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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 14:58:45 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/18/t13189644324yc8dui4xubt8wd.htm/, Retrieved Thu, 16 May 2024 06:12:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132511, Retrieved Thu, 16 May 2024 06:12:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrumaten eigen...] [2011-10-18 18:58:45] [cbc0158ed4ce90347cf58cee0539a6b2] [Current]
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Dataseries X:
106,19
106,2
106,09
106,23
106,23
106,22
106,22
106,61
106,95
107,74
107,8
107,8
107,2
107,56
107,72
108,14
108,16
108,16
108,16
108,1
108,95
110,49
110,72
110,82
110,82
110,75
110,71
110,86
110,84
110,84
110,84
110,92
111,46
112,46
113,04
113,15
113,15
113,21
113,37
113,47
113,71
113,71
113,71
113,8
115,46
117
117,94
118,08
118,08
118,47
118,49
118,45
118,54
118,55
118,55
118,55
119,04
121,37
122
122,14
122,14
122,03
121,91
122,23
121,73
121,83
121,83
122,49
123,02
125,98
126,13
126,39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132511&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132511&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132511&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.9958333333330.706428140661612161.369326576613
Geometric Mean113.84214009657
Harmonic Mean113.690296180143
Quadratic Mean114.151136255113
Winsorized Mean ( 1 / 24 )113.9936111111110.7053267122071161.618168060591
Winsorized Mean ( 2 / 24 )113.9897222222220.704278978798456161.853080460666
Winsorized Mean ( 3 / 24 )113.8672222222220.67756942203968168.052480702935
Winsorized Mean ( 4 / 24 )113.8377777777780.672098505797619169.376626782825
Winsorized Mean ( 5 / 24 )113.8204166666670.668751652697123170.198333279059
Winsorized Mean ( 6 / 24 )113.8129166666670.667428509458994170.524505701624
Winsorized Mean ( 7 / 24 )113.8498611111110.661625171445613172.076072714035
Winsorized Mean ( 8 / 24 )113.8754166666670.653743013065714174.189879495079
Winsorized Mean ( 9 / 24 )113.9029166666670.648477585045117175.646651932837
Winsorized Mean ( 10 / 24 )113.9404166666670.639125124513831178.275602532976
Winsorized Mean ( 11 / 24 )113.9526388888890.633569606071581179.858121028638
Winsorized Mean ( 12 / 24 )113.9559722222220.633108208682762179.994463283485
Winsorized Mean ( 13 / 24 )113.948750.628456978952087181.315115936818
Winsorized Mean ( 14 / 24 )113.878750.616360917018095184.759849068524
Winsorized Mean ( 15 / 24 )113.4558333333330.52956624224886214.242948817
Winsorized Mean ( 16 / 24 )113.3558333333330.512432168494811221.211392068336
Winsorized Mean ( 17 / 24 )113.3605555555560.511755734203512221.513014860474
Winsorized Mean ( 18 / 24 )113.3605555555560.511755734203512221.513014860474
Winsorized Mean ( 19 / 24 )113.3579166666670.511378967360801221.671057868689
Winsorized Mean ( 20 / 24 )113.5634722222220.478754953137251237.205842943343
Winsorized Mean ( 21 / 24 )114.0068055555560.420714089757378270.984044345418
Winsorized Mean ( 22 / 24 )114.0679166666670.411983110851356276.875225372582
Winsorized Mean ( 23 / 24 )113.9529166666670.39404092265713289.190564011093
Winsorized Mean ( 24 / 24 )113.9629166666670.392887241939359290.065200651785
Trimmed Mean ( 1 / 24 )113.9317142857140.695250196156636163.871531307049
Trimmed Mean ( 2 / 24 )113.8661764705880.683055034675538166.70132081623
Trimmed Mean ( 3 / 24 )113.7987878787880.668967771640939170.111016857578
Trimmed Mean ( 4 / 24 )113.7731250.663934276836445171.362029299215
Trimmed Mean ( 5 / 24 )113.754354838710.659367941704182172.520299583725
Trimmed Mean ( 6 / 24 )113.73850.654367716774798173.81435098997
Trimmed Mean ( 7 / 24 )113.7231034482760.648149033171572175.458262880988
Trimmed Mean ( 8 / 24 )113.6998214285710.641470130241192177.248816536197
Trimmed Mean ( 9 / 24 )113.6705555555560.634543774143635179.137453060606
Trimmed Mean ( 10 / 24 )113.6348076923080.626542771022385181.367997442345
Trimmed Mean ( 11 / 24 )113.59080.617955538985828183.817107920777
Trimmed Mean ( 12 / 24 )113.5414583333330.607689933941748186.841104306028
Trimmed Mean ( 13 / 24 )113.4873913043480.594101557282481191.023554665397
Trimmed Mean ( 14 / 24 )113.4293181818180.57712969857521196.540428367916
Trimmed Mean ( 15 / 24 )113.3742857142860.557555030836256203.341875588926
Trimmed Mean ( 16 / 24 )113.36450.55203109235176205.358903820155
Trimmed Mean ( 17 / 24 )113.3655263157890.54733736678787207.121846953538
Trimmed Mean ( 18 / 24 )113.3661111111110.539863780258102209.990214673991
Trimmed Mean ( 19 / 24 )113.3667647058820.528386998391524214.552525045062
Trimmed Mean ( 20 / 24 )113.36781250.511344632848871221.7052946628
Trimmed Mean ( 21 / 24 )113.3443333333330.495509880976751228.742831747186
Trimmed Mean ( 22 / 24 )113.2632142857140.486602532622207232.763306173851
Trimmed Mean ( 23 / 24 )113.1619230769230.472829134606302239.329421126189
Trimmed Mean ( 24 / 24 )113.058750.456262507273475247.793207194723
Median113.15
Midrange116.24
Midmean - Weighted Average at Xnp113.498461538462
Midmean - Weighted Average at X(n+1)p113.498461538462
Midmean - Empirical Distribution Function113.498461538462
Midmean - Empirical Distribution Function - Averaging113.498461538462
Midmean - Empirical Distribution Function - Interpolation113.498461538462
Midmean - Closest Observation113.498461538462
Midmean - True Basic - Statistics Graphics Toolkit113.498461538462
Midmean - MS Excel (old versions)113.498461538462
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.995833333333 & 0.706428140661612 & 161.369326576613 \tabularnewline
Geometric Mean & 113.84214009657 &  &  \tabularnewline
Harmonic Mean & 113.690296180143 &  &  \tabularnewline
Quadratic Mean & 114.151136255113 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 113.993611111111 & 0.7053267122071 & 161.618168060591 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 113.989722222222 & 0.704278978798456 & 161.853080460666 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 113.867222222222 & 0.67756942203968 & 168.052480702935 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 113.837777777778 & 0.672098505797619 & 169.376626782825 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 113.820416666667 & 0.668751652697123 & 170.198333279059 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 113.812916666667 & 0.667428509458994 & 170.524505701624 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 113.849861111111 & 0.661625171445613 & 172.076072714035 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 113.875416666667 & 0.653743013065714 & 174.189879495079 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 113.902916666667 & 0.648477585045117 & 175.646651932837 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 113.940416666667 & 0.639125124513831 & 178.275602532976 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 113.952638888889 & 0.633569606071581 & 179.858121028638 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 113.955972222222 & 0.633108208682762 & 179.994463283485 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 113.94875 & 0.628456978952087 & 181.315115936818 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 113.87875 & 0.616360917018095 & 184.759849068524 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 113.455833333333 & 0.52956624224886 & 214.242948817 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 113.355833333333 & 0.512432168494811 & 221.211392068336 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 113.360555555556 & 0.511755734203512 & 221.513014860474 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 113.360555555556 & 0.511755734203512 & 221.513014860474 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 113.357916666667 & 0.511378967360801 & 221.671057868689 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 113.563472222222 & 0.478754953137251 & 237.205842943343 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 114.006805555556 & 0.420714089757378 & 270.984044345418 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 114.067916666667 & 0.411983110851356 & 276.875225372582 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 113.952916666667 & 0.39404092265713 & 289.190564011093 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 113.962916666667 & 0.392887241939359 & 290.065200651785 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 113.931714285714 & 0.695250196156636 & 163.871531307049 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 113.866176470588 & 0.683055034675538 & 166.70132081623 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 113.798787878788 & 0.668967771640939 & 170.111016857578 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 113.773125 & 0.663934276836445 & 171.362029299215 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 113.75435483871 & 0.659367941704182 & 172.520299583725 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 113.7385 & 0.654367716774798 & 173.81435098997 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 113.723103448276 & 0.648149033171572 & 175.458262880988 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 113.699821428571 & 0.641470130241192 & 177.248816536197 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 113.670555555556 & 0.634543774143635 & 179.137453060606 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 113.634807692308 & 0.626542771022385 & 181.367997442345 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 113.5908 & 0.617955538985828 & 183.817107920777 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 113.541458333333 & 0.607689933941748 & 186.841104306028 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 113.487391304348 & 0.594101557282481 & 191.023554665397 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 113.429318181818 & 0.57712969857521 & 196.540428367916 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 113.374285714286 & 0.557555030836256 & 203.341875588926 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 113.3645 & 0.55203109235176 & 205.358903820155 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 113.365526315789 & 0.54733736678787 & 207.121846953538 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 113.366111111111 & 0.539863780258102 & 209.990214673991 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 113.366764705882 & 0.528386998391524 & 214.552525045062 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 113.3678125 & 0.511344632848871 & 221.7052946628 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 113.344333333333 & 0.495509880976751 & 228.742831747186 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 113.263214285714 & 0.486602532622207 & 232.763306173851 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 113.161923076923 & 0.472829134606302 & 239.329421126189 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 113.05875 & 0.456262507273475 & 247.793207194723 \tabularnewline
Median & 113.15 &  &  \tabularnewline
Midrange & 116.24 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 113.498461538462 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 113.498461538462 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 113.498461538462 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 113.498461538462 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 113.498461538462 &  &  \tabularnewline
Midmean - Closest Observation & 113.498461538462 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 113.498461538462 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 113.498461538462 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132511&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]113.995833333333[/C][C]0.706428140661612[/C][C]161.369326576613[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.84214009657[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.690296180143[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.151136255113[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]113.993611111111[/C][C]0.7053267122071[/C][C]161.618168060591[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]113.989722222222[/C][C]0.704278978798456[/C][C]161.853080460666[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]113.867222222222[/C][C]0.67756942203968[/C][C]168.052480702935[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]113.837777777778[/C][C]0.672098505797619[/C][C]169.376626782825[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]113.820416666667[/C][C]0.668751652697123[/C][C]170.198333279059[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]113.812916666667[/C][C]0.667428509458994[/C][C]170.524505701624[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]113.849861111111[/C][C]0.661625171445613[/C][C]172.076072714035[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]113.875416666667[/C][C]0.653743013065714[/C][C]174.189879495079[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]113.902916666667[/C][C]0.648477585045117[/C][C]175.646651932837[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]113.940416666667[/C][C]0.639125124513831[/C][C]178.275602532976[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]113.952638888889[/C][C]0.633569606071581[/C][C]179.858121028638[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]113.955972222222[/C][C]0.633108208682762[/C][C]179.994463283485[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]113.94875[/C][C]0.628456978952087[/C][C]181.315115936818[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]113.87875[/C][C]0.616360917018095[/C][C]184.759849068524[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]113.455833333333[/C][C]0.52956624224886[/C][C]214.242948817[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]113.355833333333[/C][C]0.512432168494811[/C][C]221.211392068336[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]113.360555555556[/C][C]0.511755734203512[/C][C]221.513014860474[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]113.360555555556[/C][C]0.511755734203512[/C][C]221.513014860474[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]113.357916666667[/C][C]0.511378967360801[/C][C]221.671057868689[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]113.563472222222[/C][C]0.478754953137251[/C][C]237.205842943343[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]114.006805555556[/C][C]0.420714089757378[/C][C]270.984044345418[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]114.067916666667[/C][C]0.411983110851356[/C][C]276.875225372582[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]113.952916666667[/C][C]0.39404092265713[/C][C]289.190564011093[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]113.962916666667[/C][C]0.392887241939359[/C][C]290.065200651785[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]113.931714285714[/C][C]0.695250196156636[/C][C]163.871531307049[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]113.866176470588[/C][C]0.683055034675538[/C][C]166.70132081623[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]113.798787878788[/C][C]0.668967771640939[/C][C]170.111016857578[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]113.773125[/C][C]0.663934276836445[/C][C]171.362029299215[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]113.75435483871[/C][C]0.659367941704182[/C][C]172.520299583725[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]113.7385[/C][C]0.654367716774798[/C][C]173.81435098997[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]113.723103448276[/C][C]0.648149033171572[/C][C]175.458262880988[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]113.699821428571[/C][C]0.641470130241192[/C][C]177.248816536197[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]113.670555555556[/C][C]0.634543774143635[/C][C]179.137453060606[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]113.634807692308[/C][C]0.626542771022385[/C][C]181.367997442345[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]113.5908[/C][C]0.617955538985828[/C][C]183.817107920777[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]113.541458333333[/C][C]0.607689933941748[/C][C]186.841104306028[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]113.487391304348[/C][C]0.594101557282481[/C][C]191.023554665397[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]113.429318181818[/C][C]0.57712969857521[/C][C]196.540428367916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]113.374285714286[/C][C]0.557555030836256[/C][C]203.341875588926[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]113.3645[/C][C]0.55203109235176[/C][C]205.358903820155[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]113.365526315789[/C][C]0.54733736678787[/C][C]207.121846953538[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]113.366111111111[/C][C]0.539863780258102[/C][C]209.990214673991[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]113.366764705882[/C][C]0.528386998391524[/C][C]214.552525045062[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]113.3678125[/C][C]0.511344632848871[/C][C]221.7052946628[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]113.344333333333[/C][C]0.495509880976751[/C][C]228.742831747186[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]113.263214285714[/C][C]0.486602532622207[/C][C]232.763306173851[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]113.161923076923[/C][C]0.472829134606302[/C][C]239.329421126189[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]113.05875[/C][C]0.456262507273475[/C][C]247.793207194723[/C][/ROW]
[ROW][C]Median[/C][C]113.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]116.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]113.498461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]113.498461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]113.498461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]113.498461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]113.498461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.498461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]113.498461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]113.498461538462[/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=132511&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132511&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 Mean113.9958333333330.706428140661612161.369326576613
Geometric Mean113.84214009657
Harmonic Mean113.690296180143
Quadratic Mean114.151136255113
Winsorized Mean ( 1 / 24 )113.9936111111110.7053267122071161.618168060591
Winsorized Mean ( 2 / 24 )113.9897222222220.704278978798456161.853080460666
Winsorized Mean ( 3 / 24 )113.8672222222220.67756942203968168.052480702935
Winsorized Mean ( 4 / 24 )113.8377777777780.672098505797619169.376626782825
Winsorized Mean ( 5 / 24 )113.8204166666670.668751652697123170.198333279059
Winsorized Mean ( 6 / 24 )113.8129166666670.667428509458994170.524505701624
Winsorized Mean ( 7 / 24 )113.8498611111110.661625171445613172.076072714035
Winsorized Mean ( 8 / 24 )113.8754166666670.653743013065714174.189879495079
Winsorized Mean ( 9 / 24 )113.9029166666670.648477585045117175.646651932837
Winsorized Mean ( 10 / 24 )113.9404166666670.639125124513831178.275602532976
Winsorized Mean ( 11 / 24 )113.9526388888890.633569606071581179.858121028638
Winsorized Mean ( 12 / 24 )113.9559722222220.633108208682762179.994463283485
Winsorized Mean ( 13 / 24 )113.948750.628456978952087181.315115936818
Winsorized Mean ( 14 / 24 )113.878750.616360917018095184.759849068524
Winsorized Mean ( 15 / 24 )113.4558333333330.52956624224886214.242948817
Winsorized Mean ( 16 / 24 )113.3558333333330.512432168494811221.211392068336
Winsorized Mean ( 17 / 24 )113.3605555555560.511755734203512221.513014860474
Winsorized Mean ( 18 / 24 )113.3605555555560.511755734203512221.513014860474
Winsorized Mean ( 19 / 24 )113.3579166666670.511378967360801221.671057868689
Winsorized Mean ( 20 / 24 )113.5634722222220.478754953137251237.205842943343
Winsorized Mean ( 21 / 24 )114.0068055555560.420714089757378270.984044345418
Winsorized Mean ( 22 / 24 )114.0679166666670.411983110851356276.875225372582
Winsorized Mean ( 23 / 24 )113.9529166666670.39404092265713289.190564011093
Winsorized Mean ( 24 / 24 )113.9629166666670.392887241939359290.065200651785
Trimmed Mean ( 1 / 24 )113.9317142857140.695250196156636163.871531307049
Trimmed Mean ( 2 / 24 )113.8661764705880.683055034675538166.70132081623
Trimmed Mean ( 3 / 24 )113.7987878787880.668967771640939170.111016857578
Trimmed Mean ( 4 / 24 )113.7731250.663934276836445171.362029299215
Trimmed Mean ( 5 / 24 )113.754354838710.659367941704182172.520299583725
Trimmed Mean ( 6 / 24 )113.73850.654367716774798173.81435098997
Trimmed Mean ( 7 / 24 )113.7231034482760.648149033171572175.458262880988
Trimmed Mean ( 8 / 24 )113.6998214285710.641470130241192177.248816536197
Trimmed Mean ( 9 / 24 )113.6705555555560.634543774143635179.137453060606
Trimmed Mean ( 10 / 24 )113.6348076923080.626542771022385181.367997442345
Trimmed Mean ( 11 / 24 )113.59080.617955538985828183.817107920777
Trimmed Mean ( 12 / 24 )113.5414583333330.607689933941748186.841104306028
Trimmed Mean ( 13 / 24 )113.4873913043480.594101557282481191.023554665397
Trimmed Mean ( 14 / 24 )113.4293181818180.57712969857521196.540428367916
Trimmed Mean ( 15 / 24 )113.3742857142860.557555030836256203.341875588926
Trimmed Mean ( 16 / 24 )113.36450.55203109235176205.358903820155
Trimmed Mean ( 17 / 24 )113.3655263157890.54733736678787207.121846953538
Trimmed Mean ( 18 / 24 )113.3661111111110.539863780258102209.990214673991
Trimmed Mean ( 19 / 24 )113.3667647058820.528386998391524214.552525045062
Trimmed Mean ( 20 / 24 )113.36781250.511344632848871221.7052946628
Trimmed Mean ( 21 / 24 )113.3443333333330.495509880976751228.742831747186
Trimmed Mean ( 22 / 24 )113.2632142857140.486602532622207232.763306173851
Trimmed Mean ( 23 / 24 )113.1619230769230.472829134606302239.329421126189
Trimmed Mean ( 24 / 24 )113.058750.456262507273475247.793207194723
Median113.15
Midrange116.24
Midmean - Weighted Average at Xnp113.498461538462
Midmean - Weighted Average at X(n+1)p113.498461538462
Midmean - Empirical Distribution Function113.498461538462
Midmean - Empirical Distribution Function - Averaging113.498461538462
Midmean - Empirical Distribution Function - Interpolation113.498461538462
Midmean - Closest Observation113.498461538462
Midmean - True Basic - Statistics Graphics Toolkit113.498461538462
Midmean - MS Excel (old versions)113.498461538462
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')