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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Oct 2012 10:23:52 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/16/t1350397563uyrk7z6wc3hvotl.htm/, Retrieved Tue, 30 Apr 2024 08:25:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=178871, Retrieved Tue, 30 Apr 2024 08:25:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact41
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-16 14:23:52] [87a39969f1a025d48c9ca00d9c3d1003] [Current]
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Dataseries X:
1,38
1,96
1,36
1,24
1,35
1,23
1,09
1,08
1,33
1,35
1,38
1,5
1,47
2,09
1,52
1,29
1,52
1,27
1,35
1,29
1,41
1,39
1,45
1,53
1,45
2,11
1,53
1,38
1,54
1,35
1,29
1,33
1,47
1,47
1,54
1,59
1,5
2
1,51
1,4
1,62
1,44
1,29
1,28
1,4
1,39
1,46
1,49
1,45
2,05
1,59
1,42
1,73
1,39
1,23
1,37
1,51
1,47
1,5
1,54
1,54
2,15
1,62
1,4
1,65
1,49
1,45
1,45
1,51
1,48
1,56
1,57




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=178871&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=178871&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=178871&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.483055555555560.024980930825053559.367505796389
Geometric Mean1.46955721460833
Harmonic Mean1.45720848577376
Quadratic Mean1.49791892674841
Winsorized Mean ( 1 / 24 )1.482638888888890.024745965238817559.9143688508526
Winsorized Mean ( 2 / 24 )1.485972222222220.023815983804873262.3939046313158
Winsorized Mean ( 3 / 24 )1.484305555555560.023232365709645363.8895570991861
Winsorized Mean ( 4 / 24 )1.482083333333330.022214047547682666.7182930149055
Winsorized Mean ( 5 / 24 )1.481388888888890.021004047560187670.5287342662852
Winsorized Mean ( 6 / 24 )1.463055555555560.015338689216788995.383349572933
Winsorized Mean ( 7 / 24 )1.456250.0134173373407153108.53494721199
Winsorized Mean ( 8 / 24 )1.452916666666670.0127704506276473113.771761782719
Winsorized Mean ( 9 / 24 )1.452916666666670.0127704506276473113.771761782719
Winsorized Mean ( 10 / 24 )1.448750.0120411681346516120.316399854168
Winsorized Mean ( 11 / 24 )1.454861111111110.0109808359445936132.490924957986
Winsorized Mean ( 12 / 24 )1.451527777777780.0104245927070215139.240718421555
Winsorized Mean ( 13 / 24 )1.453333333333330.00956609492656094151.925455945252
Winsorized Mean ( 14 / 24 )1.449444444444440.00898374660195692161.340753325424
Winsorized Mean ( 15 / 24 )1.449444444444440.00898374660195692161.340753325424
Winsorized Mean ( 16 / 24 )1.449444444444440.00898374660195692161.340753325424
Winsorized Mean ( 17 / 24 )1.451805555555560.00862250936774817168.373902959842
Winsorized Mean ( 18 / 24 )1.451805555555560.00789783747686602183.823174357299
Winsorized Mean ( 19 / 24 )1.454444444444440.00752119823452201193.379352477189
Winsorized Mean ( 20 / 24 )1.451666666666670.00713715399414573203.395732788924
Winsorized Mean ( 21 / 24 )1.451666666666670.00713715399414573203.395732788924
Winsorized Mean ( 22 / 24 )1.451666666666670.00630472907932556230.250443500731
Winsorized Mean ( 23 / 24 )1.451666666666670.00630472907932556230.250443500731
Winsorized Mean ( 24 / 24 )1.451666666666670.00630472907932556230.250443500731
Trimmed Mean ( 1 / 24 )1.479285714285710.023120282679119263.982163834948
Trimmed Mean ( 2 / 24 )1.475735294117650.021117086707931969.883469937325
Trimmed Mean ( 3 / 24 )1.470151515151520.019263226829638176.3190678360056
Trimmed Mean ( 4 / 24 )1.464843750.017224290980379685.0452277930408
Trimmed Mean ( 5 / 24 )1.459838709677420.015059360660222396.9389566141028
Trimmed Mean ( 6 / 24 )1.454666666666670.0126880580596796114.648487564014
Trimmed Mean ( 7 / 24 )1.452931034482760.0118393374184344122.720637408347
Trimmed Mean ( 8 / 24 )1.452321428571430.011367506298367127.76077623815
Trimmed Mean ( 9 / 24 )1.452222222222220.0109559395410699132.551135096936
Trimmed Mean ( 10 / 24 )1.452115384615380.0104402940068196139.087595010912
Trimmed Mean ( 11 / 24 )1.45260.00997470269619857145.628400589182
Trimmed Mean ( 12 / 24 )1.452291666666670.00964456808560755150.581306884432
Trimmed Mean ( 13 / 24 )1.452391304347830.00935186970176096155.304912350772
Trimmed Mean ( 14 / 24 )1.452272727272730.00916644097824082158.433652790665
Trimmed Mean ( 15 / 24 )1.452619047619050.00904280390238016160.638123230418
Trimmed Mean ( 16 / 24 )1.4530.00886653171287312163.874674681468
Trimmed Mean ( 17 / 24 )1.453421052631580.00861931005372247168.623827611803
Trimmed Mean ( 18 / 24 )1.453611111111110.00836804938088424173.709671746405
Trimmed Mean ( 19 / 24 )1.453823529411760.0081978074748288177.342970529096
Trimmed Mean ( 20 / 24 )1.453750.00804160050671989180.778689364784
Trimmed Mean ( 21 / 24 )1.4540.00790169485675039184.011155373566
Trimmed Mean ( 22 / 24 )1.454285714285710.00767095413980335189.583419191579
Trimmed Mean ( 23 / 24 )1.454615384615380.00756979360008773192.160508127795
Trimmed Mean ( 24 / 24 )1.4550.00737209780774486197.365802508945
Median1.455
Midrange1.615
Midmean - Weighted Average at Xnp1.45108108108108
Midmean - Weighted Average at X(n+1)p1.45361111111111
Midmean - Empirical Distribution Function1.45108108108108
Midmean - Empirical Distribution Function - Averaging1.45361111111111
Midmean - Empirical Distribution Function - Interpolation1.45361111111111
Midmean - Closest Observation1.45108108108108
Midmean - True Basic - Statistics Graphics Toolkit1.45361111111111
Midmean - MS Excel (old versions)1.45975609756098
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.48305555555556 & 0.0249809308250535 & 59.367505796389 \tabularnewline
Geometric Mean & 1.46955721460833 &  &  \tabularnewline
Harmonic Mean & 1.45720848577376 &  &  \tabularnewline
Quadratic Mean & 1.49791892674841 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.48263888888889 & 0.0247459652388175 & 59.9143688508526 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.48597222222222 & 0.0238159838048732 & 62.3939046313158 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.48430555555556 & 0.0232323657096453 & 63.8895570991861 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.48208333333333 & 0.0222140475476826 & 66.7182930149055 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.48138888888889 & 0.0210040475601876 & 70.5287342662852 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.46305555555556 & 0.0153386892167889 & 95.383349572933 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.45625 & 0.0134173373407153 & 108.53494721199 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.45291666666667 & 0.0127704506276473 & 113.771761782719 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.45291666666667 & 0.0127704506276473 & 113.771761782719 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.44875 & 0.0120411681346516 & 120.316399854168 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.45486111111111 & 0.0109808359445936 & 132.490924957986 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.45152777777778 & 0.0104245927070215 & 139.240718421555 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.45333333333333 & 0.00956609492656094 & 151.925455945252 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.44944444444444 & 0.00898374660195692 & 161.340753325424 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.44944444444444 & 0.00898374660195692 & 161.340753325424 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.44944444444444 & 0.00898374660195692 & 161.340753325424 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.45180555555556 & 0.00862250936774817 & 168.373902959842 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.45180555555556 & 0.00789783747686602 & 183.823174357299 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.45444444444444 & 0.00752119823452201 & 193.379352477189 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.45166666666667 & 0.00713715399414573 & 203.395732788924 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.45166666666667 & 0.00713715399414573 & 203.395732788924 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.45166666666667 & 0.00630472907932556 & 230.250443500731 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.45166666666667 & 0.00630472907932556 & 230.250443500731 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.45166666666667 & 0.00630472907932556 & 230.250443500731 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.47928571428571 & 0.0231202826791192 & 63.982163834948 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.47573529411765 & 0.0211170867079319 & 69.883469937325 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.47015151515152 & 0.0192632268296381 & 76.3190678360056 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.46484375 & 0.0172242909803796 & 85.0452277930408 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.45983870967742 & 0.0150593606602223 & 96.9389566141028 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.45466666666667 & 0.0126880580596796 & 114.648487564014 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.45293103448276 & 0.0118393374184344 & 122.720637408347 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.45232142857143 & 0.011367506298367 & 127.76077623815 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.45222222222222 & 0.0109559395410699 & 132.551135096936 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.45211538461538 & 0.0104402940068196 & 139.087595010912 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.4526 & 0.00997470269619857 & 145.628400589182 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.45229166666667 & 0.00964456808560755 & 150.581306884432 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.45239130434783 & 0.00935186970176096 & 155.304912350772 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.45227272727273 & 0.00916644097824082 & 158.433652790665 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.45261904761905 & 0.00904280390238016 & 160.638123230418 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.453 & 0.00886653171287312 & 163.874674681468 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.45342105263158 & 0.00861931005372247 & 168.623827611803 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.45361111111111 & 0.00836804938088424 & 173.709671746405 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.45382352941176 & 0.0081978074748288 & 177.342970529096 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.45375 & 0.00804160050671989 & 180.778689364784 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.454 & 0.00790169485675039 & 184.011155373566 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.45428571428571 & 0.00767095413980335 & 189.583419191579 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.45461538461538 & 0.00756979360008773 & 192.160508127795 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.455 & 0.00737209780774486 & 197.365802508945 \tabularnewline
Median & 1.455 &  &  \tabularnewline
Midrange & 1.615 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.45108108108108 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.45361111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.45108108108108 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.45361111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.45361111111111 &  &  \tabularnewline
Midmean - Closest Observation & 1.45108108108108 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.45361111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.45975609756098 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=178871&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]1.48305555555556[/C][C]0.0249809308250535[/C][C]59.367505796389[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.46955721460833[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.45720848577376[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.49791892674841[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.48263888888889[/C][C]0.0247459652388175[/C][C]59.9143688508526[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.48597222222222[/C][C]0.0238159838048732[/C][C]62.3939046313158[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.48430555555556[/C][C]0.0232323657096453[/C][C]63.8895570991861[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.48208333333333[/C][C]0.0222140475476826[/C][C]66.7182930149055[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.48138888888889[/C][C]0.0210040475601876[/C][C]70.5287342662852[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.46305555555556[/C][C]0.0153386892167889[/C][C]95.383349572933[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.45625[/C][C]0.0134173373407153[/C][C]108.53494721199[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.45291666666667[/C][C]0.0127704506276473[/C][C]113.771761782719[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.45291666666667[/C][C]0.0127704506276473[/C][C]113.771761782719[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.44875[/C][C]0.0120411681346516[/C][C]120.316399854168[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.45486111111111[/C][C]0.0109808359445936[/C][C]132.490924957986[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.45152777777778[/C][C]0.0104245927070215[/C][C]139.240718421555[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.45333333333333[/C][C]0.00956609492656094[/C][C]151.925455945252[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.44944444444444[/C][C]0.00898374660195692[/C][C]161.340753325424[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.44944444444444[/C][C]0.00898374660195692[/C][C]161.340753325424[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.44944444444444[/C][C]0.00898374660195692[/C][C]161.340753325424[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.45180555555556[/C][C]0.00862250936774817[/C][C]168.373902959842[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.45180555555556[/C][C]0.00789783747686602[/C][C]183.823174357299[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.45444444444444[/C][C]0.00752119823452201[/C][C]193.379352477189[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.45166666666667[/C][C]0.00713715399414573[/C][C]203.395732788924[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.45166666666667[/C][C]0.00713715399414573[/C][C]203.395732788924[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.45166666666667[/C][C]0.00630472907932556[/C][C]230.250443500731[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.45166666666667[/C][C]0.00630472907932556[/C][C]230.250443500731[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.45166666666667[/C][C]0.00630472907932556[/C][C]230.250443500731[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.47928571428571[/C][C]0.0231202826791192[/C][C]63.982163834948[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.47573529411765[/C][C]0.0211170867079319[/C][C]69.883469937325[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.47015151515152[/C][C]0.0192632268296381[/C][C]76.3190678360056[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.46484375[/C][C]0.0172242909803796[/C][C]85.0452277930408[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.45983870967742[/C][C]0.0150593606602223[/C][C]96.9389566141028[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.45466666666667[/C][C]0.0126880580596796[/C][C]114.648487564014[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.45293103448276[/C][C]0.0118393374184344[/C][C]122.720637408347[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.45232142857143[/C][C]0.011367506298367[/C][C]127.76077623815[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.45222222222222[/C][C]0.0109559395410699[/C][C]132.551135096936[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.45211538461538[/C][C]0.0104402940068196[/C][C]139.087595010912[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.4526[/C][C]0.00997470269619857[/C][C]145.628400589182[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.45229166666667[/C][C]0.00964456808560755[/C][C]150.581306884432[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.45239130434783[/C][C]0.00935186970176096[/C][C]155.304912350772[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.45227272727273[/C][C]0.00916644097824082[/C][C]158.433652790665[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.45261904761905[/C][C]0.00904280390238016[/C][C]160.638123230418[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.453[/C][C]0.00886653171287312[/C][C]163.874674681468[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.45342105263158[/C][C]0.00861931005372247[/C][C]168.623827611803[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.45361111111111[/C][C]0.00836804938088424[/C][C]173.709671746405[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.45382352941176[/C][C]0.0081978074748288[/C][C]177.342970529096[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.45375[/C][C]0.00804160050671989[/C][C]180.778689364784[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.454[/C][C]0.00790169485675039[/C][C]184.011155373566[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.45428571428571[/C][C]0.00767095413980335[/C][C]189.583419191579[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.45461538461538[/C][C]0.00756979360008773[/C][C]192.160508127795[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.455[/C][C]0.00737209780774486[/C][C]197.365802508945[/C][/ROW]
[ROW][C]Median[/C][C]1.455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.45108108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.45361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.45108108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.45361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.45361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.45108108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.45361111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.45975609756098[/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=178871&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=178871&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 Mean1.483055555555560.024980930825053559.367505796389
Geometric Mean1.46955721460833
Harmonic Mean1.45720848577376
Quadratic Mean1.49791892674841
Winsorized Mean ( 1 / 24 )1.482638888888890.024745965238817559.9143688508526
Winsorized Mean ( 2 / 24 )1.485972222222220.023815983804873262.3939046313158
Winsorized Mean ( 3 / 24 )1.484305555555560.023232365709645363.8895570991861
Winsorized Mean ( 4 / 24 )1.482083333333330.022214047547682666.7182930149055
Winsorized Mean ( 5 / 24 )1.481388888888890.021004047560187670.5287342662852
Winsorized Mean ( 6 / 24 )1.463055555555560.015338689216788995.383349572933
Winsorized Mean ( 7 / 24 )1.456250.0134173373407153108.53494721199
Winsorized Mean ( 8 / 24 )1.452916666666670.0127704506276473113.771761782719
Winsorized Mean ( 9 / 24 )1.452916666666670.0127704506276473113.771761782719
Winsorized Mean ( 10 / 24 )1.448750.0120411681346516120.316399854168
Winsorized Mean ( 11 / 24 )1.454861111111110.0109808359445936132.490924957986
Winsorized Mean ( 12 / 24 )1.451527777777780.0104245927070215139.240718421555
Winsorized Mean ( 13 / 24 )1.453333333333330.00956609492656094151.925455945252
Winsorized Mean ( 14 / 24 )1.449444444444440.00898374660195692161.340753325424
Winsorized Mean ( 15 / 24 )1.449444444444440.00898374660195692161.340753325424
Winsorized Mean ( 16 / 24 )1.449444444444440.00898374660195692161.340753325424
Winsorized Mean ( 17 / 24 )1.451805555555560.00862250936774817168.373902959842
Winsorized Mean ( 18 / 24 )1.451805555555560.00789783747686602183.823174357299
Winsorized Mean ( 19 / 24 )1.454444444444440.00752119823452201193.379352477189
Winsorized Mean ( 20 / 24 )1.451666666666670.00713715399414573203.395732788924
Winsorized Mean ( 21 / 24 )1.451666666666670.00713715399414573203.395732788924
Winsorized Mean ( 22 / 24 )1.451666666666670.00630472907932556230.250443500731
Winsorized Mean ( 23 / 24 )1.451666666666670.00630472907932556230.250443500731
Winsorized Mean ( 24 / 24 )1.451666666666670.00630472907932556230.250443500731
Trimmed Mean ( 1 / 24 )1.479285714285710.023120282679119263.982163834948
Trimmed Mean ( 2 / 24 )1.475735294117650.021117086707931969.883469937325
Trimmed Mean ( 3 / 24 )1.470151515151520.019263226829638176.3190678360056
Trimmed Mean ( 4 / 24 )1.464843750.017224290980379685.0452277930408
Trimmed Mean ( 5 / 24 )1.459838709677420.015059360660222396.9389566141028
Trimmed Mean ( 6 / 24 )1.454666666666670.0126880580596796114.648487564014
Trimmed Mean ( 7 / 24 )1.452931034482760.0118393374184344122.720637408347
Trimmed Mean ( 8 / 24 )1.452321428571430.011367506298367127.76077623815
Trimmed Mean ( 9 / 24 )1.452222222222220.0109559395410699132.551135096936
Trimmed Mean ( 10 / 24 )1.452115384615380.0104402940068196139.087595010912
Trimmed Mean ( 11 / 24 )1.45260.00997470269619857145.628400589182
Trimmed Mean ( 12 / 24 )1.452291666666670.00964456808560755150.581306884432
Trimmed Mean ( 13 / 24 )1.452391304347830.00935186970176096155.304912350772
Trimmed Mean ( 14 / 24 )1.452272727272730.00916644097824082158.433652790665
Trimmed Mean ( 15 / 24 )1.452619047619050.00904280390238016160.638123230418
Trimmed Mean ( 16 / 24 )1.4530.00886653171287312163.874674681468
Trimmed Mean ( 17 / 24 )1.453421052631580.00861931005372247168.623827611803
Trimmed Mean ( 18 / 24 )1.453611111111110.00836804938088424173.709671746405
Trimmed Mean ( 19 / 24 )1.453823529411760.0081978074748288177.342970529096
Trimmed Mean ( 20 / 24 )1.453750.00804160050671989180.778689364784
Trimmed Mean ( 21 / 24 )1.4540.00790169485675039184.011155373566
Trimmed Mean ( 22 / 24 )1.454285714285710.00767095413980335189.583419191579
Trimmed Mean ( 23 / 24 )1.454615384615380.00756979360008773192.160508127795
Trimmed Mean ( 24 / 24 )1.4550.00737209780774486197.365802508945
Median1.455
Midrange1.615
Midmean - Weighted Average at Xnp1.45108108108108
Midmean - Weighted Average at X(n+1)p1.45361111111111
Midmean - Empirical Distribution Function1.45108108108108
Midmean - Empirical Distribution Function - Averaging1.45361111111111
Midmean - Empirical Distribution Function - Interpolation1.45361111111111
Midmean - Closest Observation1.45108108108108
Midmean - True Basic - Statistics Graphics Toolkit1.45361111111111
Midmean - MS Excel (old versions)1.45975609756098
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')