8693742899096 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.25041666666667 & 0.0202849781950976 & 61.6424949852231 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.25041666666667 & 0.0198462768944901 & 63.0051003175221 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.25041666666667 & 0.0198462768944901 & 63.0051003175221 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.25208333333333 & 0.0195408339162085 & 64.0752251773027 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.25388888888889 & 0.018664901362239 & 67.1789721549579 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.25583333333333 & 0.0183245284020643 & 68.5329142326994 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.26208333333333 & 0.0172661408687866 & 73.0958552304473 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.26208333333333 & 0.016619578434002 & 75.9395515563282 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.26916666666667 & 0.0148397148271196 & 85.5250037788636 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.26666666666667 & 0.0145350474933453 & 87.1456847489901 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.27194444444444 & 0.0137502865084518 & 92.5031230194825 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.27472222222222 & 0.0133508866588828 & 95.4784693175496 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.27763888888889 & 0.0129409593695206 & 98.7282976792333 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.27458333333333 & 0.0125736290036878 & 101.36956744624 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.27458333333333 & 0.0125736290036878 & 101.36956744624 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.27791666666667 & 0.0121124386395373 & 105.504490441363 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.25042857142857 & 0.0216450145492177 & 57.7698189384568 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.25176470588235 & 0.0214498017170165 & 58.3578684034784 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.25318181818182 & 0.0212062346144375 & 59.0949709350397 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.2546875 & 0.0209709369350189 & 59.8298256242822 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.25629032258065 & 0.0206763402353937 & 60.7598012161811 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.258 & 0.0204563749681159 & 61.4967217779674 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.2598275862069 & 0.0202487426201166 & 62.2175712261408 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.26178571428571 & 0.0199774339297943 & 63.1605499845449 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.26388888888889 & 0.0197121434665687 & 64.1172732449118 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.26596153846154 & 0.0194208367508823 & 65.1857360576405 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.2682 & 0.0191336651705088 & 66.2810804254433 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.270625 & 0.0187494828533883 & 67.7685358009955 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.27304347826087 & 0.0183125562510023 & 69.5175190624296 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.27545454545455 & 0.0179306113389014 & 71.1327975018555 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.27785714285714 & 0.0174924430814478 & 73.0519537440953 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.27975 & 0.0171549779723196 & 74.5993379918612 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.28184210526316 & 0.0168241480549521 & 76.1906101323123 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.28333333333333 & 0.0167711013731908 & 76.5205161412231 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.28529411764706 & 0.016698198127293 & 76.9720246369731 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.286875 & 0.0167310165657255 & 76.9155296060278 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.28833333333333 & 0.0167954792311909 & 76.707149322704 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.28964285714286 & 0.0168990321163712 & 76.3145988635348 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.29153846153846 & 0.017013047551284 & 75.9145860049625 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.29375 & 0.0170337739952642 & 75.952046819436 \tabularnewline
Median & 1.335 &  &  \tabularnewline
Midrange & 1.205 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.27864864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.27864864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.27864864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.27864864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.27864864864865 &  &  \tabularnewline
Midmean - Closest Observation & 1.27864864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.27864864864865 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.28184210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255040&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]1.24916666666667[/C][C]0.0219052858756916[/C][C]57.0258098321772[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.2346859908837[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.21946552036284[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.26272962708218[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.24916666666667[/C][C]0.0217996550632428[/C][C]57.3021299209881[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.24916666666667[/C][C]0.0217996550632428[/C][C]57.3021299209881[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.24916666666667[/C][C]0.0216483761728985[/C][C]57.7025573045287[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.24916666666667[/C][C]0.0216483761728985[/C][C]57.7025573045287[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.24916666666667[/C][C]0.0211640418320005[/C][C]59.0230673603139[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.24916666666667[/C][C]0.0208849126755366[/C][C]59.8119171515556[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.24916666666667[/C][C]0.0208849126755366[/C][C]59.8119171515555[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.24916666666667[/C][C]0.0205220881804553[/C][C]60.8693742899096[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.25041666666667[/C][C]0.0202849781950976[/C][C]61.6424949852231[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.25041666666667[/C][C]0.0198462768944901[/C][C]63.0051003175221[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.25041666666667[/C][C]0.0198462768944901[/C][C]63.0051003175221[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.25208333333333[/C][C]0.0195408339162085[/C][C]64.0752251773027[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.25388888888889[/C][C]0.018664901362239[/C][C]67.1789721549579[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.25583333333333[/C][C]0.0183245284020643[/C][C]68.5329142326994[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.26208333333333[/C][C]0.0172661408687866[/C][C]73.0958552304473[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.26208333333333[/C][C]0.016619578434002[/C][C]75.9395515563282[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.26916666666667[/C][C]0.0148397148271196[/C][C]85.5250037788636[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.26666666666667[/C][C]0.0145350474933453[/C][C]87.1456847489901[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.27194444444444[/C][C]0.0137502865084518[/C][C]92.5031230194825[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.27472222222222[/C][C]0.0133508866588828[/C][C]95.4784693175496[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.27763888888889[/C][C]0.0129409593695206[/C][C]98.7282976792333[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.27458333333333[/C][C]0.0125736290036878[/C][C]101.36956744624[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.27458333333333[/C][C]0.0125736290036878[/C][C]101.36956744624[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.27791666666667[/C][C]0.0121124386395373[/C][C]105.504490441363[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.25042857142857[/C][C]0.0216450145492177[/C][C]57.7698189384568[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.25176470588235[/C][C]0.0214498017170165[/C][C]58.3578684034784[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.25318181818182[/C][C]0.0212062346144375[/C][C]59.0949709350397[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.2546875[/C][C]0.0209709369350189[/C][C]59.8298256242822[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.25629032258065[/C][C]0.0206763402353937[/C][C]60.7598012161811[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.258[/C][C]0.0204563749681159[/C][C]61.4967217779674[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.2598275862069[/C][C]0.0202487426201166[/C][C]62.2175712261408[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.26178571428571[/C][C]0.0199774339297943[/C][C]63.1605499845449[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.26388888888889[/C][C]0.0197121434665687[/C][C]64.1172732449118[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.26596153846154[/C][C]0.0194208367508823[/C][C]65.1857360576405[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.2682[/C][C]0.0191336651705088[/C][C]66.2810804254433[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.270625[/C][C]0.0187494828533883[/C][C]67.7685358009955[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.27304347826087[/C][C]0.0183125562510023[/C][C]69.5175190624296[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.27545454545455[/C][C]0.0179306113389014[/C][C]71.1327975018555[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.27785714285714[/C][C]0.0174924430814478[/C][C]73.0519537440953[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.27975[/C][C]0.0171549779723196[/C][C]74.5993379918612[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.28184210526316[/C][C]0.0168241480549521[/C][C]76.1906101323123[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.28333333333333[/C][C]0.0167711013731908[/C][C]76.5205161412231[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.28529411764706[/C][C]0.016698198127293[/C][C]76.9720246369731[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.286875[/C][C]0.0167310165657255[/C][C]76.9155296060278[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.28833333333333[/C][C]0.0167954792311909[/C][C]76.707149322704[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.28964285714286[/C][C]0.0168990321163712[/C][C]76.3145988635348[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.29153846153846[/C][C]0.017013047551284[/C][C]75.9145860049625[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.29375[/C][C]0.0170337739952642[/C][C]75.952046819436[/C][/ROW]
[ROW][C]Median[/C][C]1.335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.27864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.27864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.27864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.27864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.27864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.27864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.27864864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.28184210526316[/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=255040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255040&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	1.24916666666667	0.0219052858756916	57.0258098321772
Geometric Mean	1.2346859908837
Harmonic Mean	1.21946552036284
Quadratic Mean	1.26272962708218
Winsorized Mean ( 1 / 24 )	1.24916666666667	0.0217996550632428	57.3021299209881
Winsorized Mean ( 2 / 24 )	1.24916666666667	0.0217996550632428	57.3021299209881
Winsorized Mean ( 3 / 24 )	1.24916666666667	0.0216483761728985	57.7025573045287
Winsorized Mean ( 4 / 24 )	1.24916666666667	0.0216483761728985	57.7025573045287
Winsorized Mean ( 5 / 24 )	1.24916666666667	0.0211640418320005	59.0230673603139
Winsorized Mean ( 6 / 24 )	1.24916666666667	0.0208849126755366	59.8119171515556
Winsorized Mean ( 7 / 24 )	1.24916666666667	0.0208849126755366	59.8119171515555
Winsorized Mean ( 8 / 24 )	1.24916666666667	0.0205220881804553	60.8693742899096
Winsorized Mean ( 9 / 24 )	1.25041666666667	0.0202849781950976	61.6424949852231
Winsorized Mean ( 10 / 24 )	1.25041666666667	0.0198462768944901	63.0051003175221
Winsorized Mean ( 11 / 24 )	1.25041666666667	0.0198462768944901	63.0051003175221
Winsorized Mean ( 12 / 24 )	1.25208333333333	0.0195408339162085	64.0752251773027
Winsorized Mean ( 13 / 24 )	1.25388888888889	0.018664901362239	67.1789721549579
Winsorized Mean ( 14 / 24 )	1.25583333333333	0.0183245284020643	68.5329142326994
Winsorized Mean ( 15 / 24 )	1.26208333333333	0.0172661408687866	73.0958552304473
Winsorized Mean ( 16 / 24 )	1.26208333333333	0.016619578434002	75.9395515563282
Winsorized Mean ( 17 / 24 )	1.26916666666667	0.0148397148271196	85.5250037788636
Winsorized Mean ( 18 / 24 )	1.26666666666667	0.0145350474933453	87.1456847489901
Winsorized Mean ( 19 / 24 )	1.27194444444444	0.0137502865084518	92.5031230194825
Winsorized Mean ( 20 / 24 )	1.27472222222222	0.0133508866588828	95.4784693175496
Winsorized Mean ( 21 / 24 )	1.27763888888889	0.0129409593695206	98.7282976792333
Winsorized Mean ( 22 / 24 )	1.27458333333333	0.0125736290036878	101.36956744624
Winsorized Mean ( 23 / 24 )	1.27458333333333	0.0125736290036878	101.36956744624
Winsorized Mean ( 24 / 24 )	1.27791666666667	0.0121124386395373	105.504490441363
Trimmed Mean ( 1 / 24 )	1.25042857142857	0.0216450145492177	57.7698189384568
Trimmed Mean ( 2 / 24 )	1.25176470588235	0.0214498017170165	58.3578684034784
Trimmed Mean ( 3 / 24 )	1.25318181818182	0.0212062346144375	59.0949709350397
Trimmed Mean ( 4 / 24 )	1.2546875	0.0209709369350189	59.8298256242822
Trimmed Mean ( 5 / 24 )	1.25629032258065	0.0206763402353937	60.7598012161811
Trimmed Mean ( 6 / 24 )	1.258	0.0204563749681159	61.4967217779674
Trimmed Mean ( 7 / 24 )	1.2598275862069	0.0202487426201166	62.2175712261408
Trimmed Mean ( 8 / 24 )	1.26178571428571	0.0199774339297943	63.1605499845449
Trimmed Mean ( 9 / 24 )	1.26388888888889	0.0197121434665687	64.1172732449118
Trimmed Mean ( 10 / 24 )	1.26596153846154	0.0194208367508823	65.1857360576405
Trimmed Mean ( 11 / 24 )	1.2682	0.0191336651705088	66.2810804254433
Trimmed Mean ( 12 / 24 )	1.270625	0.0187494828533883	67.7685358009955
Trimmed Mean ( 13 / 24 )	1.27304347826087	0.0183125562510023	69.5175190624296
Trimmed Mean ( 14 / 24 )	1.27545454545455	0.0179306113389014	71.1327975018555
Trimmed Mean ( 15 / 24 )	1.27785714285714	0.0174924430814478	73.0519537440953
Trimmed Mean ( 16 / 24 )	1.27975	0.0171549779723196	74.5993379918612
Trimmed Mean ( 17 / 24 )	1.28184210526316	0.0168241480549521	76.1906101323123
Trimmed Mean ( 18 / 24 )	1.28333333333333	0.0167711013731908	76.5205161412231
Trimmed Mean ( 19 / 24 )	1.28529411764706	0.016698198127293	76.9720246369731
Trimmed Mean ( 20 / 24 )	1.286875	0.0167310165657255	76.9155296060278
Trimmed Mean ( 21 / 24 )	1.28833333333333	0.0167954792311909	76.707149322704
Trimmed Mean ( 22 / 24 )	1.28964285714286	0.0168990321163712	76.3145988635348
Trimmed Mean ( 23 / 24 )	1.29153846153846	0.017013047551284	75.9145860049625
Trimmed Mean ( 24 / 24 )	1.29375	0.0170337739952642	75.952046819436
Median	1.335
Midrange	1.205
Midmean - Weighted Average at Xnp	1.27864864864865
Midmean - Weighted Average at X(n+1)p	1.27864864864865
Midmean - Empirical Distribution Function	1.27864864864865
Midmean - Empirical Distribution Function - Averaging	1.27864864864865
Midmean - Empirical Distribution Function - Interpolation	1.27864864864865
Midmean - Closest Observation	1.27864864864865
Midmean - True Basic - Statistics Graphics Toolkit	1.27864864864865
Midmean - MS Excel (old versions)	1.28184210526316
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