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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 19 Oct 2008 11:29:50 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/19/t12244376708vrdcqb44tifqmv.htm/, Retrieved Sun, 19 May 2024 14:45:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16989, Retrieved Sun, 19 May 2024 14:45:25 +0000
QR Codes:

Original text written by user:Werkelijk begonnen woongebouwen - koninkrijk, Aantal gebouwen
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [blog 1e tijdreeks...] [2008-10-13 19:23:31] [7173087adebe3e3a714c80ea2417b3eb]
- RMPD    [Central Tendency] [tijdreeks 4 centr...] [2008-10-19 17:29:50] [95d95b0e883740fcbc85e18ec42dcafb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.712
2.641
2.267
2.126
2.231
1.517
2.010
2.628
2.115
1.829
1.636
1.787
2.122
2.620
2.555
2.337
2.524
1.801
2.417
2.389
2.267
2.135
1.760
1.905
2.176
2.344
2.673
2.766
2.785
2.003
2.588
2.739
2.703
2.464
1.974
2.164
2.385
2.936
2.700
2.855
2.764
1.808
2.588
2.600
2.526
2.259
1.738
1.902
2.137
2.460
2.495
2.525
2.465
1.828
2.273
2.377
2.344
2.071
1.611
1.671

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16989&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16989&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16989&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.267133333333330.047064983724973448.1702776438092
Geometric Mean2.23694317632963
Harmonic Mean2.20553667758703
Quadratic Mean2.29577551167356
Winsorized Mean ( 1 / 20 )2.267350.046357465314612348.9101374419906
Winsorized Mean ( 2 / 20 )2.265850.045684528806986549.597753532121
Winsorized Mean ( 3 / 20 )2.266650.045103514494704450.2543986958295
Winsorized Mean ( 4 / 20 )2.269250.044482235551521251.0147471651163
Winsorized Mean ( 5 / 20 )2.269333333333330.04364216762177351.9986393205907
Winsorized Mean ( 6 / 20 )2.267933333333330.042552114054957853.2977828176575
Winsorized Mean ( 7 / 20 )2.270733333333330.041864186295232854.2404745984973
Winsorized Mean ( 8 / 20 )2.2690.040885882248419755.4959285509291
Winsorized Mean ( 9 / 20 )2.265250.039896763847920356.777788008941
Winsorized Mean ( 10 / 20 )2.266416666666670.038911077037212158.246053289638
Winsorized Mean ( 11 / 20 )2.265133333333330.038646401274246758.611753194282
Winsorized Mean ( 12 / 20 )2.275733333333330.035314213993534864.4424178250142
Winsorized Mean ( 13 / 20 )2.273783333333330.034796219449061865.3457004621414
Winsorized Mean ( 14 / 20 )2.289883333333330.031999126856614271.5608067555761
Winsorized Mean ( 15 / 20 )2.288883333333330.02951442328307677.551348755163
Winsorized Mean ( 16 / 20 )2.283016666666670.028047976368051081.3968407812555
Winsorized Mean ( 17 / 20 )2.300016666666670.025246328721934491.1030150957504
Winsorized Mean ( 18 / 20 )2.312916666666670.023230207439125199.5650457589619
Winsorized Mean ( 19 / 20 )2.305950.0215177817020838107.164857043637
Winsorized Mean ( 20 / 20 )2.297283333333330.0198624804816801115.659438178036
Trimmed Mean ( 1 / 20 )2.268534482758620.045456954073432449.9051141678777
Trimmed Mean ( 2 / 20 )2.269803571428570.044338276241051951.192869093251
Trimmed Mean ( 3 / 20 )2.2720.043387017222345852.3658952713127
Trimmed Mean ( 4 / 20 )2.274057692307690.042464015583826153.552582369856
Trimmed Mean ( 5 / 20 )2.27550.041531942464782054.7891542017224
Trimmed Mean ( 6 / 20 )2.277041666666670.040618871150709356.058713651054
Trimmed Mean ( 7 / 20 )2.279021739130430.039765040470296157.3121946357085
Trimmed Mean ( 8 / 20 )2.280636363636360.038837372899444958.7227248748578
Trimmed Mean ( 9 / 20 )2.282714285714290.037870129037322660.277436167819
Trimmed Mean ( 10 / 20 )2.2856250.036825466514008562.0664234933872
Trimmed Mean ( 11 / 20 )2.288657894736840.035666271134063364.1686899685749
Trimmed Mean ( 12 / 20 )2.292222222222220.034121843097447867.1775617652282
Trimmed Mean ( 13 / 20 )2.294647058823530.032972437102408269.5928860731964
Trimmed Mean ( 14 / 20 )2.297656250.031457331873168073.0404046746197
Trimmed Mean ( 15 / 20 )2.298766666666670.030182535992311976.162144468318
Trimmed Mean ( 16 / 20 )2.300178571428570.029081351575334779.0946241088555
Trimmed Mean ( 17 / 20 )2.302653846153850.027846001912037782.6924401365648
Trimmed Mean ( 18 / 20 )2.303041666666670.026949528723707885.4575859295326
Trimmed Mean ( 19 / 20 )2.301545454545450.026180916290382587.9092782322109
Trimmed Mean ( 20 / 20 )2.300850.025495229171872890.2462960614754
Median2.305
Midrange2.2265
Midmean - Weighted Average at Xnp2.28829032258065
Midmean - Weighted Average at X(n+1)p2.29876666666667
Midmean - Empirical Distribution Function2.28829032258065
Midmean - Empirical Distribution Function - Averaging2.29876666666667
Midmean - Empirical Distribution Function - Interpolation2.29876666666667
Midmean - Closest Observation2.28829032258065
Midmean - True Basic - Statistics Graphics Toolkit2.29876666666667
Midmean - MS Excel (old versions)2.30645454545455
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.26713333333333 & 0.0470649837249734 & 48.1702776438092 \tabularnewline
Geometric Mean & 2.23694317632963 &  &  \tabularnewline
Harmonic Mean & 2.20553667758703 &  &  \tabularnewline
Quadratic Mean & 2.29577551167356 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.26735 & 0.0463574653146123 & 48.9101374419906 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.26585 & 0.0456845288069865 & 49.597753532121 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.26665 & 0.0451035144947044 & 50.2543986958295 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.26925 & 0.0444822355515212 & 51.0147471651163 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.26933333333333 & 0.043642167621773 & 51.9986393205907 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.26793333333333 & 0.0425521140549578 & 53.2977828176575 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.27073333333333 & 0.0418641862952328 & 54.2404745984973 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.269 & 0.0408858822484197 & 55.4959285509291 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.26525 & 0.0398967638479203 & 56.777788008941 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.26641666666667 & 0.0389110770372121 & 58.246053289638 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.26513333333333 & 0.0386464012742467 & 58.611753194282 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.27573333333333 & 0.0353142139935348 & 64.4424178250142 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.27378333333333 & 0.0347962194490618 & 65.3457004621414 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.28988333333333 & 0.0319991268566142 & 71.5608067555761 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.28888333333333 & 0.029514423283076 & 77.551348755163 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.28301666666667 & 0.0280479763680510 & 81.3968407812555 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.30001666666667 & 0.0252463287219344 & 91.1030150957504 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.31291666666667 & 0.0232302074391251 & 99.5650457589619 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.30595 & 0.0215177817020838 & 107.164857043637 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.29728333333333 & 0.0198624804816801 & 115.659438178036 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.26853448275862 & 0.0454569540734324 & 49.9051141678777 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.26980357142857 & 0.0443382762410519 & 51.192869093251 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.272 & 0.0433870172223458 & 52.3658952713127 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.27405769230769 & 0.0424640155838261 & 53.552582369856 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.2755 & 0.0415319424647820 & 54.7891542017224 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.27704166666667 & 0.0406188711507093 & 56.058713651054 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.27902173913043 & 0.0397650404702961 & 57.3121946357085 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.28063636363636 & 0.0388373728994449 & 58.7227248748578 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.28271428571429 & 0.0378701290373226 & 60.277436167819 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.285625 & 0.0368254665140085 & 62.0664234933872 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.28865789473684 & 0.0356662711340633 & 64.1686899685749 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.29222222222222 & 0.0341218430974478 & 67.1775617652282 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.29464705882353 & 0.0329724371024082 & 69.5928860731964 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.29765625 & 0.0314573318731680 & 73.0404046746197 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.29876666666667 & 0.0301825359923119 & 76.162144468318 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.30017857142857 & 0.0290813515753347 & 79.0946241088555 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.30265384615385 & 0.0278460019120377 & 82.6924401365648 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.30304166666667 & 0.0269495287237078 & 85.4575859295326 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.30154545454545 & 0.0261809162903825 & 87.9092782322109 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.30085 & 0.0254952291718728 & 90.2462960614754 \tabularnewline
Median & 2.305 &  &  \tabularnewline
Midrange & 2.2265 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.28829032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.29876666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.28829032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.29876666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.29876666666667 &  &  \tabularnewline
Midmean - Closest Observation & 2.28829032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.29876666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.30645454545455 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16989&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]2.26713333333333[/C][C]0.0470649837249734[/C][C]48.1702776438092[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.23694317632963[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.20553667758703[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.29577551167356[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.26735[/C][C]0.0463574653146123[/C][C]48.9101374419906[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.26585[/C][C]0.0456845288069865[/C][C]49.597753532121[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.26665[/C][C]0.0451035144947044[/C][C]50.2543986958295[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.26925[/C][C]0.0444822355515212[/C][C]51.0147471651163[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.26933333333333[/C][C]0.043642167621773[/C][C]51.9986393205907[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.26793333333333[/C][C]0.0425521140549578[/C][C]53.2977828176575[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.27073333333333[/C][C]0.0418641862952328[/C][C]54.2404745984973[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.269[/C][C]0.0408858822484197[/C][C]55.4959285509291[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.26525[/C][C]0.0398967638479203[/C][C]56.777788008941[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.26641666666667[/C][C]0.0389110770372121[/C][C]58.246053289638[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.26513333333333[/C][C]0.0386464012742467[/C][C]58.611753194282[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.27573333333333[/C][C]0.0353142139935348[/C][C]64.4424178250142[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.27378333333333[/C][C]0.0347962194490618[/C][C]65.3457004621414[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.28988333333333[/C][C]0.0319991268566142[/C][C]71.5608067555761[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.28888333333333[/C][C]0.029514423283076[/C][C]77.551348755163[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.28301666666667[/C][C]0.0280479763680510[/C][C]81.3968407812555[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.30001666666667[/C][C]0.0252463287219344[/C][C]91.1030150957504[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.31291666666667[/C][C]0.0232302074391251[/C][C]99.5650457589619[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.30595[/C][C]0.0215177817020838[/C][C]107.164857043637[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.29728333333333[/C][C]0.0198624804816801[/C][C]115.659438178036[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.26853448275862[/C][C]0.0454569540734324[/C][C]49.9051141678777[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.26980357142857[/C][C]0.0443382762410519[/C][C]51.192869093251[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.272[/C][C]0.0433870172223458[/C][C]52.3658952713127[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.27405769230769[/C][C]0.0424640155838261[/C][C]53.552582369856[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.2755[/C][C]0.0415319424647820[/C][C]54.7891542017224[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.27704166666667[/C][C]0.0406188711507093[/C][C]56.058713651054[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.27902173913043[/C][C]0.0397650404702961[/C][C]57.3121946357085[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.28063636363636[/C][C]0.0388373728994449[/C][C]58.7227248748578[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.28271428571429[/C][C]0.0378701290373226[/C][C]60.277436167819[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.285625[/C][C]0.0368254665140085[/C][C]62.0664234933872[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.28865789473684[/C][C]0.0356662711340633[/C][C]64.1686899685749[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.29222222222222[/C][C]0.0341218430974478[/C][C]67.1775617652282[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.29464705882353[/C][C]0.0329724371024082[/C][C]69.5928860731964[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.29765625[/C][C]0.0314573318731680[/C][C]73.0404046746197[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.29876666666667[/C][C]0.0301825359923119[/C][C]76.162144468318[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.30017857142857[/C][C]0.0290813515753347[/C][C]79.0946241088555[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.30265384615385[/C][C]0.0278460019120377[/C][C]82.6924401365648[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.30304166666667[/C][C]0.0269495287237078[/C][C]85.4575859295326[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.30154545454545[/C][C]0.0261809162903825[/C][C]87.9092782322109[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.30085[/C][C]0.0254952291718728[/C][C]90.2462960614754[/C][/ROW]
[ROW][C]Median[/C][C]2.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.2265[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.28829032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.29876666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.28829032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.29876666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.29876666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.28829032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.29876666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.30645454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16989&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16989&T=1

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.267133333333330.047064983724973448.1702776438092
Geometric Mean2.23694317632963
Harmonic Mean2.20553667758703
Quadratic Mean2.29577551167356
Winsorized Mean ( 1 / 20 )2.267350.046357465314612348.9101374419906
Winsorized Mean ( 2 / 20 )2.265850.045684528806986549.597753532121
Winsorized Mean ( 3 / 20 )2.266650.045103514494704450.2543986958295
Winsorized Mean ( 4 / 20 )2.269250.044482235551521251.0147471651163
Winsorized Mean ( 5 / 20 )2.269333333333330.04364216762177351.9986393205907
Winsorized Mean ( 6 / 20 )2.267933333333330.042552114054957853.2977828176575
Winsorized Mean ( 7 / 20 )2.270733333333330.041864186295232854.2404745984973
Winsorized Mean ( 8 / 20 )2.2690.040885882248419755.4959285509291
Winsorized Mean ( 9 / 20 )2.265250.039896763847920356.777788008941
Winsorized Mean ( 10 / 20 )2.266416666666670.038911077037212158.246053289638
Winsorized Mean ( 11 / 20 )2.265133333333330.038646401274246758.611753194282
Winsorized Mean ( 12 / 20 )2.275733333333330.035314213993534864.4424178250142
Winsorized Mean ( 13 / 20 )2.273783333333330.034796219449061865.3457004621414
Winsorized Mean ( 14 / 20 )2.289883333333330.031999126856614271.5608067555761
Winsorized Mean ( 15 / 20 )2.288883333333330.02951442328307677.551348755163
Winsorized Mean ( 16 / 20 )2.283016666666670.028047976368051081.3968407812555
Winsorized Mean ( 17 / 20 )2.300016666666670.025246328721934491.1030150957504
Winsorized Mean ( 18 / 20 )2.312916666666670.023230207439125199.5650457589619
Winsorized Mean ( 19 / 20 )2.305950.0215177817020838107.164857043637
Winsorized Mean ( 20 / 20 )2.297283333333330.0198624804816801115.659438178036
Trimmed Mean ( 1 / 20 )2.268534482758620.045456954073432449.9051141678777
Trimmed Mean ( 2 / 20 )2.269803571428570.044338276241051951.192869093251
Trimmed Mean ( 3 / 20 )2.2720.043387017222345852.3658952713127
Trimmed Mean ( 4 / 20 )2.274057692307690.042464015583826153.552582369856
Trimmed Mean ( 5 / 20 )2.27550.041531942464782054.7891542017224
Trimmed Mean ( 6 / 20 )2.277041666666670.040618871150709356.058713651054
Trimmed Mean ( 7 / 20 )2.279021739130430.039765040470296157.3121946357085
Trimmed Mean ( 8 / 20 )2.280636363636360.038837372899444958.7227248748578
Trimmed Mean ( 9 / 20 )2.282714285714290.037870129037322660.277436167819
Trimmed Mean ( 10 / 20 )2.2856250.036825466514008562.0664234933872
Trimmed Mean ( 11 / 20 )2.288657894736840.035666271134063364.1686899685749
Trimmed Mean ( 12 / 20 )2.292222222222220.034121843097447867.1775617652282
Trimmed Mean ( 13 / 20 )2.294647058823530.032972437102408269.5928860731964
Trimmed Mean ( 14 / 20 )2.297656250.031457331873168073.0404046746197
Trimmed Mean ( 15 / 20 )2.298766666666670.030182535992311976.162144468318
Trimmed Mean ( 16 / 20 )2.300178571428570.029081351575334779.0946241088555
Trimmed Mean ( 17 / 20 )2.302653846153850.027846001912037782.6924401365648
Trimmed Mean ( 18 / 20 )2.303041666666670.026949528723707885.4575859295326
Trimmed Mean ( 19 / 20 )2.301545454545450.026180916290382587.9092782322109
Trimmed Mean ( 20 / 20 )2.300850.025495229171872890.2462960614754
Median2.305
Midrange2.2265
Midmean - Weighted Average at Xnp2.28829032258065
Midmean - Weighted Average at X(n+1)p2.29876666666667
Midmean - Empirical Distribution Function2.28829032258065
Midmean - Empirical Distribution Function - Averaging2.29876666666667
Midmean - Empirical Distribution Function - Interpolation2.29876666666667
Midmean - Closest Observation2.28829032258065
Midmean - True Basic - Statistics Graphics Toolkit2.29876666666667
Midmean - MS Excel (old versions)2.30645454545455
Number of observations60


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')