Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 03 Jan 2016 13:00:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/03/t14518260631qc6ubz5nuowey2.htm/, Retrieved Fri, 03 May 2024 07:02:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287288, Retrieved Fri, 03 May 2024 07:02:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2015-09-25 19:44:43] [ba9845715efdcdf5bf90594b26d5ea9c]
- R PD  [Univariate Data Series] [] [2015-10-02 11:08:09] [ba9845715efdcdf5bf90594b26d5ea9c]
- RMP     [Histogram] [] [2015-10-02 11:09:44] [ba9845715efdcdf5bf90594b26d5ea9c]
- RMPD        [Central Tendency] [] [2016-01-03 13:00:16] [eed3b94f44ab74d862a61d666a631b56] [Current]
Feedback Forum

Post a new message
Dataseries X:
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100,4
100,4
100,4
100,4
100,4
100,4
100,4
100,4
100,4
100,4
101,4
101,4
102
102
102,6
102,6
102,6
102,6
102,6
102,6
102,3
102,4
102,4
102,4
102,9
102,9
102,9
104,9
104,9
105,5
105,5
105,5
105,5
105,5
105,5
105,5




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' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287288&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287288&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.5483333333330.248048788561023409.388547803172
Geometric Mean101.530678735931
Harmonic Mean101.513243085104
Quadratic Mean101.566205829826
Winsorized Mean ( 1 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 2 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 3 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 4 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 5 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 6 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 7 / 20 )101.4783333333330.229739371696976441.710676684457
Winsorized Mean ( 8 / 20 )101.4783333333330.229739371696976441.710676684457
Winsorized Mean ( 9 / 20 )101.1783333333330.163179767541322620.042146510056
Winsorized Mean ( 10 / 20 )101.1783333333330.163179767541322620.042146510056
Winsorized Mean ( 11 / 20 )101.1783333333330.163179767541322620.042146510056
Winsorized Mean ( 12 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 13 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 14 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 15 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 16 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 17 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 18 / 20 )101.0583333333330.143174100225976705.842279950281
Winsorized Mean ( 19 / 20 )101.0583333333330.143174100225976705.842279950281
Winsorized Mean ( 20 / 20 )101.0583333333330.143174100225976705.842279950281
Trimmed Mean ( 1 / 20 )101.5068965517240.245773247578824413.010356300757
Trimmed Mean ( 2 / 20 )101.46250.24266596275646418.115910643093
Trimmed Mean ( 3 / 20 )101.4148148148150.238508166326992425.204790161258
Trimmed Mean ( 4 / 20 )101.3634615384620.233004975480021435.027026052295
Trimmed Mean ( 5 / 20 )101.3080.225747556318277448.766762538807
Trimmed Mean ( 6 / 20 )101.2479166666670.216147555641263468.420363886542
Trimmed Mean ( 7 / 20 )101.1826086956520.203313240818299497.668564469341
Trimmed Mean ( 8 / 20 )101.1250.192626362249314524.980064094837
Trimmed Mean ( 9 / 20 )101.0619047619050.177933432493678567.975918553111
Trimmed Mean ( 10 / 20 )101.04250.179024690318374564.405389113133
Trimmed Mean ( 11 / 20 )101.0210526315790.179780089101168561.914576506474
Trimmed Mean ( 12 / 20 )100.9972222222220.180056697909522560.918996042973
Trimmed Mean ( 13 / 20 )100.9794117647060.182270264737753554.009245062509
Trimmed Mean ( 14 / 20 )100.9593750.184251940890114547.94198917129
Trimmed Mean ( 15 / 20 )100.9366666666670.185848989083328543.111195624585
Trimmed Mean ( 16 / 20 )100.9107142857140.186823862787191540.138249901517
Trimmed Mean ( 17 / 20 )100.8807692307690.186796411657944540.05731874282
Trimmed Mean ( 18 / 20 )100.8458333333330.185134025743305544.717984327526
Trimmed Mean ( 19 / 20 )100.8136363636360.184730464062149545.733682180971
Trimmed Mean ( 20 / 20 )100.7750.181785732750342554.361436815289
Median100.4
Midrange102.75
Midmean - Weighted Average at Xnp100.747916666667
Midmean - Weighted Average at X(n+1)p100.747916666667
Midmean - Empirical Distribution Function100.747916666667
Midmean - Empirical Distribution Function - Averaging100.747916666667
Midmean - Empirical Distribution Function - Interpolation100.747916666667
Midmean - Closest Observation100.747916666667
Midmean - True Basic - Statistics Graphics Toolkit100.747916666667
Midmean - MS Excel (old versions)100.747916666667
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.548333333333 & 0.248048788561023 & 409.388547803172 \tabularnewline
Geometric Mean & 101.530678735931 &  &  \tabularnewline
Harmonic Mean & 101.513243085104 &  &  \tabularnewline
Quadratic Mean & 101.566205829826 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.548333333333 & 0.248048788561023 & 409.388547803172 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.548333333333 & 0.248048788561023 & 409.388547803172 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.548333333333 & 0.248048788561023 & 409.388547803172 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.548333333333 & 0.248048788561023 & 409.388547803172 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.548333333333 & 0.248048788561023 & 409.388547803172 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.548333333333 & 0.248048788561023 & 409.388547803172 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.478333333333 & 0.229739371696976 & 441.710676684457 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.478333333333 & 0.229739371696976 & 441.710676684457 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.178333333333 & 0.163179767541322 & 620.042146510056 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.178333333333 & 0.163179767541322 & 620.042146510056 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.178333333333 & 0.163179767541322 & 620.042146510056 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.118333333333 & 0.152872526688728 & 661.455236749151 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.118333333333 & 0.152872526688728 & 661.455236749151 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.118333333333 & 0.152872526688728 & 661.455236749151 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.118333333333 & 0.152872526688728 & 661.455236749151 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.118333333333 & 0.152872526688728 & 661.455236749151 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.118333333333 & 0.152872526688728 & 661.455236749151 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.058333333333 & 0.143174100225976 & 705.842279950281 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.058333333333 & 0.143174100225976 & 705.842279950281 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.058333333333 & 0.143174100225976 & 705.842279950281 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.506896551724 & 0.245773247578824 & 413.010356300757 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.4625 & 0.24266596275646 & 418.115910643093 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.414814814815 & 0.238508166326992 & 425.204790161258 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.363461538462 & 0.233004975480021 & 435.027026052295 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.308 & 0.225747556318277 & 448.766762538807 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.247916666667 & 0.216147555641263 & 468.420363886542 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.182608695652 & 0.203313240818299 & 497.668564469341 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.125 & 0.192626362249314 & 524.980064094837 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.061904761905 & 0.177933432493678 & 567.975918553111 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.0425 & 0.179024690318374 & 564.405389113133 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.021052631579 & 0.179780089101168 & 561.914576506474 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 100.997222222222 & 0.180056697909522 & 560.918996042973 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 100.979411764706 & 0.182270264737753 & 554.009245062509 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 100.959375 & 0.184251940890114 & 547.94198917129 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 100.936666666667 & 0.185848989083328 & 543.111195624585 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 100.910714285714 & 0.186823862787191 & 540.138249901517 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 100.880769230769 & 0.186796411657944 & 540.05731874282 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 100.845833333333 & 0.185134025743305 & 544.717984327526 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 100.813636363636 & 0.184730464062149 & 545.733682180971 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 100.775 & 0.181785732750342 & 554.361436815289 \tabularnewline
Median & 100.4 &  &  \tabularnewline
Midrange & 102.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.747916666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.747916666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.747916666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.747916666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.747916666667 &  &  \tabularnewline
Midmean - Closest Observation & 100.747916666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.747916666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.747916666667 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287288&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]101.548333333333[/C][C]0.248048788561023[/C][C]409.388547803172[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.530678735931[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.513243085104[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.566205829826[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.548333333333[/C][C]0.248048788561023[/C][C]409.388547803172[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.548333333333[/C][C]0.248048788561023[/C][C]409.388547803172[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.548333333333[/C][C]0.248048788561023[/C][C]409.388547803172[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.548333333333[/C][C]0.248048788561023[/C][C]409.388547803172[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.548333333333[/C][C]0.248048788561023[/C][C]409.388547803172[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.548333333333[/C][C]0.248048788561023[/C][C]409.388547803172[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.478333333333[/C][C]0.229739371696976[/C][C]441.710676684457[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.478333333333[/C][C]0.229739371696976[/C][C]441.710676684457[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.178333333333[/C][C]0.163179767541322[/C][C]620.042146510056[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.178333333333[/C][C]0.163179767541322[/C][C]620.042146510056[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.178333333333[/C][C]0.163179767541322[/C][C]620.042146510056[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.118333333333[/C][C]0.152872526688728[/C][C]661.455236749151[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.118333333333[/C][C]0.152872526688728[/C][C]661.455236749151[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.118333333333[/C][C]0.152872526688728[/C][C]661.455236749151[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.118333333333[/C][C]0.152872526688728[/C][C]661.455236749151[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.118333333333[/C][C]0.152872526688728[/C][C]661.455236749151[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.118333333333[/C][C]0.152872526688728[/C][C]661.455236749151[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.058333333333[/C][C]0.143174100225976[/C][C]705.842279950281[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.058333333333[/C][C]0.143174100225976[/C][C]705.842279950281[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.058333333333[/C][C]0.143174100225976[/C][C]705.842279950281[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.506896551724[/C][C]0.245773247578824[/C][C]413.010356300757[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.4625[/C][C]0.24266596275646[/C][C]418.115910643093[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.414814814815[/C][C]0.238508166326992[/C][C]425.204790161258[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.363461538462[/C][C]0.233004975480021[/C][C]435.027026052295[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.308[/C][C]0.225747556318277[/C][C]448.766762538807[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.247916666667[/C][C]0.216147555641263[/C][C]468.420363886542[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.182608695652[/C][C]0.203313240818299[/C][C]497.668564469341[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.125[/C][C]0.192626362249314[/C][C]524.980064094837[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.061904761905[/C][C]0.177933432493678[/C][C]567.975918553111[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.0425[/C][C]0.179024690318374[/C][C]564.405389113133[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.021052631579[/C][C]0.179780089101168[/C][C]561.914576506474[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]100.997222222222[/C][C]0.180056697909522[/C][C]560.918996042973[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]100.979411764706[/C][C]0.182270264737753[/C][C]554.009245062509[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]100.959375[/C][C]0.184251940890114[/C][C]547.94198917129[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]100.936666666667[/C][C]0.185848989083328[/C][C]543.111195624585[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]100.910714285714[/C][C]0.186823862787191[/C][C]540.138249901517[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]100.880769230769[/C][C]0.186796411657944[/C][C]540.05731874282[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]100.845833333333[/C][C]0.185134025743305[/C][C]544.717984327526[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]100.813636363636[/C][C]0.184730464062149[/C][C]545.733682180971[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]100.775[/C][C]0.181785732750342[/C][C]554.361436815289[/C][/ROW]
[ROW][C]Median[/C][C]100.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.747916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.747916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.747916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.747916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.747916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.747916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.747916666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.747916666667[/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=287288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287288&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 Mean101.5483333333330.248048788561023409.388547803172
Geometric Mean101.530678735931
Harmonic Mean101.513243085104
Quadratic Mean101.566205829826
Winsorized Mean ( 1 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 2 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 3 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 4 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 5 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 6 / 20 )101.5483333333330.248048788561023409.388547803172
Winsorized Mean ( 7 / 20 )101.4783333333330.229739371696976441.710676684457
Winsorized Mean ( 8 / 20 )101.4783333333330.229739371696976441.710676684457
Winsorized Mean ( 9 / 20 )101.1783333333330.163179767541322620.042146510056
Winsorized Mean ( 10 / 20 )101.1783333333330.163179767541322620.042146510056
Winsorized Mean ( 11 / 20 )101.1783333333330.163179767541322620.042146510056
Winsorized Mean ( 12 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 13 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 14 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 15 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 16 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 17 / 20 )101.1183333333330.152872526688728661.455236749151
Winsorized Mean ( 18 / 20 )101.0583333333330.143174100225976705.842279950281
Winsorized Mean ( 19 / 20 )101.0583333333330.143174100225976705.842279950281
Winsorized Mean ( 20 / 20 )101.0583333333330.143174100225976705.842279950281
Trimmed Mean ( 1 / 20 )101.5068965517240.245773247578824413.010356300757
Trimmed Mean ( 2 / 20 )101.46250.24266596275646418.115910643093
Trimmed Mean ( 3 / 20 )101.4148148148150.238508166326992425.204790161258
Trimmed Mean ( 4 / 20 )101.3634615384620.233004975480021435.027026052295
Trimmed Mean ( 5 / 20 )101.3080.225747556318277448.766762538807
Trimmed Mean ( 6 / 20 )101.2479166666670.216147555641263468.420363886542
Trimmed Mean ( 7 / 20 )101.1826086956520.203313240818299497.668564469341
Trimmed Mean ( 8 / 20 )101.1250.192626362249314524.980064094837
Trimmed Mean ( 9 / 20 )101.0619047619050.177933432493678567.975918553111
Trimmed Mean ( 10 / 20 )101.04250.179024690318374564.405389113133
Trimmed Mean ( 11 / 20 )101.0210526315790.179780089101168561.914576506474
Trimmed Mean ( 12 / 20 )100.9972222222220.180056697909522560.918996042973
Trimmed Mean ( 13 / 20 )100.9794117647060.182270264737753554.009245062509
Trimmed Mean ( 14 / 20 )100.9593750.184251940890114547.94198917129
Trimmed Mean ( 15 / 20 )100.9366666666670.185848989083328543.111195624585
Trimmed Mean ( 16 / 20 )100.9107142857140.186823862787191540.138249901517
Trimmed Mean ( 17 / 20 )100.8807692307690.186796411657944540.05731874282
Trimmed Mean ( 18 / 20 )100.8458333333330.185134025743305544.717984327526
Trimmed Mean ( 19 / 20 )100.8136363636360.184730464062149545.733682180971
Trimmed Mean ( 20 / 20 )100.7750.181785732750342554.361436815289
Median100.4
Midrange102.75
Midmean - Weighted Average at Xnp100.747916666667
Midmean - Weighted Average at X(n+1)p100.747916666667
Midmean - Empirical Distribution Function100.747916666667
Midmean - Empirical Distribution Function - Averaging100.747916666667
Midmean - Empirical Distribution Function - Interpolation100.747916666667
Midmean - Closest Observation100.747916666667
Midmean - True Basic - Statistics Graphics Toolkit100.747916666667
Midmean - MS Excel (old versions)100.747916666667
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')