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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 14 Nov 2008 06:40:51 -0700
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/Nov/14/t1226670244zcbobknfslq8b9v.htm/, Retrieved Mon, 20 May 2024 12:12:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24933, Retrieved Mon, 20 May 2024 12:12:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper central ten...] [2008-11-14 13:40:51] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
- RMPD    [Notched Boxplots] [hypothese notched...] [2008-11-30 11:09:52] [077ffec662d24c06be4c491541a44245]
- RMPD    [Mean Plot] [paper seizoenalit...] [2008-11-30 12:54:18] [077ffec662d24c06be4c491541a44245]
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Dataseries X:
15370.60
14956.90
15469.70
15101.80
11703.70
16283.60
16726.50
14968.90
14861.00
14583.30
15305.80
17903.90
16379.40
15420.30
17870.50
15912.80
13866.50
17823.20
17872.00
17420.40
16704.40
15991.20
16583.60
19123.50
17838.70
17209.40
18586.50
16258.10
15141.60
19202.10
17746.50
19090.10
18040.30
17515.50
17751.80
21072.40
17170.00
19439.50
19795.40
17574.90
16165.40
19464.60
19932.10
19961.20
17343.40
18924.20
18574.10
21350.60
18594.60
19823.10
20844.40
19640.20
17735.40
19813.60
22238.50
20682.20
17818.60
21872.10
22117.00
21865.90




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24933&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=24933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24933&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17806.625289.97442411693761.4075708719028
Geometric Mean17664.2467603428
Harmonic Mean17518.0236876422
Quadratic Mean17945.3871154261
Winsorized Mean ( 1 / 20 )17840.6466666667278.62087192782864.0319820378999
Winsorized Mean ( 2 / 20 )17856.3766666667271.19617383480365.8430257852523
Winsorized Mean ( 3 / 20 )17869.9516666667268.37820947156366.5849574816549
Winsorized Mean ( 4 / 20 )17841.9916666667258.87945678035368.9200753453556
Winsorized Mean ( 5 / 20 )17819.8083333333253.50467725759770.2938049353065
Winsorized Mean ( 6 / 20 )17810.2983333333246.13595318259772.3595968124198
Winsorized Mean ( 7 / 20 )17796.0183333333241.37523481123573.7276065096343
Winsorized Mean ( 8 / 20 )17721.7783333333219.15511945811180.8640855716842
Winsorized Mean ( 9 / 20 )17727.1333333333216.59618164240981.8441636362734
Winsorized Mean ( 10 / 20 )17717.25211.97461173398683.581943399118
Winsorized Mean ( 11 / 20 )17724.565210.02544489141384.3924649661563
Winsorized Mean ( 12 / 20 )17809.545193.96759666519991.8171143334854
Winsorized Mean ( 13 / 20 )17792.905185.40207750018495.9692859967136
Winsorized Mean ( 14 / 20 )17792.5783333333171.952450924809103.473828012568
Winsorized Mean ( 15 / 20 )17809.4783333333167.236142021568106.492999169022
Winsorized Mean ( 16 / 20 )17752.9716666667155.935443075965113.848213827938
Winsorized Mean ( 17 / 20 )17757.845148.132523131083119.878097156868
Winsorized Mean ( 18 / 20 )17809.085137.076932187711129.920364541078
Winsorized Mean ( 19 / 20 )17794.8033333333123.053909204190144.609817342783
Winsorized Mean ( 20 / 20 )17692.3033333333105.367061903969167.911138581979
Trimmed Mean ( 1 / 20 )17835.4362068966269.84240397059766.0957504990208
Trimmed Mean ( 2 / 20 )17829.8535714286259.01922091799168.8360250186752
Trimmed Mean ( 3 / 20 )17815.1185185185250.60970801575271.0871045641965
Trimmed Mean ( 4 / 20 )17794.0288461538241.43689160311173.7005381737799
Trimmed Mean ( 5 / 20 )17779.64233.76329437257376.0583052515623
Trimmed Mean ( 6 / 20 )17769.5979166667225.90790263777578.658593653356
Trimmed Mean ( 7 / 20 )17760.75218.20347685496381.3953574708866
Trimmed Mean ( 8 / 20 )17753.8795454545209.65278084404284.6822993426517
Trimmed Mean ( 9 / 20 )17759.6119047619204.89760722092286.6755456329628
Trimmed Mean ( 10 / 20 )17765.025199.14323255817189.207274441579
Trimmed Mean ( 11 / 20 )17772.5684210526192.55516266789892.2985817404708
Trimmed Mean ( 12 / 20 )17779.8416666667184.00318019918296.6279041885043
Trimmed Mean ( 13 / 20 )17775.4735294118176.899081692201100.483695898097
Trimmed Mean ( 14 / 20 )17772.959375169.350118030675104.948018824414
Trimmed Mean ( 15 / 20 )17770.1566666667162.607686595212109.282390265491
Trimmed Mean ( 16 / 20 )17764.5392857143154.002980055967115.351919029478
Trimmed Mean ( 17 / 20 )17766.2076923077145.020717662958122.508066286074
Trimmed Mean ( 18 / 20 )17767.4375133.952195643984132.640136390313
Trimmed Mean ( 19 / 20 )17761.1272727273120.899030747052146.908764801329
Trimmed Mean ( 20 / 20 )17755.81106.163748620010167.249275113232
Median17785.2
Midrange16971.1
Midmean - Weighted Average at Xnp17718.3903225806
Midmean - Weighted Average at X(n+1)p17770.1566666667
Midmean - Empirical Distribution Function17718.3903225806
Midmean - Empirical Distribution Function - Averaging17770.1566666667
Midmean - Empirical Distribution Function - Interpolation17770.1566666667
Midmean - Closest Observation17718.3903225806
Midmean - True Basic - Statistics Graphics Toolkit17770.1566666667
Midmean - MS Excel (old versions)17772.959375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17806.625 & 289.974424116937 & 61.4075708719028 \tabularnewline
Geometric Mean & 17664.2467603428 &  &  \tabularnewline
Harmonic Mean & 17518.0236876422 &  &  \tabularnewline
Quadratic Mean & 17945.3871154261 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17840.6466666667 & 278.620871927828 & 64.0319820378999 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17856.3766666667 & 271.196173834803 & 65.8430257852523 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17869.9516666667 & 268.378209471563 & 66.5849574816549 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17841.9916666667 & 258.879456780353 & 68.9200753453556 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17819.8083333333 & 253.504677257597 & 70.2938049353065 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 17810.2983333333 & 246.135953182597 & 72.3595968124198 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 17796.0183333333 & 241.375234811235 & 73.7276065096343 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17721.7783333333 & 219.155119458111 & 80.8640855716842 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17727.1333333333 & 216.596181642409 & 81.8441636362734 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17717.25 & 211.974611733986 & 83.581943399118 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17724.565 & 210.025444891413 & 84.3924649661563 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17809.545 & 193.967596665199 & 91.8171143334854 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17792.905 & 185.402077500184 & 95.9692859967136 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17792.5783333333 & 171.952450924809 & 103.473828012568 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17809.4783333333 & 167.236142021568 & 106.492999169022 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 17752.9716666667 & 155.935443075965 & 113.848213827938 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17757.845 & 148.132523131083 & 119.878097156868 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17809.085 & 137.076932187711 & 129.920364541078 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17794.8033333333 & 123.053909204190 & 144.609817342783 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 17692.3033333333 & 105.367061903969 & 167.911138581979 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17835.4362068966 & 269.842403970597 & 66.0957504990208 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17829.8535714286 & 259.019220917991 & 68.8360250186752 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17815.1185185185 & 250.609708015752 & 71.0871045641965 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17794.0288461538 & 241.436891603111 & 73.7005381737799 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17779.64 & 233.763294372573 & 76.0583052515623 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17769.5979166667 & 225.907902637775 & 78.658593653356 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17760.75 & 218.203476854963 & 81.3953574708866 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17753.8795454545 & 209.652780844042 & 84.6822993426517 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17759.6119047619 & 204.897607220922 & 86.6755456329628 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17765.025 & 199.143232558171 & 89.207274441579 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17772.5684210526 & 192.555162667898 & 92.2985817404708 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17779.8416666667 & 184.003180199182 & 96.6279041885043 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17775.4735294118 & 176.899081692201 & 100.483695898097 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17772.959375 & 169.350118030675 & 104.948018824414 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 17770.1566666667 & 162.607686595212 & 109.282390265491 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 17764.5392857143 & 154.002980055967 & 115.351919029478 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 17766.2076923077 & 145.020717662958 & 122.508066286074 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 17767.4375 & 133.952195643984 & 132.640136390313 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17761.1272727273 & 120.899030747052 & 146.908764801329 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17755.81 & 106.163748620010 & 167.249275113232 \tabularnewline
Median & 17785.2 &  &  \tabularnewline
Midrange & 16971.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17718.3903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17770.1566666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17718.3903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17770.1566666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17770.1566666667 &  &  \tabularnewline
Midmean - Closest Observation & 17718.3903225806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17770.1566666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17772.959375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24933&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]17806.625[/C][C]289.974424116937[/C][C]61.4075708719028[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17664.2467603428[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17518.0236876422[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17945.3871154261[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17840.6466666667[/C][C]278.620871927828[/C][C]64.0319820378999[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17856.3766666667[/C][C]271.196173834803[/C][C]65.8430257852523[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17869.9516666667[/C][C]268.378209471563[/C][C]66.5849574816549[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17841.9916666667[/C][C]258.879456780353[/C][C]68.9200753453556[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17819.8083333333[/C][C]253.504677257597[/C][C]70.2938049353065[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]17810.2983333333[/C][C]246.135953182597[/C][C]72.3595968124198[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]17796.0183333333[/C][C]241.375234811235[/C][C]73.7276065096343[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17721.7783333333[/C][C]219.155119458111[/C][C]80.8640855716842[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17727.1333333333[/C][C]216.596181642409[/C][C]81.8441636362734[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17717.25[/C][C]211.974611733986[/C][C]83.581943399118[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17724.565[/C][C]210.025444891413[/C][C]84.3924649661563[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17809.545[/C][C]193.967596665199[/C][C]91.8171143334854[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17792.905[/C][C]185.402077500184[/C][C]95.9692859967136[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17792.5783333333[/C][C]171.952450924809[/C][C]103.473828012568[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17809.4783333333[/C][C]167.236142021568[/C][C]106.492999169022[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]17752.9716666667[/C][C]155.935443075965[/C][C]113.848213827938[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17757.845[/C][C]148.132523131083[/C][C]119.878097156868[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17809.085[/C][C]137.076932187711[/C][C]129.920364541078[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17794.8033333333[/C][C]123.053909204190[/C][C]144.609817342783[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]17692.3033333333[/C][C]105.367061903969[/C][C]167.911138581979[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17835.4362068966[/C][C]269.842403970597[/C][C]66.0957504990208[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17829.8535714286[/C][C]259.019220917991[/C][C]68.8360250186752[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17815.1185185185[/C][C]250.609708015752[/C][C]71.0871045641965[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17794.0288461538[/C][C]241.436891603111[/C][C]73.7005381737799[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17779.64[/C][C]233.763294372573[/C][C]76.0583052515623[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17769.5979166667[/C][C]225.907902637775[/C][C]78.658593653356[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17760.75[/C][C]218.203476854963[/C][C]81.3953574708866[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17753.8795454545[/C][C]209.652780844042[/C][C]84.6822993426517[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17759.6119047619[/C][C]204.897607220922[/C][C]86.6755456329628[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17765.025[/C][C]199.143232558171[/C][C]89.207274441579[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17772.5684210526[/C][C]192.555162667898[/C][C]92.2985817404708[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17779.8416666667[/C][C]184.003180199182[/C][C]96.6279041885043[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17775.4735294118[/C][C]176.899081692201[/C][C]100.483695898097[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17772.959375[/C][C]169.350118030675[/C][C]104.948018824414[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]17770.1566666667[/C][C]162.607686595212[/C][C]109.282390265491[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]17764.5392857143[/C][C]154.002980055967[/C][C]115.351919029478[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]17766.2076923077[/C][C]145.020717662958[/C][C]122.508066286074[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]17767.4375[/C][C]133.952195643984[/C][C]132.640136390313[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17761.1272727273[/C][C]120.899030747052[/C][C]146.908764801329[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17755.81[/C][C]106.163748620010[/C][C]167.249275113232[/C][/ROW]
[ROW][C]Median[/C][C]17785.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16971.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17718.3903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17770.1566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17718.3903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17770.1566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17770.1566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17718.3903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17770.1566666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17772.959375[/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=24933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24933&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17806.625289.97442411693761.4075708719028
Geometric Mean17664.2467603428
Harmonic Mean17518.0236876422
Quadratic Mean17945.3871154261
Winsorized Mean ( 1 / 20 )17840.6466666667278.62087192782864.0319820378999
Winsorized Mean ( 2 / 20 )17856.3766666667271.19617383480365.8430257852523
Winsorized Mean ( 3 / 20 )17869.9516666667268.37820947156366.5849574816549
Winsorized Mean ( 4 / 20 )17841.9916666667258.87945678035368.9200753453556
Winsorized Mean ( 5 / 20 )17819.8083333333253.50467725759770.2938049353065
Winsorized Mean ( 6 / 20 )17810.2983333333246.13595318259772.3595968124198
Winsorized Mean ( 7 / 20 )17796.0183333333241.37523481123573.7276065096343
Winsorized Mean ( 8 / 20 )17721.7783333333219.15511945811180.8640855716842
Winsorized Mean ( 9 / 20 )17727.1333333333216.59618164240981.8441636362734
Winsorized Mean ( 10 / 20 )17717.25211.97461173398683.581943399118
Winsorized Mean ( 11 / 20 )17724.565210.02544489141384.3924649661563
Winsorized Mean ( 12 / 20 )17809.545193.96759666519991.8171143334854
Winsorized Mean ( 13 / 20 )17792.905185.40207750018495.9692859967136
Winsorized Mean ( 14 / 20 )17792.5783333333171.952450924809103.473828012568
Winsorized Mean ( 15 / 20 )17809.4783333333167.236142021568106.492999169022
Winsorized Mean ( 16 / 20 )17752.9716666667155.935443075965113.848213827938
Winsorized Mean ( 17 / 20 )17757.845148.132523131083119.878097156868
Winsorized Mean ( 18 / 20 )17809.085137.076932187711129.920364541078
Winsorized Mean ( 19 / 20 )17794.8033333333123.053909204190144.609817342783
Winsorized Mean ( 20 / 20 )17692.3033333333105.367061903969167.911138581979
Trimmed Mean ( 1 / 20 )17835.4362068966269.84240397059766.0957504990208
Trimmed Mean ( 2 / 20 )17829.8535714286259.01922091799168.8360250186752
Trimmed Mean ( 3 / 20 )17815.1185185185250.60970801575271.0871045641965
Trimmed Mean ( 4 / 20 )17794.0288461538241.43689160311173.7005381737799
Trimmed Mean ( 5 / 20 )17779.64233.76329437257376.0583052515623
Trimmed Mean ( 6 / 20 )17769.5979166667225.90790263777578.658593653356
Trimmed Mean ( 7 / 20 )17760.75218.20347685496381.3953574708866
Trimmed Mean ( 8 / 20 )17753.8795454545209.65278084404284.6822993426517
Trimmed Mean ( 9 / 20 )17759.6119047619204.89760722092286.6755456329628
Trimmed Mean ( 10 / 20 )17765.025199.14323255817189.207274441579
Trimmed Mean ( 11 / 20 )17772.5684210526192.55516266789892.2985817404708
Trimmed Mean ( 12 / 20 )17779.8416666667184.00318019918296.6279041885043
Trimmed Mean ( 13 / 20 )17775.4735294118176.899081692201100.483695898097
Trimmed Mean ( 14 / 20 )17772.959375169.350118030675104.948018824414
Trimmed Mean ( 15 / 20 )17770.1566666667162.607686595212109.282390265491
Trimmed Mean ( 16 / 20 )17764.5392857143154.002980055967115.351919029478
Trimmed Mean ( 17 / 20 )17766.2076923077145.020717662958122.508066286074
Trimmed Mean ( 18 / 20 )17767.4375133.952195643984132.640136390313
Trimmed Mean ( 19 / 20 )17761.1272727273120.899030747052146.908764801329
Trimmed Mean ( 20 / 20 )17755.81106.163748620010167.249275113232
Median17785.2
Midrange16971.1
Midmean - Weighted Average at Xnp17718.3903225806
Midmean - Weighted Average at X(n+1)p17770.1566666667
Midmean - Empirical Distribution Function17718.3903225806
Midmean - Empirical Distribution Function - Averaging17770.1566666667
Midmean - Empirical Distribution Function - Interpolation17770.1566666667
Midmean - Closest Observation17718.3903225806
Midmean - True Basic - Statistics Graphics Toolkit17770.1566666667
Midmean - MS Excel (old versions)17772.959375
Number of observations60



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')