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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Oct 2012 12:48:26 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/11/t134997415967gvda94ob3y1bm.htm/, Retrieved Thu, 02 May 2024 15:20:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175163, Retrieved Thu, 02 May 2024 15:20:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robustheid] [2012-10-11 16:48:26] [21b9ad762194a0cf58934491430d34cc] [Current]
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Dataseries X:
46,56
46,72
47,01
47,26
47,49
47,51
47,52
47,66
47,71
47,87
48
48
48,05
48,25
48,72
48,94
49,16
49,18
49,25
49,34
49,49
49,57
49,63
49,67
49,7
49,8
50,09
50,49
50,73
51,12
51,15
51,41
51,61
52,06
52,17
52,18
52,19
52,74
53,05
53,38
53,78
53,82
53,88
53,96
54,14
54,2
54,35
54,36
54,39
54,77
54,91
55,06
55,38
55,41
55,47
55,58
55,67
55,97
56,03
56,06
56,08
56,43
56,65
56,96
57,37
57,51
57,61
57,7
57,91
58,12
58,18
58,16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175163&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175163&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175163&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean52.33750.419625072519145124.724434805101
Geometric Mean52.2179149324512
Harmonic Mean52.0984095455154
Quadratic Mean52.4568008513249
Winsorized Mean ( 1 / 24 )52.33944444444440.419145391842372124.871811698523
Winsorized Mean ( 2 / 24 )52.34638888888890.417442672005878125.397790880736
Winsorized Mean ( 3 / 24 )52.34805555555560.413922684811926126.468196782549
Winsorized Mean ( 4 / 24 )52.34916666666670.409571264729374127.814549444177
Winsorized Mean ( 5 / 24 )52.34430555555560.408196577002887128.233083040247
Winsorized Mean ( 6 / 24 )52.33680555555560.406553745308405128.73280878486
Winsorized Mean ( 7 / 24 )52.33680555555560.401882251107752130.229203731426
Winsorized Mean ( 8 / 24 )52.29680555555560.393145038601172133.021659745803
Winsorized Mean ( 9 / 24 )52.27805555555560.383533711605316136.306285402503
Winsorized Mean ( 10 / 24 )52.26555555555560.375790709870216139.081553063422
Winsorized Mean ( 11 / 24 )52.21208333333330.367653704429949142.014299609163
Winsorized Mean ( 12 / 24 )52.21708333333330.365819306708116142.740097025543
Winsorized Mean ( 13 / 24 )52.24777777777780.359290033180669145.419502220105
Winsorized Mean ( 14 / 24 )52.32750.343627759599613152.279606458369
Winsorized Mean ( 15 / 24 )52.31083333333330.327737403351457159.612033287627
Winsorized Mean ( 16 / 24 )52.33972222222220.317871440104894164.656888347537
Winsorized Mean ( 17 / 24 )52.31847222222220.313502580134934166.883705389933
Winsorized Mean ( 18 / 24 )52.32097222222220.308925466174455169.36438704822
Winsorized Mean ( 19 / 24 )52.33680555555560.304502006694443171.876718067325
Winsorized Mean ( 20 / 24 )52.28958333333330.286428785287846182.557012490155
Winsorized Mean ( 21 / 24 )52.26916666666670.277308404300089188.487495712909
Winsorized Mean ( 22 / 24 )52.24472222222220.269100758091768194.14557800839
Winsorized Mean ( 23 / 24 )52.13611111111110.251654272893495207.173558039192
Winsorized Mean ( 24 / 24 )52.13611111111110.249015554343479209.368893636247
Trimmed Mean ( 1 / 24 )52.33657142857140.415196123963879126.052649357402
Trimmed Mean ( 2 / 24 )52.33352941176470.410350701458234127.53366626593
Trimmed Mean ( 3 / 24 )52.32651515151520.405483365322892129.04725477418
Trimmed Mean ( 4 / 24 )52.31843750.401046140590382130.454908312998
Trimmed Mean ( 5 / 24 )52.30951612903230.397047167302445131.746352667431
Trimmed Mean ( 6 / 24 )52.30116666666670.392401061096334133.28497767193
Trimmed Mean ( 7 / 24 )52.29379310344830.386981730192909135.132459812457
Trimmed Mean ( 8 / 24 )52.28589285714290.381319545650595137.118313114358
Trimmed Mean ( 9 / 24 )52.28407407407410.376205216173761138.97753626554
Trimmed Mean ( 10 / 24 )52.2850.371756713858193140.643055124336
Trimmed Mean ( 11 / 24 )52.28780.367546669534243142.261661808171
Trimmed Mean ( 12 / 24 )52.2981250.363567291157315143.847167421259
Trimmed Mean ( 13 / 24 )52.30869565217390.358470531024667145.921885134191
Trimmed Mean ( 14 / 24 )52.31636363636360.352935154299619148.232226229157
Trimmed Mean ( 15 / 24 )52.3150.348708126839019150.025181443939
Trimmed Mean ( 16 / 24 )52.31550.345987985192312151.206117665968
Trimmed Mean ( 17 / 24 )52.31263157894740.343740549428714152.186384951933
Trimmed Mean ( 18 / 24 )52.31194444444440.340805725845326153.494910669975
Trimmed Mean ( 19 / 24 )52.31088235294120.336932891239664155.25608722994
Trimmed Mean ( 20 / 24 )52.30781250.331674251864383157.708390705553
Trimmed Mean ( 21 / 24 )52.310.328026141374872159.468997747407
Trimmed Mean ( 22 / 24 )52.3150.323964977857649161.48350462434
Trimmed Mean ( 23 / 24 )52.32384615384620.318907788419777164.072023493426
Trimmed Mean ( 24 / 24 )52.34833333333330.31502281184174166.173151167325
Median52.185
Midrange52.37
Midmean - Weighted Average at Xnp52.2272972972973
Midmean - Weighted Average at X(n+1)p52.3119444444444
Midmean - Empirical Distribution Function52.2272972972973
Midmean - Empirical Distribution Function - Averaging52.3119444444444
Midmean - Empirical Distribution Function - Interpolation52.3119444444444
Midmean - Closest Observation52.2272972972973
Midmean - True Basic - Statistics Graphics Toolkit52.3119444444444
Midmean - MS Excel (old versions)52.3126315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 52.3375 & 0.419625072519145 & 124.724434805101 \tabularnewline
Geometric Mean & 52.2179149324512 &  &  \tabularnewline
Harmonic Mean & 52.0984095455154 &  &  \tabularnewline
Quadratic Mean & 52.4568008513249 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 52.3394444444444 & 0.419145391842372 & 124.871811698523 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 52.3463888888889 & 0.417442672005878 & 125.397790880736 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 52.3480555555556 & 0.413922684811926 & 126.468196782549 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 52.3491666666667 & 0.409571264729374 & 127.814549444177 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 52.3443055555556 & 0.408196577002887 & 128.233083040247 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 52.3368055555556 & 0.406553745308405 & 128.73280878486 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 52.3368055555556 & 0.401882251107752 & 130.229203731426 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 52.2968055555556 & 0.393145038601172 & 133.021659745803 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 52.2780555555556 & 0.383533711605316 & 136.306285402503 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 52.2655555555556 & 0.375790709870216 & 139.081553063422 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 52.2120833333333 & 0.367653704429949 & 142.014299609163 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 52.2170833333333 & 0.365819306708116 & 142.740097025543 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 52.2477777777778 & 0.359290033180669 & 145.419502220105 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 52.3275 & 0.343627759599613 & 152.279606458369 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 52.3108333333333 & 0.327737403351457 & 159.612033287627 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 52.3397222222222 & 0.317871440104894 & 164.656888347537 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 52.3184722222222 & 0.313502580134934 & 166.883705389933 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 52.3209722222222 & 0.308925466174455 & 169.36438704822 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 52.3368055555556 & 0.304502006694443 & 171.876718067325 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 52.2895833333333 & 0.286428785287846 & 182.557012490155 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 52.2691666666667 & 0.277308404300089 & 188.487495712909 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 52.2447222222222 & 0.269100758091768 & 194.14557800839 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 52.1361111111111 & 0.251654272893495 & 207.173558039192 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 52.1361111111111 & 0.249015554343479 & 209.368893636247 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 52.3365714285714 & 0.415196123963879 & 126.052649357402 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 52.3335294117647 & 0.410350701458234 & 127.53366626593 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 52.3265151515152 & 0.405483365322892 & 129.04725477418 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 52.3184375 & 0.401046140590382 & 130.454908312998 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 52.3095161290323 & 0.397047167302445 & 131.746352667431 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 52.3011666666667 & 0.392401061096334 & 133.28497767193 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 52.2937931034483 & 0.386981730192909 & 135.132459812457 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 52.2858928571429 & 0.381319545650595 & 137.118313114358 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 52.2840740740741 & 0.376205216173761 & 138.97753626554 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 52.285 & 0.371756713858193 & 140.643055124336 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 52.2878 & 0.367546669534243 & 142.261661808171 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 52.298125 & 0.363567291157315 & 143.847167421259 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 52.3086956521739 & 0.358470531024667 & 145.921885134191 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 52.3163636363636 & 0.352935154299619 & 148.232226229157 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 52.315 & 0.348708126839019 & 150.025181443939 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 52.3155 & 0.345987985192312 & 151.206117665968 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 52.3126315789474 & 0.343740549428714 & 152.186384951933 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 52.3119444444444 & 0.340805725845326 & 153.494910669975 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 52.3108823529412 & 0.336932891239664 & 155.25608722994 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 52.3078125 & 0.331674251864383 & 157.708390705553 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 52.31 & 0.328026141374872 & 159.468997747407 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 52.315 & 0.323964977857649 & 161.48350462434 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 52.3238461538462 & 0.318907788419777 & 164.072023493426 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 52.3483333333333 & 0.31502281184174 & 166.173151167325 \tabularnewline
Median & 52.185 &  &  \tabularnewline
Midrange & 52.37 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.2272972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.3119444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.2272972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.3119444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.3119444444444 &  &  \tabularnewline
Midmean - Closest Observation & 52.2272972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.3119444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.3126315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175163&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]52.3375[/C][C]0.419625072519145[/C][C]124.724434805101[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]52.2179149324512[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]52.0984095455154[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]52.4568008513249[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]52.3394444444444[/C][C]0.419145391842372[/C][C]124.871811698523[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]52.3463888888889[/C][C]0.417442672005878[/C][C]125.397790880736[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]52.3480555555556[/C][C]0.413922684811926[/C][C]126.468196782549[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]52.3491666666667[/C][C]0.409571264729374[/C][C]127.814549444177[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]52.3443055555556[/C][C]0.408196577002887[/C][C]128.233083040247[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]52.3368055555556[/C][C]0.406553745308405[/C][C]128.73280878486[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]52.3368055555556[/C][C]0.401882251107752[/C][C]130.229203731426[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]52.2968055555556[/C][C]0.393145038601172[/C][C]133.021659745803[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]52.2780555555556[/C][C]0.383533711605316[/C][C]136.306285402503[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]52.2655555555556[/C][C]0.375790709870216[/C][C]139.081553063422[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]52.2120833333333[/C][C]0.367653704429949[/C][C]142.014299609163[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]52.2170833333333[/C][C]0.365819306708116[/C][C]142.740097025543[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]52.2477777777778[/C][C]0.359290033180669[/C][C]145.419502220105[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]52.3275[/C][C]0.343627759599613[/C][C]152.279606458369[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]52.3108333333333[/C][C]0.327737403351457[/C][C]159.612033287627[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]52.3397222222222[/C][C]0.317871440104894[/C][C]164.656888347537[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]52.3184722222222[/C][C]0.313502580134934[/C][C]166.883705389933[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]52.3209722222222[/C][C]0.308925466174455[/C][C]169.36438704822[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]52.3368055555556[/C][C]0.304502006694443[/C][C]171.876718067325[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]52.2895833333333[/C][C]0.286428785287846[/C][C]182.557012490155[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]52.2691666666667[/C][C]0.277308404300089[/C][C]188.487495712909[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]52.2447222222222[/C][C]0.269100758091768[/C][C]194.14557800839[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]52.1361111111111[/C][C]0.251654272893495[/C][C]207.173558039192[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]52.1361111111111[/C][C]0.249015554343479[/C][C]209.368893636247[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]52.3365714285714[/C][C]0.415196123963879[/C][C]126.052649357402[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]52.3335294117647[/C][C]0.410350701458234[/C][C]127.53366626593[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]52.3265151515152[/C][C]0.405483365322892[/C][C]129.04725477418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]52.3184375[/C][C]0.401046140590382[/C][C]130.454908312998[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]52.3095161290323[/C][C]0.397047167302445[/C][C]131.746352667431[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]52.3011666666667[/C][C]0.392401061096334[/C][C]133.28497767193[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]52.2937931034483[/C][C]0.386981730192909[/C][C]135.132459812457[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]52.2858928571429[/C][C]0.381319545650595[/C][C]137.118313114358[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]52.2840740740741[/C][C]0.376205216173761[/C][C]138.97753626554[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]52.285[/C][C]0.371756713858193[/C][C]140.643055124336[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]52.2878[/C][C]0.367546669534243[/C][C]142.261661808171[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]52.298125[/C][C]0.363567291157315[/C][C]143.847167421259[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]52.3086956521739[/C][C]0.358470531024667[/C][C]145.921885134191[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]52.3163636363636[/C][C]0.352935154299619[/C][C]148.232226229157[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]52.315[/C][C]0.348708126839019[/C][C]150.025181443939[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]52.3155[/C][C]0.345987985192312[/C][C]151.206117665968[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]52.3126315789474[/C][C]0.343740549428714[/C][C]152.186384951933[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]52.3119444444444[/C][C]0.340805725845326[/C][C]153.494910669975[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]52.3108823529412[/C][C]0.336932891239664[/C][C]155.25608722994[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]52.3078125[/C][C]0.331674251864383[/C][C]157.708390705553[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]52.31[/C][C]0.328026141374872[/C][C]159.468997747407[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]52.315[/C][C]0.323964977857649[/C][C]161.48350462434[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]52.3238461538462[/C][C]0.318907788419777[/C][C]164.072023493426[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]52.3483333333333[/C][C]0.31502281184174[/C][C]166.173151167325[/C][/ROW]
[ROW][C]Median[/C][C]52.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]52.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.2272972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.3119444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.2272972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.3119444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.3119444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.2272972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.3119444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.3126315789474[/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=175163&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175163&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean52.33750.419625072519145124.724434805101
Geometric Mean52.2179149324512
Harmonic Mean52.0984095455154
Quadratic Mean52.4568008513249
Winsorized Mean ( 1 / 24 )52.33944444444440.419145391842372124.871811698523
Winsorized Mean ( 2 / 24 )52.34638888888890.417442672005878125.397790880736
Winsorized Mean ( 3 / 24 )52.34805555555560.413922684811926126.468196782549
Winsorized Mean ( 4 / 24 )52.34916666666670.409571264729374127.814549444177
Winsorized Mean ( 5 / 24 )52.34430555555560.408196577002887128.233083040247
Winsorized Mean ( 6 / 24 )52.33680555555560.406553745308405128.73280878486
Winsorized Mean ( 7 / 24 )52.33680555555560.401882251107752130.229203731426
Winsorized Mean ( 8 / 24 )52.29680555555560.393145038601172133.021659745803
Winsorized Mean ( 9 / 24 )52.27805555555560.383533711605316136.306285402503
Winsorized Mean ( 10 / 24 )52.26555555555560.375790709870216139.081553063422
Winsorized Mean ( 11 / 24 )52.21208333333330.367653704429949142.014299609163
Winsorized Mean ( 12 / 24 )52.21708333333330.365819306708116142.740097025543
Winsorized Mean ( 13 / 24 )52.24777777777780.359290033180669145.419502220105
Winsorized Mean ( 14 / 24 )52.32750.343627759599613152.279606458369
Winsorized Mean ( 15 / 24 )52.31083333333330.327737403351457159.612033287627
Winsorized Mean ( 16 / 24 )52.33972222222220.317871440104894164.656888347537
Winsorized Mean ( 17 / 24 )52.31847222222220.313502580134934166.883705389933
Winsorized Mean ( 18 / 24 )52.32097222222220.308925466174455169.36438704822
Winsorized Mean ( 19 / 24 )52.33680555555560.304502006694443171.876718067325
Winsorized Mean ( 20 / 24 )52.28958333333330.286428785287846182.557012490155
Winsorized Mean ( 21 / 24 )52.26916666666670.277308404300089188.487495712909
Winsorized Mean ( 22 / 24 )52.24472222222220.269100758091768194.14557800839
Winsorized Mean ( 23 / 24 )52.13611111111110.251654272893495207.173558039192
Winsorized Mean ( 24 / 24 )52.13611111111110.249015554343479209.368893636247
Trimmed Mean ( 1 / 24 )52.33657142857140.415196123963879126.052649357402
Trimmed Mean ( 2 / 24 )52.33352941176470.410350701458234127.53366626593
Trimmed Mean ( 3 / 24 )52.32651515151520.405483365322892129.04725477418
Trimmed Mean ( 4 / 24 )52.31843750.401046140590382130.454908312998
Trimmed Mean ( 5 / 24 )52.30951612903230.397047167302445131.746352667431
Trimmed Mean ( 6 / 24 )52.30116666666670.392401061096334133.28497767193
Trimmed Mean ( 7 / 24 )52.29379310344830.386981730192909135.132459812457
Trimmed Mean ( 8 / 24 )52.28589285714290.381319545650595137.118313114358
Trimmed Mean ( 9 / 24 )52.28407407407410.376205216173761138.97753626554
Trimmed Mean ( 10 / 24 )52.2850.371756713858193140.643055124336
Trimmed Mean ( 11 / 24 )52.28780.367546669534243142.261661808171
Trimmed Mean ( 12 / 24 )52.2981250.363567291157315143.847167421259
Trimmed Mean ( 13 / 24 )52.30869565217390.358470531024667145.921885134191
Trimmed Mean ( 14 / 24 )52.31636363636360.352935154299619148.232226229157
Trimmed Mean ( 15 / 24 )52.3150.348708126839019150.025181443939
Trimmed Mean ( 16 / 24 )52.31550.345987985192312151.206117665968
Trimmed Mean ( 17 / 24 )52.31263157894740.343740549428714152.186384951933
Trimmed Mean ( 18 / 24 )52.31194444444440.340805725845326153.494910669975
Trimmed Mean ( 19 / 24 )52.31088235294120.336932891239664155.25608722994
Trimmed Mean ( 20 / 24 )52.30781250.331674251864383157.708390705553
Trimmed Mean ( 21 / 24 )52.310.328026141374872159.468997747407
Trimmed Mean ( 22 / 24 )52.3150.323964977857649161.48350462434
Trimmed Mean ( 23 / 24 )52.32384615384620.318907788419777164.072023493426
Trimmed Mean ( 24 / 24 )52.34833333333330.31502281184174166.173151167325
Median52.185
Midrange52.37
Midmean - Weighted Average at Xnp52.2272972972973
Midmean - Weighted Average at X(n+1)p52.3119444444444
Midmean - Empirical Distribution Function52.2272972972973
Midmean - Empirical Distribution Function - Averaging52.3119444444444
Midmean - Empirical Distribution Function - Interpolation52.3119444444444
Midmean - Closest Observation52.2272972972973
Midmean - True Basic - Statistics Graphics Toolkit52.3119444444444
Midmean - MS Excel (old versions)52.3126315789474
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')