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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 28 Oct 2009 15:39:32 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/28/t1256766363fxv2rp650tn3kjy.htm/, Retrieved Tue, 07 May 2024 13:42:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51863, Retrieved Tue, 07 May 2024 13:42:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-28 21:39:32] [58d9ccda37eeb031a0ffa1e9ea016ece] [Current]
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Dataseries X:
4,26
4,26
4,07
4,26
4,4
4,46
4,34
4,18
4,11
3,98
3,85
3,66
3,59
3,57
3,76
3,6
3,43
3,26
3,3
3,31
3,14
3,3
3,49
3,39
3,37
3,54
3,7
3,96
4,03
4,02
4,04
3,92
3,79
3,83
3,76
3,82
4,06
4,11
4,01
4,22
4,34
4,64
4,62
4,44
4,39
4,42
4,28
4,41
4,25
4,23
4,23
4,37
4,51
4,84
4,85
4,58
4,56
4,46
4,26
3,87
4,13
4,24
4,03
3,93
4,03
4,12
3,92
3,77




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51863&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51863&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51863&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.02750.0487028288700782.6954017546828
Geometric Mean4.00722951528942
Harmonic Mean3.98641767526744
Quadratic Mean4.04718148112689
Winsorized Mean ( 1 / 22 )4.029117647058820.048215629624015983.564555279642
Winsorized Mean ( 2 / 22 )4.024411764705880.046618481393286686.326530689724
Winsorized Mean ( 3 / 22 )4.023529411764710.04644696613472686.6263126873322
Winsorized Mean ( 4 / 22 )4.021764705882350.04587120820952887.6751422703312
Winsorized Mean ( 5 / 22 )4.024705882352940.044611517245547190.2167451557516
Winsorized Mean ( 6 / 22 )4.022058823529410.043461687700599492.5426286074469
Winsorized Mean ( 7 / 22 )4.021029411764710.041743783324747896.3264249548947
Winsorized Mean ( 8 / 22 )4.028088235294120.040293729130481599.9681171789816
Winsorized Mean ( 9 / 22 )4.032058823529410.0385830909706152104.503260938845
Winsorized Mean ( 10 / 22 )4.033529411764710.0372942201221094108.154276951175
Winsorized Mean ( 11 / 22 )4.035147058823530.0364499564613483110.703755245974
Winsorized Mean ( 12 / 22 )4.035147058823530.0358598705816477112.525421686509
Winsorized Mean ( 13 / 22 )4.044705882352940.0335455808709835120.573434036182
Winsorized Mean ( 14 / 22 )4.048823529411760.0315306959234249128.408949147355
Winsorized Mean ( 15 / 22 )4.055441176470590.0284092704449403142.750627276065
Winsorized Mean ( 16 / 22 )4.055441176470590.0284092704449403142.750627276065
Winsorized Mean ( 17 / 22 )4.042941176470590.0258669341094992156.297656280258
Winsorized Mean ( 18 / 22 )4.042941176470590.0243241018858204166.211323873273
Winsorized Mean ( 19 / 22 )4.051323529411770.0230450797025555175.799935678353
Winsorized Mean ( 20 / 22 )4.054264705882350.0226069948234176179.336737923376
Winsorized Mean ( 21 / 22 )4.060441176470590.0217025888491144187.094784161489
Winsorized Mean ( 22 / 22 )4.063676470588240.0203307856060962199.877985500459
Trimmed Mean ( 1 / 22 )4.028484848484850.046666121753849486.3256833240603
Trimmed Mean ( 2 / 22 )4.02781250.044802514605546089.9014828846551
Trimmed Mean ( 3 / 22 )4.029677419354840.04359746143009292.4291756256583
Trimmed Mean ( 4 / 22 )4.0320.042210663498627395.5208865677063
Trimmed Mean ( 5 / 22 )4.0350.040733036693596999.0596412035808
Trimmed Mean ( 6 / 22 )4.03750.0393413714363583102.627332311772
Trimmed Mean ( 7 / 22 )4.040740740740740.0379597159048372106.448129139603
Trimmed Mean ( 8 / 22 )4.044423076923080.0367129970508249110.163250124310
Trimmed Mean ( 9 / 22 )4.04720.0355367472929539113.887744610843
Trimmed Mean ( 10 / 22 )4.049583333333330.0344806430604605117.445122071318
Trimmed Mean ( 11 / 22 )4.051956521739130.0334398581423634121.171462644630
Trimmed Mean ( 12 / 22 )4.054318181818180.0322916115133684125.553293620535
Trimmed Mean ( 13 / 22 )4.056904761904760.0309236219472525131.191125309473
Trimmed Mean ( 14 / 22 )4.05850.0297221103919935136.548177315608
Trimmed Mean ( 15 / 22 )4.059736842105260.0286303930910811141.798152375698
Trimmed Mean ( 16 / 22 )4.060277777777780.0279469057579942145.285414168484
Trimmed Mean ( 17 / 22 )4.060882352941180.0269625991934931150.611679675200
Trimmed Mean ( 18 / 22 )4.0631250.0262372761021045154.8607783898
Trimmed Mean ( 19 / 22 )4.065666666666670.0255814378346062158.930342107928
Trimmed Mean ( 20 / 22 )4.06750.0249635978362739162.937250739140
Trimmed Mean ( 21 / 22 )4.069230769230770.0241018548722712168.834755283186
Trimmed Mean ( 22 / 22 )4.070416666666670.0230428017515316176.645909232636
Median4.05
Midrange3.995
Midmean - Weighted Average at Xnp4.04416666666667
Midmean - Weighted Average at X(n+1)p4.06088235294118
Midmean - Empirical Distribution Function4.04416666666667
Midmean - Empirical Distribution Function - Averaging4.06088235294118
Midmean - Empirical Distribution Function - Interpolation4.06088235294118
Midmean - Closest Observation4.04416666666667
Midmean - True Basic - Statistics Graphics Toolkit4.06088235294118
Midmean - MS Excel (old versions)4.05973684210526
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.0275 & 0.04870282887007 & 82.6954017546828 \tabularnewline
Geometric Mean & 4.00722951528942 &  &  \tabularnewline
Harmonic Mean & 3.98641767526744 &  &  \tabularnewline
Quadratic Mean & 4.04718148112689 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 4.02911764705882 & 0.0482156296240159 & 83.564555279642 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 4.02441176470588 & 0.0466184813932866 & 86.326530689724 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 4.02352941176471 & 0.046446966134726 & 86.6263126873322 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 4.02176470588235 & 0.045871208209528 & 87.6751422703312 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 4.02470588235294 & 0.0446115172455471 & 90.2167451557516 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 4.02205882352941 & 0.0434616877005994 & 92.5426286074469 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 4.02102941176471 & 0.0417437833247478 & 96.3264249548947 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 4.02808823529412 & 0.0402937291304815 & 99.9681171789816 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 4.03205882352941 & 0.0385830909706152 & 104.503260938845 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 4.03352941176471 & 0.0372942201221094 & 108.154276951175 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 4.03514705882353 & 0.0364499564613483 & 110.703755245974 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 4.03514705882353 & 0.0358598705816477 & 112.525421686509 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 4.04470588235294 & 0.0335455808709835 & 120.573434036182 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 4.04882352941176 & 0.0315306959234249 & 128.408949147355 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 4.05544117647059 & 0.0284092704449403 & 142.750627276065 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 4.05544117647059 & 0.0284092704449403 & 142.750627276065 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 4.04294117647059 & 0.0258669341094992 & 156.297656280258 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 4.04294117647059 & 0.0243241018858204 & 166.211323873273 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 4.05132352941177 & 0.0230450797025555 & 175.799935678353 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 4.05426470588235 & 0.0226069948234176 & 179.336737923376 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 4.06044117647059 & 0.0217025888491144 & 187.094784161489 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 4.06367647058824 & 0.0203307856060962 & 199.877985500459 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 4.02848484848485 & 0.0466661217538494 & 86.3256833240603 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 4.0278125 & 0.0448025146055460 & 89.9014828846551 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 4.02967741935484 & 0.043597461430092 & 92.4291756256583 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 4.032 & 0.0422106634986273 & 95.5208865677063 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 4.035 & 0.0407330366935969 & 99.0596412035808 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 4.0375 & 0.0393413714363583 & 102.627332311772 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 4.04074074074074 & 0.0379597159048372 & 106.448129139603 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 4.04442307692308 & 0.0367129970508249 & 110.163250124310 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 4.0472 & 0.0355367472929539 & 113.887744610843 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 4.04958333333333 & 0.0344806430604605 & 117.445122071318 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 4.05195652173913 & 0.0334398581423634 & 121.171462644630 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 4.05431818181818 & 0.0322916115133684 & 125.553293620535 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 4.05690476190476 & 0.0309236219472525 & 131.191125309473 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 4.0585 & 0.0297221103919935 & 136.548177315608 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 4.05973684210526 & 0.0286303930910811 & 141.798152375698 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 4.06027777777778 & 0.0279469057579942 & 145.285414168484 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 4.06088235294118 & 0.0269625991934931 & 150.611679675200 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 4.063125 & 0.0262372761021045 & 154.8607783898 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 4.06566666666667 & 0.0255814378346062 & 158.930342107928 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 4.0675 & 0.0249635978362739 & 162.937250739140 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 4.06923076923077 & 0.0241018548722712 & 168.834755283186 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 4.07041666666667 & 0.0230428017515316 & 176.645909232636 \tabularnewline
Median & 4.05 &  &  \tabularnewline
Midrange & 3.995 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.04416666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.06088235294118 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.04416666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.06088235294118 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.06088235294118 &  &  \tabularnewline
Midmean - Closest Observation & 4.04416666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.06088235294118 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.05973684210526 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51863&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]4.0275[/C][C]0.04870282887007[/C][C]82.6954017546828[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.00722951528942[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.98641767526744[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.04718148112689[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]4.02911764705882[/C][C]0.0482156296240159[/C][C]83.564555279642[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]4.02441176470588[/C][C]0.0466184813932866[/C][C]86.326530689724[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]4.02352941176471[/C][C]0.046446966134726[/C][C]86.6263126873322[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]4.02176470588235[/C][C]0.045871208209528[/C][C]87.6751422703312[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]4.02470588235294[/C][C]0.0446115172455471[/C][C]90.2167451557516[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]4.02205882352941[/C][C]0.0434616877005994[/C][C]92.5426286074469[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]4.02102941176471[/C][C]0.0417437833247478[/C][C]96.3264249548947[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]4.02808823529412[/C][C]0.0402937291304815[/C][C]99.9681171789816[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]4.03205882352941[/C][C]0.0385830909706152[/C][C]104.503260938845[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]4.03352941176471[/C][C]0.0372942201221094[/C][C]108.154276951175[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]4.03514705882353[/C][C]0.0364499564613483[/C][C]110.703755245974[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]4.03514705882353[/C][C]0.0358598705816477[/C][C]112.525421686509[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]4.04470588235294[/C][C]0.0335455808709835[/C][C]120.573434036182[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]4.04882352941176[/C][C]0.0315306959234249[/C][C]128.408949147355[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]4.05544117647059[/C][C]0.0284092704449403[/C][C]142.750627276065[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]4.05544117647059[/C][C]0.0284092704449403[/C][C]142.750627276065[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]4.04294117647059[/C][C]0.0258669341094992[/C][C]156.297656280258[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]4.04294117647059[/C][C]0.0243241018858204[/C][C]166.211323873273[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]4.05132352941177[/C][C]0.0230450797025555[/C][C]175.799935678353[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]4.05426470588235[/C][C]0.0226069948234176[/C][C]179.336737923376[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]4.06044117647059[/C][C]0.0217025888491144[/C][C]187.094784161489[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]4.06367647058824[/C][C]0.0203307856060962[/C][C]199.877985500459[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]4.02848484848485[/C][C]0.0466661217538494[/C][C]86.3256833240603[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]4.0278125[/C][C]0.0448025146055460[/C][C]89.9014828846551[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]4.02967741935484[/C][C]0.043597461430092[/C][C]92.4291756256583[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]4.032[/C][C]0.0422106634986273[/C][C]95.5208865677063[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]4.035[/C][C]0.0407330366935969[/C][C]99.0596412035808[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]4.0375[/C][C]0.0393413714363583[/C][C]102.627332311772[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]4.04074074074074[/C][C]0.0379597159048372[/C][C]106.448129139603[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]4.04442307692308[/C][C]0.0367129970508249[/C][C]110.163250124310[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]4.0472[/C][C]0.0355367472929539[/C][C]113.887744610843[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]4.04958333333333[/C][C]0.0344806430604605[/C][C]117.445122071318[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]4.05195652173913[/C][C]0.0334398581423634[/C][C]121.171462644630[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]4.05431818181818[/C][C]0.0322916115133684[/C][C]125.553293620535[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]4.05690476190476[/C][C]0.0309236219472525[/C][C]131.191125309473[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]4.0585[/C][C]0.0297221103919935[/C][C]136.548177315608[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]4.05973684210526[/C][C]0.0286303930910811[/C][C]141.798152375698[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]4.06027777777778[/C][C]0.0279469057579942[/C][C]145.285414168484[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]4.06088235294118[/C][C]0.0269625991934931[/C][C]150.611679675200[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]4.063125[/C][C]0.0262372761021045[/C][C]154.8607783898[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]4.06566666666667[/C][C]0.0255814378346062[/C][C]158.930342107928[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]4.0675[/C][C]0.0249635978362739[/C][C]162.937250739140[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]4.06923076923077[/C][C]0.0241018548722712[/C][C]168.834755283186[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]4.07041666666667[/C][C]0.0230428017515316[/C][C]176.645909232636[/C][/ROW]
[ROW][C]Median[/C][C]4.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.995[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.04416666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.06088235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.04416666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.06088235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.06088235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.04416666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.06088235294118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.05973684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51863&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51863&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 Mean4.02750.0487028288700782.6954017546828
Geometric Mean4.00722951528942
Harmonic Mean3.98641767526744
Quadratic Mean4.04718148112689
Winsorized Mean ( 1 / 22 )4.029117647058820.048215629624015983.564555279642
Winsorized Mean ( 2 / 22 )4.024411764705880.046618481393286686.326530689724
Winsorized Mean ( 3 / 22 )4.023529411764710.04644696613472686.6263126873322
Winsorized Mean ( 4 / 22 )4.021764705882350.04587120820952887.6751422703312
Winsorized Mean ( 5 / 22 )4.024705882352940.044611517245547190.2167451557516
Winsorized Mean ( 6 / 22 )4.022058823529410.043461687700599492.5426286074469
Winsorized Mean ( 7 / 22 )4.021029411764710.041743783324747896.3264249548947
Winsorized Mean ( 8 / 22 )4.028088235294120.040293729130481599.9681171789816
Winsorized Mean ( 9 / 22 )4.032058823529410.0385830909706152104.503260938845
Winsorized Mean ( 10 / 22 )4.033529411764710.0372942201221094108.154276951175
Winsorized Mean ( 11 / 22 )4.035147058823530.0364499564613483110.703755245974
Winsorized Mean ( 12 / 22 )4.035147058823530.0358598705816477112.525421686509
Winsorized Mean ( 13 / 22 )4.044705882352940.0335455808709835120.573434036182
Winsorized Mean ( 14 / 22 )4.048823529411760.0315306959234249128.408949147355
Winsorized Mean ( 15 / 22 )4.055441176470590.0284092704449403142.750627276065
Winsorized Mean ( 16 / 22 )4.055441176470590.0284092704449403142.750627276065
Winsorized Mean ( 17 / 22 )4.042941176470590.0258669341094992156.297656280258
Winsorized Mean ( 18 / 22 )4.042941176470590.0243241018858204166.211323873273
Winsorized Mean ( 19 / 22 )4.051323529411770.0230450797025555175.799935678353
Winsorized Mean ( 20 / 22 )4.054264705882350.0226069948234176179.336737923376
Winsorized Mean ( 21 / 22 )4.060441176470590.0217025888491144187.094784161489
Winsorized Mean ( 22 / 22 )4.063676470588240.0203307856060962199.877985500459
Trimmed Mean ( 1 / 22 )4.028484848484850.046666121753849486.3256833240603
Trimmed Mean ( 2 / 22 )4.02781250.044802514605546089.9014828846551
Trimmed Mean ( 3 / 22 )4.029677419354840.04359746143009292.4291756256583
Trimmed Mean ( 4 / 22 )4.0320.042210663498627395.5208865677063
Trimmed Mean ( 5 / 22 )4.0350.040733036693596999.0596412035808
Trimmed Mean ( 6 / 22 )4.03750.0393413714363583102.627332311772
Trimmed Mean ( 7 / 22 )4.040740740740740.0379597159048372106.448129139603
Trimmed Mean ( 8 / 22 )4.044423076923080.0367129970508249110.163250124310
Trimmed Mean ( 9 / 22 )4.04720.0355367472929539113.887744610843
Trimmed Mean ( 10 / 22 )4.049583333333330.0344806430604605117.445122071318
Trimmed Mean ( 11 / 22 )4.051956521739130.0334398581423634121.171462644630
Trimmed Mean ( 12 / 22 )4.054318181818180.0322916115133684125.553293620535
Trimmed Mean ( 13 / 22 )4.056904761904760.0309236219472525131.191125309473
Trimmed Mean ( 14 / 22 )4.05850.0297221103919935136.548177315608
Trimmed Mean ( 15 / 22 )4.059736842105260.0286303930910811141.798152375698
Trimmed Mean ( 16 / 22 )4.060277777777780.0279469057579942145.285414168484
Trimmed Mean ( 17 / 22 )4.060882352941180.0269625991934931150.611679675200
Trimmed Mean ( 18 / 22 )4.0631250.0262372761021045154.8607783898
Trimmed Mean ( 19 / 22 )4.065666666666670.0255814378346062158.930342107928
Trimmed Mean ( 20 / 22 )4.06750.0249635978362739162.937250739140
Trimmed Mean ( 21 / 22 )4.069230769230770.0241018548722712168.834755283186
Trimmed Mean ( 22 / 22 )4.070416666666670.0230428017515316176.645909232636
Median4.05
Midrange3.995
Midmean - Weighted Average at Xnp4.04416666666667
Midmean - Weighted Average at X(n+1)p4.06088235294118
Midmean - Empirical Distribution Function4.04416666666667
Midmean - Empirical Distribution Function - Averaging4.06088235294118
Midmean - Empirical Distribution Function - Interpolation4.06088235294118
Midmean - Closest Observation4.04416666666667
Midmean - True Basic - Statistics Graphics Toolkit4.06088235294118
Midmean - MS Excel (old versions)4.05973684210526
Number of observations68



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')