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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 computationSat, 05 Mar 2016 17:28:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/05/t14571990640zl6ij838xiptcl.htm/, Retrieved Sat, 27 Apr 2024 10:49:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293525, Retrieved Sat, 27 Apr 2024 10:49:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact53

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten van ...] [2016-03-05 17:28:49] [4e1138fa3bff5f7fc8fdb388bb0b126b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99.13
100.46
101.83
100.82
100.99
99.11
98.99
99.8
100.3
101.56
98.83
101.29
98.24
98.37
99.68
97.8
98.34
98.06
97.19
99.44
99.04
100.81
98.49
101.03
98.59
101.07
99.28
101.65
100.59
101.84
100.27
100.04
97.78
97.59
97.68
100.56
98.9
100.08
101.7
100.9
100.67
100.51
100.01
99.8
97.7
98.14
101.77
99.82
100.03
101.83
98.25
99.88
98.96
98.37
97.52
99.59
97.99
100.68
100.39
99.31
96.93
102.06
97.9
102.29
100.55
100.77
100.68
100.75
100.21
99.85
100.59
101.45

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293525&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293525&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293525&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.76902777777780.161572156649804617.488989727481
Geometric Mean99.7597227250873
Harmonic Mean99.7504019622452
Quadratic Mean99.7783162746852
Winsorized Mean ( 1 / 24 )99.76944444444440.160042161024875623.394759265575
Winsorized Mean ( 2 / 24 )99.77250.15689022980958635.938261554564
Winsorized Mean ( 3 / 24 )99.7750.156230789116354638.638520385966
Winsorized Mean ( 4 / 24 )99.780.155262033042654642.655503374659
Winsorized Mean ( 5 / 24 )99.77722222222220.154231425584419646.931854802892
Winsorized Mean ( 6 / 24 )99.77805555555560.151931054560748656.732462260772
Winsorized Mean ( 7 / 24 )99.77513888888890.150712573641033662.022659944307
Winsorized Mean ( 8 / 24 )99.776250.146956664524083678.950153932277
Winsorized Mean ( 9 / 24 )99.773750.142640321256102699.477883402005
Winsorized Mean ( 10 / 24 )99.761250.137353270337684726.311428586564
Winsorized Mean ( 11 / 24 )99.73986111111110.130170150635292766.22682407859
Winsorized Mean ( 12 / 24 )99.74986111111110.126369259984987789.352261166692
Winsorized Mean ( 13 / 24 )99.74444444444440.125043480526803797.678087847725
Winsorized Mean ( 14 / 24 )99.74444444444450.119706031569374833.244934584928
Winsorized Mean ( 15 / 24 )99.73402777777780.116445911151375856.48372529051
Winsorized Mean ( 16 / 24 )99.73180555555560.11615469933657858.611886778445
Winsorized Mean ( 17 / 24 )99.75069444444440.110301253153079904.347789285836
Winsorized Mean ( 18 / 24 )99.77069444444440.105669178149699944.179714382764
Winsorized Mean ( 19 / 24 )99.81555555555560.09356253063928931066.83257574951
Winsorized Mean ( 20 / 24 )99.8350.09070817711723211100.61742141475
Winsorized Mean ( 21 / 24 )99.84958333333330.08780567833510191137.16544563629
Winsorized Mean ( 22 / 24 )99.83430555555550.08332671954714571198.10675492955
Winsorized Mean ( 23 / 24 )99.85027777777780.08106248006196111231.76934262875
Winsorized Mean ( 24 / 24 )99.86361111111110.07651733403796061305.1109577546
Trimmed Mean ( 1 / 24 )99.77357142857140.15698690266139635.553474443509
Trimmed Mean ( 2 / 24 )99.77794117647060.153343560458066650.682303700365
Trimmed Mean ( 3 / 24 )99.78090909090910.150971944671792660.923519981342
Trimmed Mean ( 4 / 24 )99.7831250.148388144467982672.446746724636
Trimmed Mean ( 5 / 24 )99.78403225806450.145592656266815685.364460108474
Trimmed Mean ( 6 / 24 )99.78566666666670.142496380500502700.268079204405
Trimmed Mean ( 7 / 24 )99.78724137931030.139345282915307716.114957690818
Trimmed Mean ( 8 / 24 )99.78946428571430.135768237310953734.998599541102
Trimmed Mean ( 9 / 24 )99.79166666666670.13226583939604754.478005222975
Trimmed Mean ( 10 / 24 )99.79442307692310.128912498958588774.125270110395
Trimmed Mean ( 11 / 24 )99.79920.125886194149919792.773192278325
Trimmed Mean ( 12 / 24 )99.80729166666670.12358229362006807.618055491937
Trimmed Mean ( 13 / 24 )99.81478260869570.121386809019377822.286897687228
Trimmed Mean ( 14 / 24 )99.82363636363640.118722539234612840.81453283585
Trimmed Mean ( 15 / 24 )99.83333333333330.11633219019103858.174621911584
Trimmed Mean ( 16 / 24 )99.845250.113746224225866877.789576572994
Trimmed Mean ( 17 / 24 )99.85868421052630.110184231505019906.28833950689
Trimmed Mean ( 18 / 24 )99.87138888888890.106756028622586935.510529732836
Trimmed Mean ( 19 / 24 )99.88323529411770.103164476423641968.194079558465
Trimmed Mean ( 20 / 24 )99.891250.101377359166694985.340817921183
Trimmed Mean ( 21 / 24 )99.8980.09936048383098011005.4097579671
Trimmed Mean ( 22 / 24 )99.90392857142860.09699361688171771030.00518779767
Trimmed Mean ( 23 / 24 )99.91269230769230.09449714312703631057.30913127581
Trimmed Mean ( 24 / 24 )99.92083333333330.0911121236835451096.67988510929
Median99.945
Midrange99.61
Midmean - Weighted Average at Xnp99.8340540540541
Midmean - Weighted Average at X(n+1)p99.8713888888889
Midmean - Empirical Distribution Function99.8340540540541
Midmean - Empirical Distribution Function - Averaging99.8713888888889
Midmean - Empirical Distribution Function - Interpolation99.8713888888889
Midmean - Closest Observation99.8340540540541
Midmean - True Basic - Statistics Graphics Toolkit99.8713888888889
Midmean - MS Excel (old versions)99.8586842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.7690277777778 & 0.161572156649804 & 617.488989727481 \tabularnewline
Geometric Mean & 99.7597227250873 &  &  \tabularnewline
Harmonic Mean & 99.7504019622452 &  &  \tabularnewline
Quadratic Mean & 99.7783162746852 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.7694444444444 & 0.160042161024875 & 623.394759265575 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.7725 & 0.15689022980958 & 635.938261554564 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.775 & 0.156230789116354 & 638.638520385966 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.78 & 0.155262033042654 & 642.655503374659 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.7772222222222 & 0.154231425584419 & 646.931854802892 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.7780555555556 & 0.151931054560748 & 656.732462260772 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.7751388888889 & 0.150712573641033 & 662.022659944307 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.77625 & 0.146956664524083 & 678.950153932277 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.77375 & 0.142640321256102 & 699.477883402005 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.76125 & 0.137353270337684 & 726.311428586564 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.7398611111111 & 0.130170150635292 & 766.22682407859 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.7498611111111 & 0.126369259984987 & 789.352261166692 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.7444444444444 & 0.125043480526803 & 797.678087847725 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.7444444444445 & 0.119706031569374 & 833.244934584928 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.7340277777778 & 0.116445911151375 & 856.48372529051 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.7318055555556 & 0.11615469933657 & 858.611886778445 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.7506944444444 & 0.110301253153079 & 904.347789285836 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.7706944444444 & 0.105669178149699 & 944.179714382764 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.8155555555556 & 0.0935625306392893 & 1066.83257574951 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.835 & 0.0907081771172321 & 1100.61742141475 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.8495833333333 & 0.0878056783351019 & 1137.16544563629 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 99.8343055555555 & 0.0833267195471457 & 1198.10675492955 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 99.8502777777778 & 0.0810624800619611 & 1231.76934262875 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 99.8636111111111 & 0.0765173340379606 & 1305.1109577546 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.7735714285714 & 0.15698690266139 & 635.553474443509 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.7779411764706 & 0.153343560458066 & 650.682303700365 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.7809090909091 & 0.150971944671792 & 660.923519981342 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.783125 & 0.148388144467982 & 672.446746724636 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.7840322580645 & 0.145592656266815 & 685.364460108474 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.7856666666667 & 0.142496380500502 & 700.268079204405 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.7872413793103 & 0.139345282915307 & 716.114957690818 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.7894642857143 & 0.135768237310953 & 734.998599541102 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 99.7916666666667 & 0.13226583939604 & 754.478005222975 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.7944230769231 & 0.128912498958588 & 774.125270110395 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.7992 & 0.125886194149919 & 792.773192278325 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.8072916666667 & 0.12358229362006 & 807.618055491937 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.8147826086957 & 0.121386809019377 & 822.286897687228 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.8236363636364 & 0.118722539234612 & 840.81453283585 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.8333333333333 & 0.11633219019103 & 858.174621911584 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.84525 & 0.113746224225866 & 877.789576572994 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.8586842105263 & 0.110184231505019 & 906.28833950689 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.8713888888889 & 0.106756028622586 & 935.510529732836 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.8832352941177 & 0.103164476423641 & 968.194079558465 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.89125 & 0.101377359166694 & 985.340817921183 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.898 & 0.0993604838309801 & 1005.4097579671 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.9039285714286 & 0.0969936168817177 & 1030.00518779767 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.9126923076923 & 0.0944971431270363 & 1057.30913127581 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.9208333333333 & 0.091112123683545 & 1096.67988510929 \tabularnewline
Median & 99.945 &  &  \tabularnewline
Midrange & 99.61 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.8340540540541 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.8713888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.8340540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.8713888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.8713888888889 &  &  \tabularnewline
Midmean - Closest Observation & 99.8340540540541 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.8713888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.8586842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293525&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]99.7690277777778[/C][C]0.161572156649804[/C][C]617.488989727481[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.7597227250873[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.7504019622452[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.7783162746852[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.7694444444444[/C][C]0.160042161024875[/C][C]623.394759265575[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.7725[/C][C]0.15689022980958[/C][C]635.938261554564[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.775[/C][C]0.156230789116354[/C][C]638.638520385966[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.78[/C][C]0.155262033042654[/C][C]642.655503374659[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.7772222222222[/C][C]0.154231425584419[/C][C]646.931854802892[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.7780555555556[/C][C]0.151931054560748[/C][C]656.732462260772[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.7751388888889[/C][C]0.150712573641033[/C][C]662.022659944307[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.77625[/C][C]0.146956664524083[/C][C]678.950153932277[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.77375[/C][C]0.142640321256102[/C][C]699.477883402005[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.76125[/C][C]0.137353270337684[/C][C]726.311428586564[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.7398611111111[/C][C]0.130170150635292[/C][C]766.22682407859[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.7498611111111[/C][C]0.126369259984987[/C][C]789.352261166692[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.7444444444444[/C][C]0.125043480526803[/C][C]797.678087847725[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.7444444444445[/C][C]0.119706031569374[/C][C]833.244934584928[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.7340277777778[/C][C]0.116445911151375[/C][C]856.48372529051[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.7318055555556[/C][C]0.11615469933657[/C][C]858.611886778445[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.7506944444444[/C][C]0.110301253153079[/C][C]904.347789285836[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.7706944444444[/C][C]0.105669178149699[/C][C]944.179714382764[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.8155555555556[/C][C]0.0935625306392893[/C][C]1066.83257574951[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.835[/C][C]0.0907081771172321[/C][C]1100.61742141475[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.8495833333333[/C][C]0.0878056783351019[/C][C]1137.16544563629[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]99.8343055555555[/C][C]0.0833267195471457[/C][C]1198.10675492955[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]99.8502777777778[/C][C]0.0810624800619611[/C][C]1231.76934262875[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]99.8636111111111[/C][C]0.0765173340379606[/C][C]1305.1109577546[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.7735714285714[/C][C]0.15698690266139[/C][C]635.553474443509[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.7779411764706[/C][C]0.153343560458066[/C][C]650.682303700365[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.7809090909091[/C][C]0.150971944671792[/C][C]660.923519981342[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.783125[/C][C]0.148388144467982[/C][C]672.446746724636[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.7840322580645[/C][C]0.145592656266815[/C][C]685.364460108474[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.7856666666667[/C][C]0.142496380500502[/C][C]700.268079204405[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.7872413793103[/C][C]0.139345282915307[/C][C]716.114957690818[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.7894642857143[/C][C]0.135768237310953[/C][C]734.998599541102[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]99.7916666666667[/C][C]0.13226583939604[/C][C]754.478005222975[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.7944230769231[/C][C]0.128912498958588[/C][C]774.125270110395[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.7992[/C][C]0.125886194149919[/C][C]792.773192278325[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.8072916666667[/C][C]0.12358229362006[/C][C]807.618055491937[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.8147826086957[/C][C]0.121386809019377[/C][C]822.286897687228[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.8236363636364[/C][C]0.118722539234612[/C][C]840.81453283585[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.8333333333333[/C][C]0.11633219019103[/C][C]858.174621911584[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.84525[/C][C]0.113746224225866[/C][C]877.789576572994[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.8586842105263[/C][C]0.110184231505019[/C][C]906.28833950689[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.8713888888889[/C][C]0.106756028622586[/C][C]935.510529732836[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.8832352941177[/C][C]0.103164476423641[/C][C]968.194079558465[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.89125[/C][C]0.101377359166694[/C][C]985.340817921183[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.898[/C][C]0.0993604838309801[/C][C]1005.4097579671[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.9039285714286[/C][C]0.0969936168817177[/C][C]1030.00518779767[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.9126923076923[/C][C]0.0944971431270363[/C][C]1057.30913127581[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.9208333333333[/C][C]0.091112123683545[/C][C]1096.67988510929[/C][/ROW]
[ROW][C]Median[/C][C]99.945[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.61[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.8340540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.8713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.8340540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.8713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.8713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.8340540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.8713888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.8586842105263[/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=293525&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293525&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 Mean99.76902777777780.161572156649804617.488989727481
Geometric Mean99.7597227250873
Harmonic Mean99.7504019622452
Quadratic Mean99.7783162746852
Winsorized Mean ( 1 / 24 )99.76944444444440.160042161024875623.394759265575
Winsorized Mean ( 2 / 24 )99.77250.15689022980958635.938261554564
Winsorized Mean ( 3 / 24 )99.7750.156230789116354638.638520385966
Winsorized Mean ( 4 / 24 )99.780.155262033042654642.655503374659
Winsorized Mean ( 5 / 24 )99.77722222222220.154231425584419646.931854802892
Winsorized Mean ( 6 / 24 )99.77805555555560.151931054560748656.732462260772
Winsorized Mean ( 7 / 24 )99.77513888888890.150712573641033662.022659944307
Winsorized Mean ( 8 / 24 )99.776250.146956664524083678.950153932277
Winsorized Mean ( 9 / 24 )99.773750.142640321256102699.477883402005
Winsorized Mean ( 10 / 24 )99.761250.137353270337684726.311428586564
Winsorized Mean ( 11 / 24 )99.73986111111110.130170150635292766.22682407859
Winsorized Mean ( 12 / 24 )99.74986111111110.126369259984987789.352261166692
Winsorized Mean ( 13 / 24 )99.74444444444440.125043480526803797.678087847725
Winsorized Mean ( 14 / 24 )99.74444444444450.119706031569374833.244934584928
Winsorized Mean ( 15 / 24 )99.73402777777780.116445911151375856.48372529051
Winsorized Mean ( 16 / 24 )99.73180555555560.11615469933657858.611886778445
Winsorized Mean ( 17 / 24 )99.75069444444440.110301253153079904.347789285836
Winsorized Mean ( 18 / 24 )99.77069444444440.105669178149699944.179714382764
Winsorized Mean ( 19 / 24 )99.81555555555560.09356253063928931066.83257574951
Winsorized Mean ( 20 / 24 )99.8350.09070817711723211100.61742141475
Winsorized Mean ( 21 / 24 )99.84958333333330.08780567833510191137.16544563629
Winsorized Mean ( 22 / 24 )99.83430555555550.08332671954714571198.10675492955
Winsorized Mean ( 23 / 24 )99.85027777777780.08106248006196111231.76934262875
Winsorized Mean ( 24 / 24 )99.86361111111110.07651733403796061305.1109577546
Trimmed Mean ( 1 / 24 )99.77357142857140.15698690266139635.553474443509
Trimmed Mean ( 2 / 24 )99.77794117647060.153343560458066650.682303700365
Trimmed Mean ( 3 / 24 )99.78090909090910.150971944671792660.923519981342
Trimmed Mean ( 4 / 24 )99.7831250.148388144467982672.446746724636
Trimmed Mean ( 5 / 24 )99.78403225806450.145592656266815685.364460108474
Trimmed Mean ( 6 / 24 )99.78566666666670.142496380500502700.268079204405
Trimmed Mean ( 7 / 24 )99.78724137931030.139345282915307716.114957690818
Trimmed Mean ( 8 / 24 )99.78946428571430.135768237310953734.998599541102
Trimmed Mean ( 9 / 24 )99.79166666666670.13226583939604754.478005222975
Trimmed Mean ( 10 / 24 )99.79442307692310.128912498958588774.125270110395
Trimmed Mean ( 11 / 24 )99.79920.125886194149919792.773192278325
Trimmed Mean ( 12 / 24 )99.80729166666670.12358229362006807.618055491937
Trimmed Mean ( 13 / 24 )99.81478260869570.121386809019377822.286897687228
Trimmed Mean ( 14 / 24 )99.82363636363640.118722539234612840.81453283585
Trimmed Mean ( 15 / 24 )99.83333333333330.11633219019103858.174621911584
Trimmed Mean ( 16 / 24 )99.845250.113746224225866877.789576572994
Trimmed Mean ( 17 / 24 )99.85868421052630.110184231505019906.28833950689
Trimmed Mean ( 18 / 24 )99.87138888888890.106756028622586935.510529732836
Trimmed Mean ( 19 / 24 )99.88323529411770.103164476423641968.194079558465
Trimmed Mean ( 20 / 24 )99.891250.101377359166694985.340817921183
Trimmed Mean ( 21 / 24 )99.8980.09936048383098011005.4097579671
Trimmed Mean ( 22 / 24 )99.90392857142860.09699361688171771030.00518779767
Trimmed Mean ( 23 / 24 )99.91269230769230.09449714312703631057.30913127581
Trimmed Mean ( 24 / 24 )99.92083333333330.0911121236835451096.67988510929
Median99.945
Midrange99.61
Midmean - Weighted Average at Xnp99.8340540540541
Midmean - Weighted Average at X(n+1)p99.8713888888889
Midmean - Empirical Distribution Function99.8340540540541
Midmean - Empirical Distribution Function - Averaging99.8713888888889
Midmean - Empirical Distribution Function - Interpolation99.8713888888889
Midmean - Closest Observation99.8340540540541
Midmean - True Basic - Statistics Graphics Toolkit99.8713888888889
Midmean - MS Excel (old versions)99.8586842105263
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')