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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 10:53:31 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444384450t63eu7qa0boau1a.htm/, Retrieved Mon, 13 May 2024 23:50:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281786, Retrieved Mon, 13 May 2024 23:50:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 09:53:31] [f03ff3651993e75eb8cd64bbe7aa965c] [Current]
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Dataseries X:
93,58
95,79
94,77
94,2
96,23
92,3
88,86
86,44
86,21
88,57
90,69
89
86,88
90,65
90,68
89,64
102,62
101,84
92,51
94,29
94,68
96,94
94,03
89,65
84,9
89,07
89,8
93,22
92,23
98,41
96,63
89,8
90
92,13
93,27
90,81
85,42
88,28
88,73
90,18
92,74
96,13
94,85
94,25
96,94
101,22
98,71
95,51
93,91
98,17
97,59
99,64
107,88
108,49
100,25
99,27
101,73
101,25
97,09
94,74
94,53
93,48
96,05
106,22
98,33
99,86
93,78
88,96
83,77
89,46
86,78
88,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281786&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281786&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.94319444444440.628340363915938149.510042390039
Geometric Mean93.7963408230052
Harmonic Mean93.6517333363581
Quadratic Mean94.0922707077709
Winsorized Mean ( 1 / 24 )93.95041666666670.62222524709156150.991007044177
Winsorized Mean ( 2 / 24 )93.918750.605440608885881155.124629272601
Winsorized Mean ( 3 / 24 )93.80166666666670.560784926651307167.268523472622
Winsorized Mean ( 4 / 24 )93.77111111111110.549078633420581170.779020350779
Winsorized Mean ( 5 / 24 )93.78708333333330.54313576283117172.677053789379
Winsorized Mean ( 6 / 24 )93.75541666666670.533544630147427175.721788523596
Winsorized Mean ( 7 / 24 )93.88861111111110.510027666006618184.085329814036
Winsorized Mean ( 8 / 24 )93.79416666666670.486963048457868192.610439259606
Winsorized Mean ( 9 / 24 )93.76666666666670.474706976581368197.525360469596
Winsorized Mean ( 10 / 24 )93.75833333333330.465824903129477201.273767682775
Winsorized Mean ( 11 / 24 )93.72166666666670.452908484643044206.932901114742
Winsorized Mean ( 12 / 24 )93.6450.434664576667691215.44198682561
Winsorized Mean ( 13 / 24 )93.59805555555550.424798517963749220.335174435667
Winsorized Mean ( 14 / 24 )93.59611111111110.42025374049363222.713332667005
Winsorized Mean ( 15 / 24 )93.64402777777780.402862588542729232.446572208443
Winsorized Mean ( 16 / 24 )93.55513888888890.377086941624401248.099651729852
Winsorized Mean ( 17 / 24 )93.43944444444440.359387514146348259.996357042038
Winsorized Mean ( 18 / 24 )93.43944444444440.348509226705606268.111823975826
Winsorized Mean ( 19 / 24 )93.43944444444440.348509226705606268.111823975825
Winsorized Mean ( 20 / 24 )93.40888888888890.32831584970225284.509227847518
Winsorized Mean ( 21 / 24 )93.34472222222220.304789363386804306.259776210628
Winsorized Mean ( 22 / 24 )93.45777777777780.280043397474013333.726053250195
Winsorized Mean ( 23 / 24 )93.44180555555550.275267001296369339.458798604598
Winsorized Mean ( 24 / 24 )93.35847222222220.263372750639526354.472784278281
Trimmed Mean ( 1 / 24 )93.88071428571430.593773814261136158.10854576424
Trimmed Mean ( 2 / 24 )93.80691176470590.559438263089544167.680543062338
Trimmed Mean ( 3 / 24 )93.74590909090910.529155987915203177.161198648161
Trimmed Mean ( 4 / 24 )93.7250.514101398574127182.308393363544
Trimmed Mean ( 5 / 24 )93.71161290322580.500323279601795187.302123894396
Trimmed Mean ( 6 / 24 )93.69350.485484662316569192.989618977717
Trimmed Mean ( 7 / 24 )93.68068965517240.470171215295037199.248032647823
Trimmed Mean ( 8 / 24 )93.64250.457526257141627204.671313478328
Trimmed Mean ( 9 / 24 )93.61722222222220.447666472060746209.122701977822
Trimmed Mean ( 10 / 24 )93.59423076923080.438135734713249213.619258494143
Trimmed Mean ( 11 / 24 )93.57060.428021400380487218.611966403598
Trimmed Mean ( 12 / 24 )93.550.417986774028092223.810909370335
Trimmed Mean ( 13 / 24 )93.53760869565220.409106270495462228.638902509048
Trimmed Mean ( 14 / 24 )93.530.399602736130578234.057456427018
Trimmed Mean ( 15 / 24 )93.52190476190480.387960993719125241.060071182343
Trimmed Mean ( 16 / 24 )93.507250.376447801315647248.393667523629
Trimmed Mean ( 17 / 24 )93.50157894736840.367071476544712254.723085071905
Trimmed Mean ( 18 / 24 )93.50888888888890.35827314616967260.998877221474
Trimmed Mean ( 19 / 24 )93.51705882352940.348414419532663268.407544524036
Trimmed Mean ( 20 / 24 )93.526250.334004825998551280.014666615643
Trimmed Mean ( 21 / 24 )93.54033333333330.319109927131497293.12887309453
Trimmed Mean ( 22 / 24 )93.56428571428570.304400889845074307.371919188231
Trimmed Mean ( 23 / 24 )93.57769230769230.290808585045378321.784490279372
Trimmed Mean ( 24 / 24 )93.59541666666670.270713616238468345.735903377021
Median93.845
Midrange96.13
Midmean - Weighted Average at Xnp93.4045945945946
Midmean - Weighted Average at X(n+1)p93.5088888888889
Midmean - Empirical Distribution Function93.4045945945946
Midmean - Empirical Distribution Function - Averaging93.5088888888889
Midmean - Empirical Distribution Function - Interpolation93.5088888888889
Midmean - Closest Observation93.4045945945946
Midmean - True Basic - Statistics Graphics Toolkit93.5088888888889
Midmean - MS Excel (old versions)93.5015789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93.9431944444444 & 0.628340363915938 & 149.510042390039 \tabularnewline
Geometric Mean & 93.7963408230052 &  &  \tabularnewline
Harmonic Mean & 93.6517333363581 &  &  \tabularnewline
Quadratic Mean & 94.0922707077709 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 93.9504166666667 & 0.62222524709156 & 150.991007044177 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 93.91875 & 0.605440608885881 & 155.124629272601 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 93.8016666666667 & 0.560784926651307 & 167.268523472622 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 93.7711111111111 & 0.549078633420581 & 170.779020350779 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 93.7870833333333 & 0.54313576283117 & 172.677053789379 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 93.7554166666667 & 0.533544630147427 & 175.721788523596 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 93.8886111111111 & 0.510027666006618 & 184.085329814036 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 93.7941666666667 & 0.486963048457868 & 192.610439259606 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 93.7666666666667 & 0.474706976581368 & 197.525360469596 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 93.7583333333333 & 0.465824903129477 & 201.273767682775 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 93.7216666666667 & 0.452908484643044 & 206.932901114742 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 93.645 & 0.434664576667691 & 215.44198682561 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 93.5980555555555 & 0.424798517963749 & 220.335174435667 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 93.5961111111111 & 0.42025374049363 & 222.713332667005 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 93.6440277777778 & 0.402862588542729 & 232.446572208443 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 93.5551388888889 & 0.377086941624401 & 248.099651729852 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 93.4394444444444 & 0.359387514146348 & 259.996357042038 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 93.4394444444444 & 0.348509226705606 & 268.111823975826 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 93.4394444444444 & 0.348509226705606 & 268.111823975825 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 93.4088888888889 & 0.32831584970225 & 284.509227847518 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 93.3447222222222 & 0.304789363386804 & 306.259776210628 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 93.4577777777778 & 0.280043397474013 & 333.726053250195 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 93.4418055555555 & 0.275267001296369 & 339.458798604598 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 93.3584722222222 & 0.263372750639526 & 354.472784278281 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 93.8807142857143 & 0.593773814261136 & 158.10854576424 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.8069117647059 & 0.559438263089544 & 167.680543062338 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.7459090909091 & 0.529155987915203 & 177.161198648161 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.725 & 0.514101398574127 & 182.308393363544 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 93.7116129032258 & 0.500323279601795 & 187.302123894396 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 93.6935 & 0.485484662316569 & 192.989618977717 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 93.6806896551724 & 0.470171215295037 & 199.248032647823 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 93.6425 & 0.457526257141627 & 204.671313478328 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 93.6172222222222 & 0.447666472060746 & 209.122701977822 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 93.5942307692308 & 0.438135734713249 & 213.619258494143 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 93.5706 & 0.428021400380487 & 218.611966403598 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 93.55 & 0.417986774028092 & 223.810909370335 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 93.5376086956522 & 0.409106270495462 & 228.638902509048 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 93.53 & 0.399602736130578 & 234.057456427018 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 93.5219047619048 & 0.387960993719125 & 241.060071182343 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 93.50725 & 0.376447801315647 & 248.393667523629 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 93.5015789473684 & 0.367071476544712 & 254.723085071905 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 93.5088888888889 & 0.35827314616967 & 260.998877221474 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 93.5170588235294 & 0.348414419532663 & 268.407544524036 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 93.52625 & 0.334004825998551 & 280.014666615643 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 93.5403333333333 & 0.319109927131497 & 293.12887309453 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 93.5642857142857 & 0.304400889845074 & 307.371919188231 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 93.5776923076923 & 0.290808585045378 & 321.784490279372 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 93.5954166666667 & 0.270713616238468 & 345.735903377021 \tabularnewline
Median & 93.845 &  &  \tabularnewline
Midrange & 96.13 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 93.4045945945946 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93.5088888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 93.4045945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93.5088888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93.5088888888889 &  &  \tabularnewline
Midmean - Closest Observation & 93.4045945945946 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93.5088888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93.5015789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281786&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]93.9431944444444[/C][C]0.628340363915938[/C][C]149.510042390039[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.7963408230052[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]93.6517333363581[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]94.0922707077709[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]93.9504166666667[/C][C]0.62222524709156[/C][C]150.991007044177[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]93.91875[/C][C]0.605440608885881[/C][C]155.124629272601[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]93.8016666666667[/C][C]0.560784926651307[/C][C]167.268523472622[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]93.7711111111111[/C][C]0.549078633420581[/C][C]170.779020350779[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]93.7870833333333[/C][C]0.54313576283117[/C][C]172.677053789379[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]93.7554166666667[/C][C]0.533544630147427[/C][C]175.721788523596[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]93.8886111111111[/C][C]0.510027666006618[/C][C]184.085329814036[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]93.7941666666667[/C][C]0.486963048457868[/C][C]192.610439259606[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]93.7666666666667[/C][C]0.474706976581368[/C][C]197.525360469596[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]93.7583333333333[/C][C]0.465824903129477[/C][C]201.273767682775[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]93.7216666666667[/C][C]0.452908484643044[/C][C]206.932901114742[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]93.645[/C][C]0.434664576667691[/C][C]215.44198682561[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]93.5980555555555[/C][C]0.424798517963749[/C][C]220.335174435667[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]93.5961111111111[/C][C]0.42025374049363[/C][C]222.713332667005[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]93.6440277777778[/C][C]0.402862588542729[/C][C]232.446572208443[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]93.5551388888889[/C][C]0.377086941624401[/C][C]248.099651729852[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]93.4394444444444[/C][C]0.359387514146348[/C][C]259.996357042038[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]93.4394444444444[/C][C]0.348509226705606[/C][C]268.111823975826[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]93.4394444444444[/C][C]0.348509226705606[/C][C]268.111823975825[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]93.4088888888889[/C][C]0.32831584970225[/C][C]284.509227847518[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]93.3447222222222[/C][C]0.304789363386804[/C][C]306.259776210628[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]93.4577777777778[/C][C]0.280043397474013[/C][C]333.726053250195[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]93.4418055555555[/C][C]0.275267001296369[/C][C]339.458798604598[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]93.3584722222222[/C][C]0.263372750639526[/C][C]354.472784278281[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]93.8807142857143[/C][C]0.593773814261136[/C][C]158.10854576424[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.8069117647059[/C][C]0.559438263089544[/C][C]167.680543062338[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.7459090909091[/C][C]0.529155987915203[/C][C]177.161198648161[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.725[/C][C]0.514101398574127[/C][C]182.308393363544[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]93.7116129032258[/C][C]0.500323279601795[/C][C]187.302123894396[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]93.6935[/C][C]0.485484662316569[/C][C]192.989618977717[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]93.6806896551724[/C][C]0.470171215295037[/C][C]199.248032647823[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]93.6425[/C][C]0.457526257141627[/C][C]204.671313478328[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]93.6172222222222[/C][C]0.447666472060746[/C][C]209.122701977822[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]93.5942307692308[/C][C]0.438135734713249[/C][C]213.619258494143[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]93.5706[/C][C]0.428021400380487[/C][C]218.611966403598[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]93.55[/C][C]0.417986774028092[/C][C]223.810909370335[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]93.5376086956522[/C][C]0.409106270495462[/C][C]228.638902509048[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]93.53[/C][C]0.399602736130578[/C][C]234.057456427018[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]93.5219047619048[/C][C]0.387960993719125[/C][C]241.060071182343[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]93.50725[/C][C]0.376447801315647[/C][C]248.393667523629[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]93.5015789473684[/C][C]0.367071476544712[/C][C]254.723085071905[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]93.5088888888889[/C][C]0.35827314616967[/C][C]260.998877221474[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]93.5170588235294[/C][C]0.348414419532663[/C][C]268.407544524036[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]93.52625[/C][C]0.334004825998551[/C][C]280.014666615643[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]93.5403333333333[/C][C]0.319109927131497[/C][C]293.12887309453[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]93.5642857142857[/C][C]0.304400889845074[/C][C]307.371919188231[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]93.5776923076923[/C][C]0.290808585045378[/C][C]321.784490279372[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]93.5954166666667[/C][C]0.270713616238468[/C][C]345.735903377021[/C][/ROW]
[ROW][C]Median[/C][C]93.845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]93.4045945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93.5088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]93.4045945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93.5088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93.5088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]93.4045945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93.5088888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93.5015789473684[/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=281786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281786&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 Mean93.94319444444440.628340363915938149.510042390039
Geometric Mean93.7963408230052
Harmonic Mean93.6517333363581
Quadratic Mean94.0922707077709
Winsorized Mean ( 1 / 24 )93.95041666666670.62222524709156150.991007044177
Winsorized Mean ( 2 / 24 )93.918750.605440608885881155.124629272601
Winsorized Mean ( 3 / 24 )93.80166666666670.560784926651307167.268523472622
Winsorized Mean ( 4 / 24 )93.77111111111110.549078633420581170.779020350779
Winsorized Mean ( 5 / 24 )93.78708333333330.54313576283117172.677053789379
Winsorized Mean ( 6 / 24 )93.75541666666670.533544630147427175.721788523596
Winsorized Mean ( 7 / 24 )93.88861111111110.510027666006618184.085329814036
Winsorized Mean ( 8 / 24 )93.79416666666670.486963048457868192.610439259606
Winsorized Mean ( 9 / 24 )93.76666666666670.474706976581368197.525360469596
Winsorized Mean ( 10 / 24 )93.75833333333330.465824903129477201.273767682775
Winsorized Mean ( 11 / 24 )93.72166666666670.452908484643044206.932901114742
Winsorized Mean ( 12 / 24 )93.6450.434664576667691215.44198682561
Winsorized Mean ( 13 / 24 )93.59805555555550.424798517963749220.335174435667
Winsorized Mean ( 14 / 24 )93.59611111111110.42025374049363222.713332667005
Winsorized Mean ( 15 / 24 )93.64402777777780.402862588542729232.446572208443
Winsorized Mean ( 16 / 24 )93.55513888888890.377086941624401248.099651729852
Winsorized Mean ( 17 / 24 )93.43944444444440.359387514146348259.996357042038
Winsorized Mean ( 18 / 24 )93.43944444444440.348509226705606268.111823975826
Winsorized Mean ( 19 / 24 )93.43944444444440.348509226705606268.111823975825
Winsorized Mean ( 20 / 24 )93.40888888888890.32831584970225284.509227847518
Winsorized Mean ( 21 / 24 )93.34472222222220.304789363386804306.259776210628
Winsorized Mean ( 22 / 24 )93.45777777777780.280043397474013333.726053250195
Winsorized Mean ( 23 / 24 )93.44180555555550.275267001296369339.458798604598
Winsorized Mean ( 24 / 24 )93.35847222222220.263372750639526354.472784278281
Trimmed Mean ( 1 / 24 )93.88071428571430.593773814261136158.10854576424
Trimmed Mean ( 2 / 24 )93.80691176470590.559438263089544167.680543062338
Trimmed Mean ( 3 / 24 )93.74590909090910.529155987915203177.161198648161
Trimmed Mean ( 4 / 24 )93.7250.514101398574127182.308393363544
Trimmed Mean ( 5 / 24 )93.71161290322580.500323279601795187.302123894396
Trimmed Mean ( 6 / 24 )93.69350.485484662316569192.989618977717
Trimmed Mean ( 7 / 24 )93.68068965517240.470171215295037199.248032647823
Trimmed Mean ( 8 / 24 )93.64250.457526257141627204.671313478328
Trimmed Mean ( 9 / 24 )93.61722222222220.447666472060746209.122701977822
Trimmed Mean ( 10 / 24 )93.59423076923080.438135734713249213.619258494143
Trimmed Mean ( 11 / 24 )93.57060.428021400380487218.611966403598
Trimmed Mean ( 12 / 24 )93.550.417986774028092223.810909370335
Trimmed Mean ( 13 / 24 )93.53760869565220.409106270495462228.638902509048
Trimmed Mean ( 14 / 24 )93.530.399602736130578234.057456427018
Trimmed Mean ( 15 / 24 )93.52190476190480.387960993719125241.060071182343
Trimmed Mean ( 16 / 24 )93.507250.376447801315647248.393667523629
Trimmed Mean ( 17 / 24 )93.50157894736840.367071476544712254.723085071905
Trimmed Mean ( 18 / 24 )93.50888888888890.35827314616967260.998877221474
Trimmed Mean ( 19 / 24 )93.51705882352940.348414419532663268.407544524036
Trimmed Mean ( 20 / 24 )93.526250.334004825998551280.014666615643
Trimmed Mean ( 21 / 24 )93.54033333333330.319109927131497293.12887309453
Trimmed Mean ( 22 / 24 )93.56428571428570.304400889845074307.371919188231
Trimmed Mean ( 23 / 24 )93.57769230769230.290808585045378321.784490279372
Trimmed Mean ( 24 / 24 )93.59541666666670.270713616238468345.735903377021
Median93.845
Midrange96.13
Midmean - Weighted Average at Xnp93.4045945945946
Midmean - Weighted Average at X(n+1)p93.5088888888889
Midmean - Empirical Distribution Function93.4045945945946
Midmean - Empirical Distribution Function - Averaging93.5088888888889
Midmean - Empirical Distribution Function - Interpolation93.5088888888889
Midmean - Closest Observation93.4045945945946
Midmean - True Basic - Statistics Graphics Toolkit93.5088888888889
Midmean - MS Excel (old versions)93.5015789473684
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')