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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 06 Jan 2008 10:03:11 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jan/06/t1199638984kuzoh2aev52p10s.htm/, Retrieved Sun, 05 May 2024 03:01:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7840, Retrieved Sun, 05 May 2024 03:01:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsdiesel
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [s 0650692 paper] [2008-01-06 17:03:11] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]
-  M D    [Central Tendency] [] [2010-12-17 14:20:42] [d7b28a0391ab3b2ddc9f9fba95a43f33]
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Dataseries X:
0,73
0,74
0,75
0,74
0,76
0,76
0,78
0,79
0,89
0,88
0,88
0,84
0,76
0,77
0,76
0,77
0,78
0,79
0,78
0,76
0,78
0,76
0,74
0,73
0,72
0,71
0,73
0,75
0,75
0,72
0,72
0,72
0,74
0,78
0,74
0,74
0,75
0,78
0,81
0,75
0,7
0,71
0,71
0,73
0,74
0,74
0,75
0,74
0,74
0,73
0,76
0,8
0,83
0,81
0,83
0,88
0,89
0,93
0,91
0,9
0,86
0,88
0,93
0,98
0,97
1,03
1,06
1,06
1,08
1,09
1,04
1




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7840&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7840&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.8116666666666670.012157675628273566.761664933639
Geometric Mean0.805772231261011
Harmonic Mean0.800415110238975
Quadratic Mean0.818105874702182
Winsorized Mean ( 1 / 24 )0.8116666666666670.012096378743935967.0999713094769
Winsorized Mean ( 2 / 24 )0.8111111111111110.011927919201484268.0010567987572
Winsorized Mean ( 3 / 24 )0.8111111111111110.011927919201484268.0010567987572
Winsorized Mean ( 4 / 24 )0.8105555555555560.011545122893784470.207616065476
Winsorized Mean ( 5 / 24 )0.8098611111111110.011353084583498771.3340154523479
Winsorized Mean ( 6 / 24 )0.8073611111111110.010693834708143075.4978109486142
Winsorized Mean ( 7 / 24 )0.8054166666666670.010212793650471278.863501430826
Winsorized Mean ( 8 / 24 )0.8054166666666670.009822241496344981.9992734821662
Winsorized Mean ( 9 / 24 )0.8004166666666670.0087040488033561291.9591198015849
Winsorized Mean ( 10 / 24 )0.8004166666666670.0087040488033561291.9591198015849
Winsorized Mean ( 11 / 24 )0.7973611111111110.0080830805719049798.645696281015
Winsorized Mean ( 12 / 24 )0.7956944444444440.00776167500861218102.515815666278
Winsorized Mean ( 13 / 24 )0.7956944444444440.00721844053513958110.230795775207
Winsorized Mean ( 14 / 24 )0.7956944444444440.00721844053513958110.230795775207
Winsorized Mean ( 15 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 16 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 17 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 18 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 19 / 24 )0.7883333333333330.00592070714382514133.148509828848
Winsorized Mean ( 20 / 24 )0.7827777777777780.00499695612442981156.650920737692
Winsorized Mean ( 21 / 24 )0.7798611111111110.00453422498633925171.994357020369
Winsorized Mean ( 22 / 24 )0.7798611111111110.00453422498633925171.994357020369
Winsorized Mean ( 23 / 24 )0.7766666666666670.00317092621846395244.933692289723
Winsorized Mean ( 24 / 24 )0.7766666666666670.00317092621846395244.933692289723
Trimmed Mean ( 1 / 24 )0.8092857142857140.011736092917128768.9569961656121
Trimmed Mean ( 2 / 24 )0.8067647058823530.011299345347781771.3992431464833
Trimmed Mean ( 3 / 24 )0.804393939393940.010879995517701873.9332969471528
Trimmed Mean ( 4 / 24 )0.8018750.010365050689391377.3633457307378
Trimmed Mean ( 5 / 24 )0.7993548387096770.0098826294727523480.884833425517
Trimmed Mean ( 6 / 24 )0.7968333333333330.0093503426526133685.2196933243536
Trimmed Mean ( 7 / 24 )0.7946551724137930.0089029706674495889.2573054653719
Trimmed Mean ( 8 / 24 )0.7926785714285710.008487925233417793.3889672246082
Trimmed Mean ( 9 / 24 )0.7905555555555560.008067745421686697.9896506687597
Trimmed Mean ( 10 / 24 )0.7890384615384620.00784108574080252100.62872510532
Trimmed Mean ( 11 / 24 )0.78740.0075474553084237104.326553496936
Trimmed Mean ( 12 / 24 )0.7860416666666670.00732805005928554107.264778530089
Trimmed Mean ( 13 / 24 )0.7847826086956520.00712035342467279110.216805527700
Trimmed Mean ( 14 / 24 )0.7834090909090910.00696520483663605112.474666471898
Trimmed Mean ( 15 / 24 )0.7819047619047620.0067495265480114115.845868053535
Trimmed Mean ( 16 / 24 )0.78050.00655303805057682119.105061496064
Trimmed Mean ( 17 / 24 )0.7789473684210530.00627476004408462124.139785895938
Trimmed Mean ( 18 / 24 )0.7772222222222220.00587719713878247132.243687572344
Trimmed Mean ( 19 / 24 )0.7752941176470590.00529411764705882146.444444444444
Trimmed Mean ( 20 / 24 )0.773750.00480989403679138160.866329711529
Trimmed Mean ( 21 / 24 )0.7726666666666670.00447042216457259172.839753880502
Trimmed Mean ( 22 / 24 )0.7717857142857140.00414848641450929186.040313784421
Trimmed Mean ( 23 / 24 )0.7707692307692310.00363415748031315212.090212090318
Trimmed Mean ( 24 / 24 )0.770.00345782037404063222.683632088216
Median0.765
Midrange0.895
Midmean - Weighted Average at Xnp0.78
Midmean - Weighted Average at X(n+1)p0.78
Midmean - Empirical Distribution Function0.78
Midmean - Empirical Distribution Function - Averaging0.78
Midmean - Empirical Distribution Function - Interpolation0.78
Midmean - Closest Observation0.78
Midmean - True Basic - Statistics Graphics Toolkit0.78
Midmean - MS Excel (old versions)0.78
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.811666666666667 & 0.0121576756282735 & 66.761664933639 \tabularnewline
Geometric Mean & 0.805772231261011 &  &  \tabularnewline
Harmonic Mean & 0.800415110238975 &  &  \tabularnewline
Quadratic Mean & 0.818105874702182 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.811666666666667 & 0.0120963787439359 & 67.0999713094769 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.811111111111111 & 0.0119279192014842 & 68.0010567987572 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.811111111111111 & 0.0119279192014842 & 68.0010567987572 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.810555555555556 & 0.0115451228937844 & 70.207616065476 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.809861111111111 & 0.0113530845834987 & 71.3340154523479 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.807361111111111 & 0.0106938347081430 & 75.4978109486142 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.805416666666667 & 0.0102127936504712 & 78.863501430826 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.805416666666667 & 0.0098222414963449 & 81.9992734821662 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.800416666666667 & 0.00870404880335612 & 91.9591198015849 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.800416666666667 & 0.00870404880335612 & 91.9591198015849 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.797361111111111 & 0.00808308057190497 & 98.645696281015 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.795694444444444 & 0.00776167500861218 & 102.515815666278 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.795694444444444 & 0.00721844053513958 & 110.230795775207 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.795694444444444 & 0.00721844053513958 & 110.230795775207 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.793611111111111 & 0.00684133150253119 & 116.002434733281 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.793611111111111 & 0.00684133150253119 & 116.002434733281 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.793611111111111 & 0.00684133150253119 & 116.002434733281 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.793611111111111 & 0.00684133150253119 & 116.002434733281 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.788333333333333 & 0.00592070714382514 & 133.148509828848 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.782777777777778 & 0.00499695612442981 & 156.650920737692 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.779861111111111 & 0.00453422498633925 & 171.994357020369 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.779861111111111 & 0.00453422498633925 & 171.994357020369 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.776666666666667 & 0.00317092621846395 & 244.933692289723 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.776666666666667 & 0.00317092621846395 & 244.933692289723 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.809285714285714 & 0.0117360929171287 & 68.9569961656121 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.806764705882353 & 0.0112993453477817 & 71.3992431464833 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.80439393939394 & 0.0108799955177018 & 73.9332969471528 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.801875 & 0.0103650506893913 & 77.3633457307378 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.799354838709677 & 0.00988262947275234 & 80.884833425517 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.796833333333333 & 0.00935034265261336 & 85.2196933243536 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.794655172413793 & 0.00890297066744958 & 89.2573054653719 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.792678571428571 & 0.0084879252334177 & 93.3889672246082 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.790555555555556 & 0.0080677454216866 & 97.9896506687597 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.789038461538462 & 0.00784108574080252 & 100.62872510532 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.7874 & 0.0075474553084237 & 104.326553496936 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.786041666666667 & 0.00732805005928554 & 107.264778530089 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.784782608695652 & 0.00712035342467279 & 110.216805527700 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.783409090909091 & 0.00696520483663605 & 112.474666471898 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.781904761904762 & 0.0067495265480114 & 115.845868053535 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.7805 & 0.00655303805057682 & 119.105061496064 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.778947368421053 & 0.00627476004408462 & 124.139785895938 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.777222222222222 & 0.00587719713878247 & 132.243687572344 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.775294117647059 & 0.00529411764705882 & 146.444444444444 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.77375 & 0.00480989403679138 & 160.866329711529 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.772666666666667 & 0.00447042216457259 & 172.839753880502 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.771785714285714 & 0.00414848641450929 & 186.040313784421 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.770769230769231 & 0.00363415748031315 & 212.090212090318 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.77 & 0.00345782037404063 & 222.683632088216 \tabularnewline
Median & 0.765 &  &  \tabularnewline
Midrange & 0.895 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.78 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.78 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.78 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.78 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.78 &  &  \tabularnewline
Midmean - Closest Observation & 0.78 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.78 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.78 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7840&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]0.811666666666667[/C][C]0.0121576756282735[/C][C]66.761664933639[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.805772231261011[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.800415110238975[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.818105874702182[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.811666666666667[/C][C]0.0120963787439359[/C][C]67.0999713094769[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.811111111111111[/C][C]0.0119279192014842[/C][C]68.0010567987572[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.811111111111111[/C][C]0.0119279192014842[/C][C]68.0010567987572[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.810555555555556[/C][C]0.0115451228937844[/C][C]70.207616065476[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.809861111111111[/C][C]0.0113530845834987[/C][C]71.3340154523479[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.807361111111111[/C][C]0.0106938347081430[/C][C]75.4978109486142[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.805416666666667[/C][C]0.0102127936504712[/C][C]78.863501430826[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.805416666666667[/C][C]0.0098222414963449[/C][C]81.9992734821662[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.800416666666667[/C][C]0.00870404880335612[/C][C]91.9591198015849[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.800416666666667[/C][C]0.00870404880335612[/C][C]91.9591198015849[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.797361111111111[/C][C]0.00808308057190497[/C][C]98.645696281015[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.795694444444444[/C][C]0.00776167500861218[/C][C]102.515815666278[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.795694444444444[/C][C]0.00721844053513958[/C][C]110.230795775207[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.795694444444444[/C][C]0.00721844053513958[/C][C]110.230795775207[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.793611111111111[/C][C]0.00684133150253119[/C][C]116.002434733281[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.793611111111111[/C][C]0.00684133150253119[/C][C]116.002434733281[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.793611111111111[/C][C]0.00684133150253119[/C][C]116.002434733281[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.793611111111111[/C][C]0.00684133150253119[/C][C]116.002434733281[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.788333333333333[/C][C]0.00592070714382514[/C][C]133.148509828848[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.782777777777778[/C][C]0.00499695612442981[/C][C]156.650920737692[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.779861111111111[/C][C]0.00453422498633925[/C][C]171.994357020369[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.779861111111111[/C][C]0.00453422498633925[/C][C]171.994357020369[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.776666666666667[/C][C]0.00317092621846395[/C][C]244.933692289723[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.776666666666667[/C][C]0.00317092621846395[/C][C]244.933692289723[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.809285714285714[/C][C]0.0117360929171287[/C][C]68.9569961656121[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.806764705882353[/C][C]0.0112993453477817[/C][C]71.3992431464833[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.80439393939394[/C][C]0.0108799955177018[/C][C]73.9332969471528[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.801875[/C][C]0.0103650506893913[/C][C]77.3633457307378[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.799354838709677[/C][C]0.00988262947275234[/C][C]80.884833425517[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.796833333333333[/C][C]0.00935034265261336[/C][C]85.2196933243536[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.794655172413793[/C][C]0.00890297066744958[/C][C]89.2573054653719[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.792678571428571[/C][C]0.0084879252334177[/C][C]93.3889672246082[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.790555555555556[/C][C]0.0080677454216866[/C][C]97.9896506687597[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.789038461538462[/C][C]0.00784108574080252[/C][C]100.62872510532[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.7874[/C][C]0.0075474553084237[/C][C]104.326553496936[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.786041666666667[/C][C]0.00732805005928554[/C][C]107.264778530089[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.784782608695652[/C][C]0.00712035342467279[/C][C]110.216805527700[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.783409090909091[/C][C]0.00696520483663605[/C][C]112.474666471898[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.781904761904762[/C][C]0.0067495265480114[/C][C]115.845868053535[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.7805[/C][C]0.00655303805057682[/C][C]119.105061496064[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.778947368421053[/C][C]0.00627476004408462[/C][C]124.139785895938[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.777222222222222[/C][C]0.00587719713878247[/C][C]132.243687572344[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.775294117647059[/C][C]0.00529411764705882[/C][C]146.444444444444[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.77375[/C][C]0.00480989403679138[/C][C]160.866329711529[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.772666666666667[/C][C]0.00447042216457259[/C][C]172.839753880502[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.771785714285714[/C][C]0.00414848641450929[/C][C]186.040313784421[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.770769230769231[/C][C]0.00363415748031315[/C][C]212.090212090318[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.77[/C][C]0.00345782037404063[/C][C]222.683632088216[/C][/ROW]
[ROW][C]Median[/C][C]0.765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.78[/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=7840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7840&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 Mean0.8116666666666670.012157675628273566.761664933639
Geometric Mean0.805772231261011
Harmonic Mean0.800415110238975
Quadratic Mean0.818105874702182
Winsorized Mean ( 1 / 24 )0.8116666666666670.012096378743935967.0999713094769
Winsorized Mean ( 2 / 24 )0.8111111111111110.011927919201484268.0010567987572
Winsorized Mean ( 3 / 24 )0.8111111111111110.011927919201484268.0010567987572
Winsorized Mean ( 4 / 24 )0.8105555555555560.011545122893784470.207616065476
Winsorized Mean ( 5 / 24 )0.8098611111111110.011353084583498771.3340154523479
Winsorized Mean ( 6 / 24 )0.8073611111111110.010693834708143075.4978109486142
Winsorized Mean ( 7 / 24 )0.8054166666666670.010212793650471278.863501430826
Winsorized Mean ( 8 / 24 )0.8054166666666670.009822241496344981.9992734821662
Winsorized Mean ( 9 / 24 )0.8004166666666670.0087040488033561291.9591198015849
Winsorized Mean ( 10 / 24 )0.8004166666666670.0087040488033561291.9591198015849
Winsorized Mean ( 11 / 24 )0.7973611111111110.0080830805719049798.645696281015
Winsorized Mean ( 12 / 24 )0.7956944444444440.00776167500861218102.515815666278
Winsorized Mean ( 13 / 24 )0.7956944444444440.00721844053513958110.230795775207
Winsorized Mean ( 14 / 24 )0.7956944444444440.00721844053513958110.230795775207
Winsorized Mean ( 15 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 16 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 17 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 18 / 24 )0.7936111111111110.00684133150253119116.002434733281
Winsorized Mean ( 19 / 24 )0.7883333333333330.00592070714382514133.148509828848
Winsorized Mean ( 20 / 24 )0.7827777777777780.00499695612442981156.650920737692
Winsorized Mean ( 21 / 24 )0.7798611111111110.00453422498633925171.994357020369
Winsorized Mean ( 22 / 24 )0.7798611111111110.00453422498633925171.994357020369
Winsorized Mean ( 23 / 24 )0.7766666666666670.00317092621846395244.933692289723
Winsorized Mean ( 24 / 24 )0.7766666666666670.00317092621846395244.933692289723
Trimmed Mean ( 1 / 24 )0.8092857142857140.011736092917128768.9569961656121
Trimmed Mean ( 2 / 24 )0.8067647058823530.011299345347781771.3992431464833
Trimmed Mean ( 3 / 24 )0.804393939393940.010879995517701873.9332969471528
Trimmed Mean ( 4 / 24 )0.8018750.010365050689391377.3633457307378
Trimmed Mean ( 5 / 24 )0.7993548387096770.0098826294727523480.884833425517
Trimmed Mean ( 6 / 24 )0.7968333333333330.0093503426526133685.2196933243536
Trimmed Mean ( 7 / 24 )0.7946551724137930.0089029706674495889.2573054653719
Trimmed Mean ( 8 / 24 )0.7926785714285710.008487925233417793.3889672246082
Trimmed Mean ( 9 / 24 )0.7905555555555560.008067745421686697.9896506687597
Trimmed Mean ( 10 / 24 )0.7890384615384620.00784108574080252100.62872510532
Trimmed Mean ( 11 / 24 )0.78740.0075474553084237104.326553496936
Trimmed Mean ( 12 / 24 )0.7860416666666670.00732805005928554107.264778530089
Trimmed Mean ( 13 / 24 )0.7847826086956520.00712035342467279110.216805527700
Trimmed Mean ( 14 / 24 )0.7834090909090910.00696520483663605112.474666471898
Trimmed Mean ( 15 / 24 )0.7819047619047620.0067495265480114115.845868053535
Trimmed Mean ( 16 / 24 )0.78050.00655303805057682119.105061496064
Trimmed Mean ( 17 / 24 )0.7789473684210530.00627476004408462124.139785895938
Trimmed Mean ( 18 / 24 )0.7772222222222220.00587719713878247132.243687572344
Trimmed Mean ( 19 / 24 )0.7752941176470590.00529411764705882146.444444444444
Trimmed Mean ( 20 / 24 )0.773750.00480989403679138160.866329711529
Trimmed Mean ( 21 / 24 )0.7726666666666670.00447042216457259172.839753880502
Trimmed Mean ( 22 / 24 )0.7717857142857140.00414848641450929186.040313784421
Trimmed Mean ( 23 / 24 )0.7707692307692310.00363415748031315212.090212090318
Trimmed Mean ( 24 / 24 )0.770.00345782037404063222.683632088216
Median0.765
Midrange0.895
Midmean - Weighted Average at Xnp0.78
Midmean - Weighted Average at X(n+1)p0.78
Midmean - Empirical Distribution Function0.78
Midmean - Empirical Distribution Function - Averaging0.78
Midmean - Empirical Distribution Function - Interpolation0.78
Midmean - Closest Observation0.78
Midmean - True Basic - Statistics Graphics Toolkit0.78
Midmean - MS Excel (old versions)0.78
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')