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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 12 Jan 2014 14:47:40 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/12/t1389556124hgpd4r4top6tfw5.htm/, Retrieved Sun, 24 May 2026 03:01:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233050, Retrieved Sun, 24 May 2026 03:01:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact348

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-01-12 19:47:40] [03d0abbf0157d1e4219f14a778968579] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105,38
105,38
108,37
112,21
112,05
112,05
112,06
112,05
111,36
111,36
111,36
111,36
111,78
111,89
111,89
111,89
112,02
112,02
112,02
112,02
112,02
112,02
112,02
111,28
111,28
111,28
111,28
110,56
110,56
110,56
110,56
110,56
111,37
109,43
109,43
109,57
109,57
109,57
109,57
109,57
109,39
111,68
111,68
111,68
111,93
111,93
111,93
111,93
111,56
111,89
111,89
111,89
110,82
110,82
110,82
110,82
110,98
110,98
111,78
111,78
111,78
111,78
112,6
112,6
112,6
112,6
112,6
113,25
113,25
113,25
113,25
113,25

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233050&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]3 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=233050&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233050&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.2995833333330.169968978747025654.822922122671
Geometric Mean111.290200525275
Harmonic Mean111.280644110338
Quadratic Mean111.308797502214
Winsorized Mean ( 1 / 24 )111.2995833333330.169968978747025654.822922122671
Winsorized Mean ( 2 / 24 )111.3826388888890.135796063762231820.21993718398
Winsorized Mean ( 3 / 24 )111.4251388888890.124173321662969897.335574152706
Winsorized Mean ( 4 / 24 )111.4273611111110.123664065032103901.048830007201
Winsorized Mean ( 5 / 24 )111.3822222222220.11558472531195963.64136283245
Winsorized Mean ( 6 / 24 )111.3938888888890.112868689122257986.933486648626
Winsorized Mean ( 7 / 24 )111.3938888888890.112868689122257986.933486648625
Winsorized Mean ( 8 / 24 )111.3938888888890.112868689122257986.933486648625
Winsorized Mean ( 9 / 24 )111.3938888888890.112868689122257986.933486648625
Winsorized Mean ( 10 / 24 )111.3397222222220.105618376619521054.16998240101
Winsorized Mean ( 11 / 24 )111.4680555555560.07056103111108051579.73960698048
Winsorized Mean ( 12 / 24 )111.4663888888890.07036521804573781584.11203695034
Winsorized Mean ( 13 / 24 )111.4663888888890.07036521804573781584.11203695034
Winsorized Mean ( 14 / 24 )111.4663888888890.07036521804573781584.11203695034
Winsorized Mean ( 15 / 24 )111.4601388888890.06964629311444751600.37431864077
Winsorized Mean ( 16 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 17 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 18 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 19 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 20 / 24 )111.5623611111110.05242831496730772127.90285517811
Winsorized Mean ( 21 / 24 )111.5623611111110.05242831496730772127.90285517811
Winsorized Mean ( 22 / 24 )111.6265277777780.03542120778521433151.40377071991
Winsorized Mean ( 23 / 24 )111.6265277777780.03542120778521433151.40377071991
Winsorized Mean ( 24 / 24 )111.6265277777780.03542120778521433151.40377071991
Trimmed Mean ( 1 / 24 )111.3562857142860.149956677170769742.589712010453
Trimmed Mean ( 2 / 24 )111.4163235294120.123122405029947904.92322256304
Trimmed Mean ( 3 / 24 )111.4346969696970.114659975620016971.870928518179
Trimmed Mean ( 4 / 24 )111.438281250.1101533370942121011.66504973598
Trimmed Mean ( 5 / 24 )111.4414516129030.1048874007257271062.48654120351
Trimmed Mean ( 6 / 24 )111.4556666666670.1011332305434311102.06769889352
Trimmed Mean ( 7 / 24 )111.4684482758620.09735174613610911145.00717963514
Trimmed Mean ( 8 / 24 )111.4821428571430.09264711512308851203.29858851008
Trimmed Mean ( 9 / 24 )111.4968518518520.08671254392657981285.82148329378
Trimmed Mean ( 10 / 24 )111.5126923076920.07906128910368981410.45881710128
Trimmed Mean ( 11 / 24 )111.53760.0708130969092411575.09846155937
Trimmed Mean ( 12 / 24 )111.5470833333330.06999427429301741593.6601166313
Trimmed Mean ( 13 / 24 )111.5576086956520.06887725186450631619.65824239192
Trimmed Mean ( 14 / 24 )111.5690909090910.06732884351691631657.07719130894
Trimmed Mean ( 15 / 24 )111.5816666666670.06520130239133971711.34107102571
Trimmed Mean ( 16 / 24 )111.596250.06240961413033621788.12594109206
Trimmed Mean ( 17 / 24 )111.6055263157890.06134307294746031819.36640851655
Trimmed Mean ( 18 / 24 )111.6158333333330.05974864679346981868.0897279423
Trimmed Mean ( 19 / 24 )111.6273529411760.05740109500953811944.69030464711
Trimmed Mean ( 20 / 24 )111.64031250.05393298629863462069.98203069698
Trimmed Mean ( 21 / 24 )111.6496666666670.05144684419648872170.19466228575
Trimmed Mean ( 22 / 24 )111.6603571428570.04761364056603572345.13378551666
Trimmed Mean ( 23 / 24 )111.6646153846150.04797509215682282327.55395278037
Trimmed Mean ( 24 / 24 )111.6695833333330.04809968199700052321.62830806859
Median111.78
Midrange109.315
Midmean - Weighted Average at Xnp111.606585365854
Midmean - Weighted Average at X(n+1)p111.606585365854
Midmean - Empirical Distribution Function111.606585365854
Midmean - Empirical Distribution Function - Averaging111.606585365854
Midmean - Empirical Distribution Function - Interpolation111.606585365854
Midmean - Closest Observation111.606585365854
Midmean - True Basic - Statistics Graphics Toolkit111.606585365854
Midmean - MS Excel (old versions)111.606585365854
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.299583333333 & 0.169968978747025 & 654.822922122671 \tabularnewline
Geometric Mean & 111.290200525275 &  &  \tabularnewline
Harmonic Mean & 111.280644110338 &  &  \tabularnewline
Quadratic Mean & 111.308797502214 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 111.299583333333 & 0.169968978747025 & 654.822922122671 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 111.382638888889 & 0.135796063762231 & 820.21993718398 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 111.425138888889 & 0.124173321662969 & 897.335574152706 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 111.427361111111 & 0.123664065032103 & 901.048830007201 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 111.382222222222 & 0.11558472531195 & 963.64136283245 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 111.393888888889 & 0.112868689122257 & 986.933486648626 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 111.393888888889 & 0.112868689122257 & 986.933486648625 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 111.393888888889 & 0.112868689122257 & 986.933486648625 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 111.393888888889 & 0.112868689122257 & 986.933486648625 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 111.339722222222 & 0.10561837661952 & 1054.16998240101 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 111.468055555556 & 0.0705610311110805 & 1579.73960698048 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 111.466388888889 & 0.0703652180457378 & 1584.11203695034 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 111.466388888889 & 0.0703652180457378 & 1584.11203695034 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 111.466388888889 & 0.0703652180457378 & 1584.11203695034 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 111.460138888889 & 0.0696462931144475 & 1600.37431864077 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 111.517916666667 & 0.0595831691780137 & 1871.63452708415 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 111.517916666667 & 0.0595831691780137 & 1871.63452708415 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 111.517916666667 & 0.0595831691780137 & 1871.63452708415 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 111.517916666667 & 0.0595831691780137 & 1871.63452708415 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 111.562361111111 & 0.0524283149673077 & 2127.90285517811 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 111.562361111111 & 0.0524283149673077 & 2127.90285517811 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 111.626527777778 & 0.0354212077852143 & 3151.40377071991 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 111.626527777778 & 0.0354212077852143 & 3151.40377071991 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 111.626527777778 & 0.0354212077852143 & 3151.40377071991 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 111.356285714286 & 0.149956677170769 & 742.589712010453 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 111.416323529412 & 0.123122405029947 & 904.92322256304 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 111.434696969697 & 0.114659975620016 & 971.870928518179 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 111.43828125 & 0.110153337094212 & 1011.66504973598 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 111.441451612903 & 0.104887400725727 & 1062.48654120351 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 111.455666666667 & 0.101133230543431 & 1102.06769889352 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 111.468448275862 & 0.0973517461361091 & 1145.00717963514 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 111.482142857143 & 0.0926471151230885 & 1203.29858851008 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 111.496851851852 & 0.0867125439265798 & 1285.82148329378 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 111.512692307692 & 0.0790612891036898 & 1410.45881710128 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 111.5376 & 0.070813096909241 & 1575.09846155937 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 111.547083333333 & 0.0699942742930174 & 1593.6601166313 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 111.557608695652 & 0.0688772518645063 & 1619.65824239192 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 111.569090909091 & 0.0673288435169163 & 1657.07719130894 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 111.581666666667 & 0.0652013023913397 & 1711.34107102571 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 111.59625 & 0.0624096141303362 & 1788.12594109206 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 111.605526315789 & 0.0613430729474603 & 1819.36640851655 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 111.615833333333 & 0.0597486467934698 & 1868.0897279423 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 111.627352941176 & 0.0574010950095381 & 1944.69030464711 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 111.6403125 & 0.0539329862986346 & 2069.98203069698 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 111.649666666667 & 0.0514468441964887 & 2170.19466228575 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 111.660357142857 & 0.0476136405660357 & 2345.13378551666 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 111.664615384615 & 0.0479750921568228 & 2327.55395278037 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 111.669583333333 & 0.0480996819970005 & 2321.62830806859 \tabularnewline
Median & 111.78 &  &  \tabularnewline
Midrange & 109.315 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.606585365854 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.606585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.606585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.606585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.606585365854 &  &  \tabularnewline
Midmean - Closest Observation & 111.606585365854 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.606585365854 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.606585365854 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233050&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]111.299583333333[/C][C]0.169968978747025[/C][C]654.822922122671[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.290200525275[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.280644110338[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.308797502214[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]111.299583333333[/C][C]0.169968978747025[/C][C]654.822922122671[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]111.382638888889[/C][C]0.135796063762231[/C][C]820.21993718398[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]111.425138888889[/C][C]0.124173321662969[/C][C]897.335574152706[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]111.427361111111[/C][C]0.123664065032103[/C][C]901.048830007201[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]111.382222222222[/C][C]0.11558472531195[/C][C]963.64136283245[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]111.393888888889[/C][C]0.112868689122257[/C][C]986.933486648626[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]111.393888888889[/C][C]0.112868689122257[/C][C]986.933486648625[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]111.393888888889[/C][C]0.112868689122257[/C][C]986.933486648625[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]111.393888888889[/C][C]0.112868689122257[/C][C]986.933486648625[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]111.339722222222[/C][C]0.10561837661952[/C][C]1054.16998240101[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]111.468055555556[/C][C]0.0705610311110805[/C][C]1579.73960698048[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]111.466388888889[/C][C]0.0703652180457378[/C][C]1584.11203695034[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]111.466388888889[/C][C]0.0703652180457378[/C][C]1584.11203695034[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]111.466388888889[/C][C]0.0703652180457378[/C][C]1584.11203695034[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]111.460138888889[/C][C]0.0696462931144475[/C][C]1600.37431864077[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]111.517916666667[/C][C]0.0595831691780137[/C][C]1871.63452708415[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]111.517916666667[/C][C]0.0595831691780137[/C][C]1871.63452708415[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]111.517916666667[/C][C]0.0595831691780137[/C][C]1871.63452708415[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]111.517916666667[/C][C]0.0595831691780137[/C][C]1871.63452708415[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]111.562361111111[/C][C]0.0524283149673077[/C][C]2127.90285517811[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]111.562361111111[/C][C]0.0524283149673077[/C][C]2127.90285517811[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]111.626527777778[/C][C]0.0354212077852143[/C][C]3151.40377071991[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]111.626527777778[/C][C]0.0354212077852143[/C][C]3151.40377071991[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]111.626527777778[/C][C]0.0354212077852143[/C][C]3151.40377071991[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]111.356285714286[/C][C]0.149956677170769[/C][C]742.589712010453[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]111.416323529412[/C][C]0.123122405029947[/C][C]904.92322256304[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]111.434696969697[/C][C]0.114659975620016[/C][C]971.870928518179[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]111.43828125[/C][C]0.110153337094212[/C][C]1011.66504973598[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]111.441451612903[/C][C]0.104887400725727[/C][C]1062.48654120351[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]111.455666666667[/C][C]0.101133230543431[/C][C]1102.06769889352[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]111.468448275862[/C][C]0.0973517461361091[/C][C]1145.00717963514[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]111.482142857143[/C][C]0.0926471151230885[/C][C]1203.29858851008[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]111.496851851852[/C][C]0.0867125439265798[/C][C]1285.82148329378[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]111.512692307692[/C][C]0.0790612891036898[/C][C]1410.45881710128[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]111.5376[/C][C]0.070813096909241[/C][C]1575.09846155937[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]111.547083333333[/C][C]0.0699942742930174[/C][C]1593.6601166313[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]111.557608695652[/C][C]0.0688772518645063[/C][C]1619.65824239192[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]111.569090909091[/C][C]0.0673288435169163[/C][C]1657.07719130894[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]111.581666666667[/C][C]0.0652013023913397[/C][C]1711.34107102571[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]111.59625[/C][C]0.0624096141303362[/C][C]1788.12594109206[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]111.605526315789[/C][C]0.0613430729474603[/C][C]1819.36640851655[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]111.615833333333[/C][C]0.0597486467934698[/C][C]1868.0897279423[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]111.627352941176[/C][C]0.0574010950095381[/C][C]1944.69030464711[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]111.6403125[/C][C]0.0539329862986346[/C][C]2069.98203069698[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]111.649666666667[/C][C]0.0514468441964887[/C][C]2170.19466228575[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]111.660357142857[/C][C]0.0476136405660357[/C][C]2345.13378551666[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]111.664615384615[/C][C]0.0479750921568228[/C][C]2327.55395278037[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]111.669583333333[/C][C]0.0480996819970005[/C][C]2321.62830806859[/C][/ROW]
[ROW][C]Median[/C][C]111.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.315[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.606585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.606585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.606585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.606585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.606585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.606585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.606585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.606585365854[/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=233050&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233050&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.2995833333330.169968978747025654.822922122671
Geometric Mean111.290200525275
Harmonic Mean111.280644110338
Quadratic Mean111.308797502214
Winsorized Mean ( 1 / 24 )111.2995833333330.169968978747025654.822922122671
Winsorized Mean ( 2 / 24 )111.3826388888890.135796063762231820.21993718398
Winsorized Mean ( 3 / 24 )111.4251388888890.124173321662969897.335574152706
Winsorized Mean ( 4 / 24 )111.4273611111110.123664065032103901.048830007201
Winsorized Mean ( 5 / 24 )111.3822222222220.11558472531195963.64136283245
Winsorized Mean ( 6 / 24 )111.3938888888890.112868689122257986.933486648626
Winsorized Mean ( 7 / 24 )111.3938888888890.112868689122257986.933486648625
Winsorized Mean ( 8 / 24 )111.3938888888890.112868689122257986.933486648625
Winsorized Mean ( 9 / 24 )111.3938888888890.112868689122257986.933486648625
Winsorized Mean ( 10 / 24 )111.3397222222220.105618376619521054.16998240101
Winsorized Mean ( 11 / 24 )111.4680555555560.07056103111108051579.73960698048
Winsorized Mean ( 12 / 24 )111.4663888888890.07036521804573781584.11203695034
Winsorized Mean ( 13 / 24 )111.4663888888890.07036521804573781584.11203695034
Winsorized Mean ( 14 / 24 )111.4663888888890.07036521804573781584.11203695034
Winsorized Mean ( 15 / 24 )111.4601388888890.06964629311444751600.37431864077
Winsorized Mean ( 16 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 17 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 18 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 19 / 24 )111.5179166666670.05958316917801371871.63452708415
Winsorized Mean ( 20 / 24 )111.5623611111110.05242831496730772127.90285517811
Winsorized Mean ( 21 / 24 )111.5623611111110.05242831496730772127.90285517811
Winsorized Mean ( 22 / 24 )111.6265277777780.03542120778521433151.40377071991
Winsorized Mean ( 23 / 24 )111.6265277777780.03542120778521433151.40377071991
Winsorized Mean ( 24 / 24 )111.6265277777780.03542120778521433151.40377071991
Trimmed Mean ( 1 / 24 )111.3562857142860.149956677170769742.589712010453
Trimmed Mean ( 2 / 24 )111.4163235294120.123122405029947904.92322256304
Trimmed Mean ( 3 / 24 )111.4346969696970.114659975620016971.870928518179
Trimmed Mean ( 4 / 24 )111.438281250.1101533370942121011.66504973598
Trimmed Mean ( 5 / 24 )111.4414516129030.1048874007257271062.48654120351
Trimmed Mean ( 6 / 24 )111.4556666666670.1011332305434311102.06769889352
Trimmed Mean ( 7 / 24 )111.4684482758620.09735174613610911145.00717963514
Trimmed Mean ( 8 / 24 )111.4821428571430.09264711512308851203.29858851008
Trimmed Mean ( 9 / 24 )111.4968518518520.08671254392657981285.82148329378
Trimmed Mean ( 10 / 24 )111.5126923076920.07906128910368981410.45881710128
Trimmed Mean ( 11 / 24 )111.53760.0708130969092411575.09846155937
Trimmed Mean ( 12 / 24 )111.5470833333330.06999427429301741593.6601166313
Trimmed Mean ( 13 / 24 )111.5576086956520.06887725186450631619.65824239192
Trimmed Mean ( 14 / 24 )111.5690909090910.06732884351691631657.07719130894
Trimmed Mean ( 15 / 24 )111.5816666666670.06520130239133971711.34107102571
Trimmed Mean ( 16 / 24 )111.596250.06240961413033621788.12594109206
Trimmed Mean ( 17 / 24 )111.6055263157890.06134307294746031819.36640851655
Trimmed Mean ( 18 / 24 )111.6158333333330.05974864679346981868.0897279423
Trimmed Mean ( 19 / 24 )111.6273529411760.05740109500953811944.69030464711
Trimmed Mean ( 20 / 24 )111.64031250.05393298629863462069.98203069698
Trimmed Mean ( 21 / 24 )111.6496666666670.05144684419648872170.19466228575
Trimmed Mean ( 22 / 24 )111.6603571428570.04761364056603572345.13378551666
Trimmed Mean ( 23 / 24 )111.6646153846150.04797509215682282327.55395278037
Trimmed Mean ( 24 / 24 )111.6695833333330.04809968199700052321.62830806859
Median111.78
Midrange109.315
Midmean - Weighted Average at Xnp111.606585365854
Midmean - Weighted Average at X(n+1)p111.606585365854
Midmean - Empirical Distribution Function111.606585365854
Midmean - Empirical Distribution Function - Averaging111.606585365854
Midmean - Empirical Distribution Function - Interpolation111.606585365854
Midmean - Closest Observation111.606585365854
Midmean - True Basic - Statistics Graphics Toolkit111.606585365854
Midmean - MS Excel (old versions)111.606585365854
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')