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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 computationSat, 05 Mar 2016 13:02:13 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/05/t1457182969ph9gwz98zoyn05o.htm/, Retrieved Sat, 27 Apr 2024 07:54:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293464, Retrieved Sat, 27 Apr 2024 07:54:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opdracht 5/oef2/s...] [2016-03-05 13:02:13] [efea2b8bc7c91838390b884e612c3e3f] [Current]
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Dataseries X:
92,94
92,97
93,37
92,6
92,84
92,55
92,93
92,44
93,36
93,24
92,65
92,06
92,88
91,69
91,66
90,26
91,11
92,33
91,82
92,24
93,35
93,53
93,34
92,59
92,42
92,64
94,44
93,59
93,39
93,33
93,72
95,43
97,06
97,7
97,59
96,97
97,75
99,27
100,63
99,8
99,5
99,72
99,77
100,18
101,11
100,67
101,13
100,46
101,6
102,3
103,26
104,56
104,61
104,62
105,03
104,93
104,73
104,33
104,6
104,41
104,63
105,55
106,12
106,62
106,72
106,52
106,79
106,95
106,92
106,74
108,13
107,86




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=293464&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=293464&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293464&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 Mean98.43819444444440.670512041462377146.810479689152
Geometric Mean98.2772610105438
Harmonic Mean98.1177963447007
Quadratic Mean98.6001965501196
Winsorized Mean ( 1 / 24 )98.446250.667830540313273147.412021549389
Winsorized Mean ( 2 / 24 )98.436250.660740693750532148.978640079289
Winsorized Mean ( 3 / 24 )98.436250.660333961291007149.070403417612
Winsorized Mean ( 4 / 24 )98.436250.658003763631968149.598308460523
Winsorized Mean ( 5 / 24 )98.44944444444440.655058769087243150.291010654851
Winsorized Mean ( 6 / 24 )98.46277777777780.652724284426237150.848957403706
Winsorized Mean ( 7 / 24 )98.46180555555560.649829679334163151.519403755832
Winsorized Mean ( 8 / 24 )98.46069444444440.646549476530659152.286403467184
Winsorized Mean ( 9 / 24 )98.41319444444440.637573765298376154.355777795199
Winsorized Mean ( 10 / 24 )98.34930555555550.622370378130178158.02375725373
Winsorized Mean ( 11 / 24 )98.27597222222220.608885775901809161.402969344566
Winsorized Mean ( 12 / 24 )98.26097222222220.60607307801038162.127267795484
Winsorized Mean ( 13 / 24 )98.23208333333330.599569092053887163.837803908185
Winsorized Mean ( 14 / 24 )98.21458333333330.596356469104971164.691067208069
Winsorized Mean ( 15 / 24 )98.25208333333330.590886046487383166.27924101002
Winsorized Mean ( 16 / 24 )98.258750.589404155822324166.708614164608
Winsorized Mean ( 17 / 24 )98.26819444444440.587531716800741167.255982331541
Winsorized Mean ( 18 / 24 )98.26069444444450.585695463123817167.767552646506
Winsorized Mean ( 19 / 24 )98.22902777777780.57870684315789169.73883917073
Winsorized Mean ( 20 / 24 )98.28180555555550.56585585898275173.686998191092
Winsorized Mean ( 21 / 24 )97.99597222222220.516604670660391189.692385275865
Winsorized Mean ( 22 / 24 )97.70569444444440.475144645894549205.633579771261
Winsorized Mean ( 23 / 24 )97.48527777777780.444917172059075219.108822720005
Winsorized Mean ( 24 / 24 )97.33194444444440.424394332257517229.34317696162
Trimmed Mean ( 1 / 24 )98.41657142857140.665232252464519147.943174829486
Trimmed Mean ( 2 / 24 )98.38514705882350.661696196580598148.686281661043
Trimmed Mean ( 3 / 24 )98.35727272727270.661313926471536148.730079301462
Trimmed Mean ( 4 / 24 )98.327656250.660376378603922148.89638611525
Trimmed Mean ( 5 / 24 )98.29612903225810.659374988696568149.074700613936
Trimmed Mean ( 6 / 24 )98.25933333333330.658291525526524149.264162643963
Trimmed Mean ( 7 / 24 )98.21724137931040.656793103241826149.540610116832
Trimmed Mean ( 8 / 24 )98.17232142857140.654840616628548149.917886789021
Trimmed Mean ( 9 / 24 )98.12425925925930.652323782634105150.422630404537
Trimmed Mean ( 10 / 24 )98.07980769230770.650301849531522150.821972539313
Trimmed Mean ( 11 / 24 )98.0410.649977409340556150.837550030345
Trimmed Mean ( 12 / 24 )98.00895833333330.651118870599681150.52391008583
Trimmed Mean ( 13 / 24 )97.97608695652170.651730100197517150.332303091155
Trimmed Mean ( 14 / 24 )97.94386363636360.652326314916115150.14550447648
Trimmed Mean ( 15 / 24 )97.91071428571430.652132425723696150.139312850544
Trimmed Mean ( 16 / 24 )97.869750.651198450147387150.291742828701
Trimmed Mean ( 17 / 24 )97.82368421052630.648405136186764150.868151331777
Trimmed Mean ( 18 / 24 )97.77138888888890.643131247902183152.024006309455
Trimmed Mean ( 19 / 24 )97.71382352941180.634438150907755154.01631095104
Trimmed Mean ( 20 / 24 )97.65281250.622297744441433156.922973564129
Trimmed Mean ( 21 / 24 )97.57733333333330.606410000018639160.9098354749
Trimmed Mean ( 22 / 24 )97.52607142857140.597084703093437163.337079183738
Trimmed Mean ( 23 / 24 )97.50346153846150.593807516678515164.200450145614
Trimmed Mean ( 24 / 24 )97.50583333333330.594604032372813163.98448046884
Median97.725
Midrange99.195
Midmean - Weighted Average at Xnp97.6405405405405
Midmean - Weighted Average at X(n+1)p97.7713888888889
Midmean - Empirical Distribution Function97.6405405405405
Midmean - Empirical Distribution Function - Averaging97.7713888888889
Midmean - Empirical Distribution Function - Interpolation97.7713888888889
Midmean - Closest Observation97.6405405405405
Midmean - True Basic - Statistics Graphics Toolkit97.7713888888889
Midmean - MS Excel (old versions)97.8236842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.4381944444444 & 0.670512041462377 & 146.810479689152 \tabularnewline
Geometric Mean & 98.2772610105438 &  &  \tabularnewline
Harmonic Mean & 98.1177963447007 &  &  \tabularnewline
Quadratic Mean & 98.6001965501196 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.44625 & 0.667830540313273 & 147.412021549389 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.43625 & 0.660740693750532 & 148.978640079289 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.43625 & 0.660333961291007 & 149.070403417612 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.43625 & 0.658003763631968 & 149.598308460523 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.4494444444444 & 0.655058769087243 & 150.291010654851 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.4627777777778 & 0.652724284426237 & 150.848957403706 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.4618055555556 & 0.649829679334163 & 151.519403755832 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.4606944444444 & 0.646549476530659 & 152.286403467184 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.4131944444444 & 0.637573765298376 & 154.355777795199 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.3493055555555 & 0.622370378130178 & 158.02375725373 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.2759722222222 & 0.608885775901809 & 161.402969344566 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.2609722222222 & 0.60607307801038 & 162.127267795484 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.2320833333333 & 0.599569092053887 & 163.837803908185 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.2145833333333 & 0.596356469104971 & 164.691067208069 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.2520833333333 & 0.590886046487383 & 166.27924101002 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.25875 & 0.589404155822324 & 166.708614164608 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.2681944444444 & 0.587531716800741 & 167.255982331541 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.2606944444445 & 0.585695463123817 & 167.767552646506 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.2290277777778 & 0.57870684315789 & 169.73883917073 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.2818055555555 & 0.56585585898275 & 173.686998191092 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.9959722222222 & 0.516604670660391 & 189.692385275865 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.7056944444444 & 0.475144645894549 & 205.633579771261 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.4852777777778 & 0.444917172059075 & 219.108822720005 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.3319444444444 & 0.424394332257517 & 229.34317696162 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.4165714285714 & 0.665232252464519 & 147.943174829486 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 98.3851470588235 & 0.661696196580598 & 148.686281661043 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.3572727272727 & 0.661313926471536 & 148.730079301462 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.32765625 & 0.660376378603922 & 148.89638611525 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.2961290322581 & 0.659374988696568 & 149.074700613936 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.2593333333333 & 0.658291525526524 & 149.264162643963 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.2172413793104 & 0.656793103241826 & 149.540610116832 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.1723214285714 & 0.654840616628548 & 149.917886789021 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.1242592592593 & 0.652323782634105 & 150.422630404537 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.0798076923077 & 0.650301849531522 & 150.821972539313 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.041 & 0.649977409340556 & 150.837550030345 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.0089583333333 & 0.651118870599681 & 150.52391008583 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.9760869565217 & 0.651730100197517 & 150.332303091155 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.9438636363636 & 0.652326314916115 & 150.14550447648 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.9107142857143 & 0.652132425723696 & 150.139312850544 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.86975 & 0.651198450147387 & 150.291742828701 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.8236842105263 & 0.648405136186764 & 150.868151331777 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.7713888888889 & 0.643131247902183 & 152.024006309455 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.7138235294118 & 0.634438150907755 & 154.01631095104 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.6528125 & 0.622297744441433 & 156.922973564129 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.5773333333333 & 0.606410000018639 & 160.9098354749 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.5260714285714 & 0.597084703093437 & 163.337079183738 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.5034615384615 & 0.593807516678515 & 164.200450145614 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.5058333333333 & 0.594604032372813 & 163.98448046884 \tabularnewline
Median & 97.725 &  &  \tabularnewline
Midrange & 99.195 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.6405405405405 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.7713888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.6405405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.7713888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.7713888888889 &  &  \tabularnewline
Midmean - Closest Observation & 97.6405405405405 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.7713888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.8236842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293464&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]98.4381944444444[/C][C]0.670512041462377[/C][C]146.810479689152[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.2772610105438[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.1177963447007[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.6001965501196[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.44625[/C][C]0.667830540313273[/C][C]147.412021549389[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.43625[/C][C]0.660740693750532[/C][C]148.978640079289[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.43625[/C][C]0.660333961291007[/C][C]149.070403417612[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.43625[/C][C]0.658003763631968[/C][C]149.598308460523[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.4494444444444[/C][C]0.655058769087243[/C][C]150.291010654851[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.4627777777778[/C][C]0.652724284426237[/C][C]150.848957403706[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.4618055555556[/C][C]0.649829679334163[/C][C]151.519403755832[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.4606944444444[/C][C]0.646549476530659[/C][C]152.286403467184[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.4131944444444[/C][C]0.637573765298376[/C][C]154.355777795199[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.3493055555555[/C][C]0.622370378130178[/C][C]158.02375725373[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.2759722222222[/C][C]0.608885775901809[/C][C]161.402969344566[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.2609722222222[/C][C]0.60607307801038[/C][C]162.127267795484[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.2320833333333[/C][C]0.599569092053887[/C][C]163.837803908185[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.2145833333333[/C][C]0.596356469104971[/C][C]164.691067208069[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.2520833333333[/C][C]0.590886046487383[/C][C]166.27924101002[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.25875[/C][C]0.589404155822324[/C][C]166.708614164608[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.2681944444444[/C][C]0.587531716800741[/C][C]167.255982331541[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.2606944444445[/C][C]0.585695463123817[/C][C]167.767552646506[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.2290277777778[/C][C]0.57870684315789[/C][C]169.73883917073[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.2818055555555[/C][C]0.56585585898275[/C][C]173.686998191092[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.9959722222222[/C][C]0.516604670660391[/C][C]189.692385275865[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.7056944444444[/C][C]0.475144645894549[/C][C]205.633579771261[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.4852777777778[/C][C]0.444917172059075[/C][C]219.108822720005[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.3319444444444[/C][C]0.424394332257517[/C][C]229.34317696162[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.4165714285714[/C][C]0.665232252464519[/C][C]147.943174829486[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]98.3851470588235[/C][C]0.661696196580598[/C][C]148.686281661043[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.3572727272727[/C][C]0.661313926471536[/C][C]148.730079301462[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.32765625[/C][C]0.660376378603922[/C][C]148.89638611525[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.2961290322581[/C][C]0.659374988696568[/C][C]149.074700613936[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.2593333333333[/C][C]0.658291525526524[/C][C]149.264162643963[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.2172413793104[/C][C]0.656793103241826[/C][C]149.540610116832[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.1723214285714[/C][C]0.654840616628548[/C][C]149.917886789021[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.1242592592593[/C][C]0.652323782634105[/C][C]150.422630404537[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.0798076923077[/C][C]0.650301849531522[/C][C]150.821972539313[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.041[/C][C]0.649977409340556[/C][C]150.837550030345[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.0089583333333[/C][C]0.651118870599681[/C][C]150.52391008583[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.9760869565217[/C][C]0.651730100197517[/C][C]150.332303091155[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.9438636363636[/C][C]0.652326314916115[/C][C]150.14550447648[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.9107142857143[/C][C]0.652132425723696[/C][C]150.139312850544[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.86975[/C][C]0.651198450147387[/C][C]150.291742828701[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.8236842105263[/C][C]0.648405136186764[/C][C]150.868151331777[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.7713888888889[/C][C]0.643131247902183[/C][C]152.024006309455[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.7138235294118[/C][C]0.634438150907755[/C][C]154.01631095104[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.6528125[/C][C]0.622297744441433[/C][C]156.922973564129[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.5773333333333[/C][C]0.606410000018639[/C][C]160.9098354749[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.5260714285714[/C][C]0.597084703093437[/C][C]163.337079183738[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.5034615384615[/C][C]0.593807516678515[/C][C]164.200450145614[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.5058333333333[/C][C]0.594604032372813[/C][C]163.98448046884[/C][/ROW]
[ROW][C]Median[/C][C]97.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.195[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.6405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.7713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.6405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.7713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.7713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.6405405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.7713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.8236842105263[/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=293464&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293464&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 Mean98.43819444444440.670512041462377146.810479689152
Geometric Mean98.2772610105438
Harmonic Mean98.1177963447007
Quadratic Mean98.6001965501196
Winsorized Mean ( 1 / 24 )98.446250.667830540313273147.412021549389
Winsorized Mean ( 2 / 24 )98.436250.660740693750532148.978640079289
Winsorized Mean ( 3 / 24 )98.436250.660333961291007149.070403417612
Winsorized Mean ( 4 / 24 )98.436250.658003763631968149.598308460523
Winsorized Mean ( 5 / 24 )98.44944444444440.655058769087243150.291010654851
Winsorized Mean ( 6 / 24 )98.46277777777780.652724284426237150.848957403706
Winsorized Mean ( 7 / 24 )98.46180555555560.649829679334163151.519403755832
Winsorized Mean ( 8 / 24 )98.46069444444440.646549476530659152.286403467184
Winsorized Mean ( 9 / 24 )98.41319444444440.637573765298376154.355777795199
Winsorized Mean ( 10 / 24 )98.34930555555550.622370378130178158.02375725373
Winsorized Mean ( 11 / 24 )98.27597222222220.608885775901809161.402969344566
Winsorized Mean ( 12 / 24 )98.26097222222220.60607307801038162.127267795484
Winsorized Mean ( 13 / 24 )98.23208333333330.599569092053887163.837803908185
Winsorized Mean ( 14 / 24 )98.21458333333330.596356469104971164.691067208069
Winsorized Mean ( 15 / 24 )98.25208333333330.590886046487383166.27924101002
Winsorized Mean ( 16 / 24 )98.258750.589404155822324166.708614164608
Winsorized Mean ( 17 / 24 )98.26819444444440.587531716800741167.255982331541
Winsorized Mean ( 18 / 24 )98.26069444444450.585695463123817167.767552646506
Winsorized Mean ( 19 / 24 )98.22902777777780.57870684315789169.73883917073
Winsorized Mean ( 20 / 24 )98.28180555555550.56585585898275173.686998191092
Winsorized Mean ( 21 / 24 )97.99597222222220.516604670660391189.692385275865
Winsorized Mean ( 22 / 24 )97.70569444444440.475144645894549205.633579771261
Winsorized Mean ( 23 / 24 )97.48527777777780.444917172059075219.108822720005
Winsorized Mean ( 24 / 24 )97.33194444444440.424394332257517229.34317696162
Trimmed Mean ( 1 / 24 )98.41657142857140.665232252464519147.943174829486
Trimmed Mean ( 2 / 24 )98.38514705882350.661696196580598148.686281661043
Trimmed Mean ( 3 / 24 )98.35727272727270.661313926471536148.730079301462
Trimmed Mean ( 4 / 24 )98.327656250.660376378603922148.89638611525
Trimmed Mean ( 5 / 24 )98.29612903225810.659374988696568149.074700613936
Trimmed Mean ( 6 / 24 )98.25933333333330.658291525526524149.264162643963
Trimmed Mean ( 7 / 24 )98.21724137931040.656793103241826149.540610116832
Trimmed Mean ( 8 / 24 )98.17232142857140.654840616628548149.917886789021
Trimmed Mean ( 9 / 24 )98.12425925925930.652323782634105150.422630404537
Trimmed Mean ( 10 / 24 )98.07980769230770.650301849531522150.821972539313
Trimmed Mean ( 11 / 24 )98.0410.649977409340556150.837550030345
Trimmed Mean ( 12 / 24 )98.00895833333330.651118870599681150.52391008583
Trimmed Mean ( 13 / 24 )97.97608695652170.651730100197517150.332303091155
Trimmed Mean ( 14 / 24 )97.94386363636360.652326314916115150.14550447648
Trimmed Mean ( 15 / 24 )97.91071428571430.652132425723696150.139312850544
Trimmed Mean ( 16 / 24 )97.869750.651198450147387150.291742828701
Trimmed Mean ( 17 / 24 )97.82368421052630.648405136186764150.868151331777
Trimmed Mean ( 18 / 24 )97.77138888888890.643131247902183152.024006309455
Trimmed Mean ( 19 / 24 )97.71382352941180.634438150907755154.01631095104
Trimmed Mean ( 20 / 24 )97.65281250.622297744441433156.922973564129
Trimmed Mean ( 21 / 24 )97.57733333333330.606410000018639160.9098354749
Trimmed Mean ( 22 / 24 )97.52607142857140.597084703093437163.337079183738
Trimmed Mean ( 23 / 24 )97.50346153846150.593807516678515164.200450145614
Trimmed Mean ( 24 / 24 )97.50583333333330.594604032372813163.98448046884
Median97.725
Midrange99.195
Midmean - Weighted Average at Xnp97.6405405405405
Midmean - Weighted Average at X(n+1)p97.7713888888889
Midmean - Empirical Distribution Function97.6405405405405
Midmean - Empirical Distribution Function - Averaging97.7713888888889
Midmean - Empirical Distribution Function - Interpolation97.7713888888889
Midmean - Closest Observation97.6405405405405
Midmean - True Basic - Statistics Graphics Toolkit97.7713888888889
Midmean - MS Excel (old versions)97.8236842105263
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')