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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 14 Jan 2013 14:41:21 -0500

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/2013/Jan/14/t13581925031oct6bulhp0t5l1.htm/, Retrieved Sun, 28 Apr 2024 16:43:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205361, Retrieved Sun, 28 Apr 2024 16:43:12 +0000

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No (this computation is public)

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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] [] [2013-01-14 19:41:21] [bdb7c0ed7ba273e65f9ee772c5dda4f0] [Current]

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0,51
0,50
0,47
0,47
0,44
0,43
0,45
0,46
0,46
0,45
0,45
0,45
0,44
0,43
0,45
0,45
0,44
0,47
0,46
0,48
0,49
0,52
0,56
0,58
0,58
0,55
0,55
0,53
0,56
0,57
0,61
0,57
0,59
0,53
0,43
0,38
0,40
0,45
0,40
0,37
0,37
0,40
0,41
0,43
0,45
0,44
0,47
0,47
0,52
0,55
0,54
0,54
0,53
0,52
0,50
0,50
0,53
0,54
0,59
0,66
0,67
0,61
0,62
0,65
0,63
0,58
0,60
0,60
0,61
0,61
0,59
0,60

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205361&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205361&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.509861111111111	0.00892827675445872	57.1063291532142
Geometric Mean	0.504299938085146
Harmonic Mean	0.498754547389725
Quadratic Mean	0.515381466057478
Winsorized Mean ( 1 / 24 )	0.509722222222222	0.008894205667351	57.3094710518466
Winsorized Mean ( 2 / 24 )	0.509722222222222	0.0087701750914936	58.1199596250494
Winsorized Mean ( 3 / 24 )	0.509722222222222	0.00842896355043227	60.4727045232129
Winsorized Mean ( 4 / 24 )	0.509166666666667	0.00832100026339451	61.1905600948695
Winsorized Mean ( 5 / 24 )	0.508472222222222	0.00819524014067378	62.0448227866594
Winsorized Mean ( 6 / 24 )	0.509305555555556	0.0080450764229661	63.30649067567
Winsorized Mean ( 7 / 24 )	0.51125	0.00773165327994696	66.1242791792013
Winsorized Mean ( 8 / 24 )	0.51125	0.00773165327994696	66.1242791792013
Winsorized Mean ( 9 / 24 )	0.51	0.00751368079312882	67.8761866575953
Winsorized Mean ( 10 / 24 )	0.51	0.00751368079312882	67.8761866575953
Winsorized Mean ( 11 / 24 )	0.511527777777778	0.00729347823833567	70.1349563352513
Winsorized Mean ( 12 / 24 )	0.509861111111111	0.00701689514742797	72.6619253100853
Winsorized Mean ( 13 / 24 )	0.509861111111111	0.00701689514742797	72.6619253100853
Winsorized Mean ( 14 / 24 )	0.509861111111111	0.00701689514742797	72.6619253100853
Winsorized Mean ( 15 / 24 )	0.509861111111111	0.00640475253766168	79.6066839605418
Winsorized Mean ( 16 / 24 )	0.509861111111111	0.00640475253766168	79.6066839605418
Winsorized Mean ( 17 / 24 )	0.509861111111111	0.00640475253766168	79.6066839605418
Winsorized Mean ( 18 / 24 )	0.507361111111111	0.00602872965086916	84.1572172734541
Winsorized Mean ( 19 / 24 )	0.507361111111111	0.00602872965086916	84.1572172734541
Winsorized Mean ( 20 / 24 )	0.504583333333333	0.00563265650016281	89.5817689785892
Winsorized Mean ( 21 / 24 )	0.504583333333333	0.00563265650016281	89.5817689785892
Winsorized Mean ( 22 / 24 )	0.501527777777778	0.00522071428799985	96.0649731264881
Winsorized Mean ( 23 / 24 )	0.504722222222222	0.00478804352599433	105.413039685642
Winsorized Mean ( 24 / 24 )	0.504722222222222	0.00478804352599433	105.413039685642
Trimmed Mean ( 1 / 24 )	0.509571428571429	0.00866069801069953	58.8372239676176
Trimmed Mean ( 2 / 24 )	0.509411764705882	0.00838306529326843	60.7667657217149
Trimmed Mean ( 3 / 24 )	0.509242424242424	0.00813152547657892	62.6256937531815
Trimmed Mean ( 4 / 24 )	0.5090625	0.007985970926996	63.7445972009678
Trimmed Mean ( 5 / 24 )	0.509032258064516	0.0078480737865168	64.8607890179431
Trimmed Mean ( 6 / 24 )	0.509166666666667	0.00771780415284163	65.9729965393324
Trimmed Mean ( 7 / 24 )	0.509137931034483	0.0075980562466383	67.0089710456865
Trimmed Mean ( 8 / 24 )	0.50875	0.00752512026913424	67.6068928873785
Trimmed Mean ( 9 / 24 )	0.508333333333333	0.00742890834815473	68.4263837310092
Trimmed Mean ( 10 / 24 )	0.508076923076923	0.00735359087511378	69.092356605855
Trimmed Mean ( 11 / 24 )	0.5078	0.0072522480680694	70.0196677270004
Trimmed Mean ( 12 / 24 )	0.507291666666667	0.00716286958209615	70.8224072562567
Trimmed Mean ( 13 / 24 )	0.50695652173913	0.00710085770975878	71.3937023470298
Trimmed Mean ( 14 / 24 )	0.506590909090909	0.00701058684332182	72.2608421252894
Trimmed Mean ( 15 / 24 )	0.506190476190476	0.00688340242280879	73.5378298547775
Trimmed Mean ( 16 / 24 )	0.50575	0.00683962343392885	73.9441293640759
Trimmed Mean ( 17 / 24 )	0.505263157894737	0.00676507685690549	74.6869797020837
Trimmed Mean ( 18 / 24 )	0.504722222222222	0.00664861975306238	75.9138348962948
Trimmed Mean ( 19 / 24 )	0.504411764705882	0.00657048953307169	76.7692821314138
Trimmed Mean ( 20 / 24 )	0.5040625	0.0064423525400276	78.241992636721
Trimmed Mean ( 21 / 24 )	0.504	0.0063535671942582	79.3255166098615
Trimmed Mean ( 22 / 24 )	0.503928571428571	0.0062007698300502	81.268711021401
Trimmed Mean ( 23 / 24 )	0.504230769230769	0.00608081666891437	82.9215542393242
Trimmed Mean ( 24 / 24 )	0.504166666666667	0.00601678409295664	83.7933784688823
Median	0.505
Midrange	0.52
Midmean - Weighted Average at Xnp	0.50051282051282
Midmean - Weighted Average at X(n+1)p	0.50051282051282
Midmean - Empirical Distribution Function	0.50051282051282
Midmean - Empirical Distribution Function - Averaging	0.50051282051282
Midmean - Empirical Distribution Function - Interpolation	0.50051282051282
Midmean - Closest Observation	0.50051282051282
Midmean - True Basic - Statistics Graphics Toolkit	0.50051282051282
Midmean - MS Excel (old versions)	0.506190476190476
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.509861111111111 & 0.00892827675445872 & 57.1063291532142 \tabularnewline
Geometric Mean & 0.504299938085146 &  &  \tabularnewline
Harmonic Mean & 0.498754547389725 &  &  \tabularnewline
Quadratic Mean & 0.515381466057478 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.509722222222222 & 0.008894205667351 & 57.3094710518466 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.509722222222222 & 0.0087701750914936 & 58.1199596250494 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.509722222222222 & 0.00842896355043227 & 60.4727045232129 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.509166666666667 & 0.00832100026339451 & 61.1905600948695 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.508472222222222 & 0.00819524014067378 & 62.0448227866594 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.509305555555556 & 0.0080450764229661 & 63.30649067567 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.51125 & 0.00773165327994696 & 66.1242791792013 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.51125 & 0.00773165327994696 & 66.1242791792013 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.51 & 0.00751368079312882 & 67.8761866575953 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.51 & 0.00751368079312882 & 67.8761866575953 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.511527777777778 & 0.00729347823833567 & 70.1349563352513 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.509861111111111 & 0.00701689514742797 & 72.6619253100853 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.509861111111111 & 0.00701689514742797 & 72.6619253100853 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.509861111111111 & 0.00701689514742797 & 72.6619253100853 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.509861111111111 & 0.00640475253766168 & 79.6066839605418 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.509861111111111 & 0.00640475253766168 & 79.6066839605418 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.509861111111111 & 0.00640475253766168 & 79.6066839605418 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.507361111111111 & 0.00602872965086916 & 84.1572172734541 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.507361111111111 & 0.00602872965086916 & 84.1572172734541 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.504583333333333 & 0.00563265650016281 & 89.5817689785892 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.504583333333333 & 0.00563265650016281 & 89.5817689785892 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.501527777777778 & 0.00522071428799985 & 96.0649731264881 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.504722222222222 & 0.00478804352599433 & 105.413039685642 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.504722222222222 & 0.00478804352599433 & 105.413039685642 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.509571428571429 & 0.00866069801069953 & 58.8372239676176 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.509411764705882 & 0.00838306529326843 & 60.7667657217149 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.509242424242424 & 0.00813152547657892 & 62.6256937531815 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.5090625 & 0.007985970926996 & 63.7445972009678 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.509032258064516 & 0.0078480737865168 & 64.8607890179431 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.509166666666667 & 0.00771780415284163 & 65.9729965393324 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.509137931034483 & 0.0075980562466383 & 67.0089710456865 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.50875 & 0.00752512026913424 & 67.6068928873785 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.508333333333333 & 0.00742890834815473 & 68.4263837310092 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.508076923076923 & 0.00735359087511378 & 69.092356605855 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.5078 & 0.0072522480680694 & 70.0196677270004 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.507291666666667 & 0.00716286958209615 & 70.8224072562567 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.50695652173913 & 0.00710085770975878 & 71.3937023470298 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.506590909090909 & 0.00701058684332182 & 72.2608421252894 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.506190476190476 & 0.00688340242280879 & 73.5378298547775 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.50575 & 0.00683962343392885 & 73.9441293640759 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.505263157894737 & 0.00676507685690549 & 74.6869797020837 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.504722222222222 & 0.00664861975306238 & 75.9138348962948 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.504411764705882 & 0.00657048953307169 & 76.7692821314138 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.5040625 & 0.0064423525400276 & 78.241992636721 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.504 & 0.0063535671942582 & 79.3255166098615 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.503928571428571 & 0.0062007698300502 & 81.268711021401 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.504230769230769 & 0.00608081666891437 & 82.9215542393242 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.504166666666667 & 0.00601678409295664 & 83.7933784688823 \tabularnewline
Median & 0.505 &  &  \tabularnewline
Midrange & 0.52 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.50051282051282 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.50051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.50051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.50051282051282 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.50051282051282 &  &  \tabularnewline
Midmean - Closest Observation & 0.50051282051282 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.50051282051282 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.506190476190476 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205361&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]0.509861111111111[/C][C]0.00892827675445872[/C][C]57.1063291532142[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.504299938085146[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.498754547389725[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.515381466057478[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.509722222222222[/C][C]0.008894205667351[/C][C]57.3094710518466[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.509722222222222[/C][C]0.0087701750914936[/C][C]58.1199596250494[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.509722222222222[/C][C]0.00842896355043227[/C][C]60.4727045232129[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.509166666666667[/C][C]0.00832100026339451[/C][C]61.1905600948695[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.508472222222222[/C][C]0.00819524014067378[/C][C]62.0448227866594[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.509305555555556[/C][C]0.0080450764229661[/C][C]63.30649067567[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.51125[/C][C]0.00773165327994696[/C][C]66.1242791792013[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.51125[/C][C]0.00773165327994696[/C][C]66.1242791792013[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.51[/C][C]0.00751368079312882[/C][C]67.8761866575953[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.51[/C][C]0.00751368079312882[/C][C]67.8761866575953[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.511527777777778[/C][C]0.00729347823833567[/C][C]70.1349563352513[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.509861111111111[/C][C]0.00701689514742797[/C][C]72.6619253100853[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.509861111111111[/C][C]0.00701689514742797[/C][C]72.6619253100853[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.509861111111111[/C][C]0.00701689514742797[/C][C]72.6619253100853[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.509861111111111[/C][C]0.00640475253766168[/C][C]79.6066839605418[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.509861111111111[/C][C]0.00640475253766168[/C][C]79.6066839605418[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.509861111111111[/C][C]0.00640475253766168[/C][C]79.6066839605418[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.507361111111111[/C][C]0.00602872965086916[/C][C]84.1572172734541[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.507361111111111[/C][C]0.00602872965086916[/C][C]84.1572172734541[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.504583333333333[/C][C]0.00563265650016281[/C][C]89.5817689785892[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.504583333333333[/C][C]0.00563265650016281[/C][C]89.5817689785892[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.501527777777778[/C][C]0.00522071428799985[/C][C]96.0649731264881[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.504722222222222[/C][C]0.00478804352599433[/C][C]105.413039685642[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.504722222222222[/C][C]0.00478804352599433[/C][C]105.413039685642[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.509571428571429[/C][C]0.00866069801069953[/C][C]58.8372239676176[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.509411764705882[/C][C]0.00838306529326843[/C][C]60.7667657217149[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.509242424242424[/C][C]0.00813152547657892[/C][C]62.6256937531815[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.5090625[/C][C]0.007985970926996[/C][C]63.7445972009678[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.509032258064516[/C][C]0.0078480737865168[/C][C]64.8607890179431[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.509166666666667[/C][C]0.00771780415284163[/C][C]65.9729965393324[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.509137931034483[/C][C]0.0075980562466383[/C][C]67.0089710456865[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.50875[/C][C]0.00752512026913424[/C][C]67.6068928873785[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.508333333333333[/C][C]0.00742890834815473[/C][C]68.4263837310092[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.508076923076923[/C][C]0.00735359087511378[/C][C]69.092356605855[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.5078[/C][C]0.0072522480680694[/C][C]70.0196677270004[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.507291666666667[/C][C]0.00716286958209615[/C][C]70.8224072562567[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.50695652173913[/C][C]0.00710085770975878[/C][C]71.3937023470298[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.506590909090909[/C][C]0.00701058684332182[/C][C]72.2608421252894[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.506190476190476[/C][C]0.00688340242280879[/C][C]73.5378298547775[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.50575[/C][C]0.00683962343392885[/C][C]73.9441293640759[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.505263157894737[/C][C]0.00676507685690549[/C][C]74.6869797020837[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.504722222222222[/C][C]0.00664861975306238[/C][C]75.9138348962948[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.504411764705882[/C][C]0.00657048953307169[/C][C]76.7692821314138[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.5040625[/C][C]0.0064423525400276[/C][C]78.241992636721[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.504[/C][C]0.0063535671942582[/C][C]79.3255166098615[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.503928571428571[/C][C]0.0062007698300502[/C][C]81.268711021401[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.504230769230769[/C][C]0.00608081666891437[/C][C]82.9215542393242[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.504166666666667[/C][C]0.00601678409295664[/C][C]83.7933784688823[/C][/ROW]
[ROW][C]Median[/C][C]0.505[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.50051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.50051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.50051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.50051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.50051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.50051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.50051282051282[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.506190476190476[/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=205361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205361&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	0.509861111111111	0.00892827675445872	57.1063291532142
Geometric Mean	0.504299938085146
Harmonic Mean	0.498754547389725
Quadratic Mean	0.515381466057478
Winsorized Mean ( 1 / 24 )	0.509722222222222	0.008894205667351	57.3094710518466
Winsorized Mean ( 2 / 24 )	0.509722222222222	0.0087701750914936	58.1199596250494
Winsorized Mean ( 3 / 24 )	0.509722222222222	0.00842896355043227	60.4727045232129
Winsorized Mean ( 4 / 24 )	0.509166666666667	0.00832100026339451	61.1905600948695
Winsorized Mean ( 5 / 24 )	0.508472222222222	0.00819524014067378	62.0448227866594
Winsorized Mean ( 6 / 24 )	0.509305555555556	0.0080450764229661	63.30649067567
Winsorized Mean ( 7 / 24 )	0.51125	0.00773165327994696	66.1242791792013
Winsorized Mean ( 8 / 24 )	0.51125	0.00773165327994696	66.1242791792013
Winsorized Mean ( 9 / 24 )	0.51	0.00751368079312882	67.8761866575953
Winsorized Mean ( 10 / 24 )	0.51	0.00751368079312882	67.8761866575953
Winsorized Mean ( 11 / 24 )	0.511527777777778	0.00729347823833567	70.1349563352513
Winsorized Mean ( 12 / 24 )	0.509861111111111	0.00701689514742797	72.6619253100853
Winsorized Mean ( 13 / 24 )	0.509861111111111	0.00701689514742797	72.6619253100853
Winsorized Mean ( 14 / 24 )	0.509861111111111	0.00701689514742797	72.6619253100853
Winsorized Mean ( 15 / 24 )	0.509861111111111	0.00640475253766168	79.6066839605418
Winsorized Mean ( 16 / 24 )	0.509861111111111	0.00640475253766168	79.6066839605418
Winsorized Mean ( 17 / 24 )	0.509861111111111	0.00640475253766168	79.6066839605418
Winsorized Mean ( 18 / 24 )	0.507361111111111	0.00602872965086916	84.1572172734541
Winsorized Mean ( 19 / 24 )	0.507361111111111	0.00602872965086916	84.1572172734541
Winsorized Mean ( 20 / 24 )	0.504583333333333	0.00563265650016281	89.5817689785892
Winsorized Mean ( 21 / 24 )	0.504583333333333	0.00563265650016281	89.5817689785892
Winsorized Mean ( 22 / 24 )	0.501527777777778	0.00522071428799985	96.0649731264881
Winsorized Mean ( 23 / 24 )	0.504722222222222	0.00478804352599433	105.413039685642
Winsorized Mean ( 24 / 24 )	0.504722222222222	0.00478804352599433	105.413039685642
Trimmed Mean ( 1 / 24 )	0.509571428571429	0.00866069801069953	58.8372239676176
Trimmed Mean ( 2 / 24 )	0.509411764705882	0.00838306529326843	60.7667657217149
Trimmed Mean ( 3 / 24 )	0.509242424242424	0.00813152547657892	62.6256937531815
Trimmed Mean ( 4 / 24 )	0.5090625	0.007985970926996	63.7445972009678
Trimmed Mean ( 5 / 24 )	0.509032258064516	0.0078480737865168	64.8607890179431
Trimmed Mean ( 6 / 24 )	0.509166666666667	0.00771780415284163	65.9729965393324
Trimmed Mean ( 7 / 24 )	0.509137931034483	0.0075980562466383	67.0089710456865
Trimmed Mean ( 8 / 24 )	0.50875	0.00752512026913424	67.6068928873785
Trimmed Mean ( 9 / 24 )	0.508333333333333	0.00742890834815473	68.4263837310092
Trimmed Mean ( 10 / 24 )	0.508076923076923	0.00735359087511378	69.092356605855
Trimmed Mean ( 11 / 24 )	0.5078	0.0072522480680694	70.0196677270004
Trimmed Mean ( 12 / 24 )	0.507291666666667	0.00716286958209615	70.8224072562567
Trimmed Mean ( 13 / 24 )	0.50695652173913	0.00710085770975878	71.3937023470298
Trimmed Mean ( 14 / 24 )	0.506590909090909	0.00701058684332182	72.2608421252894
Trimmed Mean ( 15 / 24 )	0.506190476190476	0.00688340242280879	73.5378298547775
Trimmed Mean ( 16 / 24 )	0.50575	0.00683962343392885	73.9441293640759
Trimmed Mean ( 17 / 24 )	0.505263157894737	0.00676507685690549	74.6869797020837
Trimmed Mean ( 18 / 24 )	0.504722222222222	0.00664861975306238	75.9138348962948
Trimmed Mean ( 19 / 24 )	0.504411764705882	0.00657048953307169	76.7692821314138
Trimmed Mean ( 20 / 24 )	0.5040625	0.0064423525400276	78.241992636721
Trimmed Mean ( 21 / 24 )	0.504	0.0063535671942582	79.3255166098615
Trimmed Mean ( 22 / 24 )	0.503928571428571	0.0062007698300502	81.268711021401
Trimmed Mean ( 23 / 24 )	0.504230769230769	0.00608081666891437	82.9215542393242
Trimmed Mean ( 24 / 24 )	0.504166666666667	0.00601678409295664	83.7933784688823
Median	0.505
Midrange	0.52
Midmean - Weighted Average at Xnp	0.50051282051282
Midmean - Weighted Average at X(n+1)p	0.50051282051282
Midmean - Empirical Distribution Function	0.50051282051282
Midmean - Empirical Distribution Function - Averaging	0.50051282051282
Midmean - Empirical Distribution Function - Interpolation	0.50051282051282
Midmean - Closest Observation	0.50051282051282
Midmean - True Basic - Statistics Graphics Toolkit	0.50051282051282
Midmean - MS Excel (old versions)	0.506190476190476
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