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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 02 Mar 2012 11:27:33 -0500
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/Mar/02/t1330705846aocjekhw3jsd9pe.htm/, Retrieved Sun, 28 Apr 2024 13:29:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163434, Retrieved Sun, 28 Apr 2024 13:29:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-02 16:27:33] [26fc2906931796130cbcdf91b421d42d] [Current]
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Dataseries X:
1,44
1,45
1,45
1,47
1,49
1,5
1,5
1,5
1,5
1,5
1,5
1,51
1,52
1,51
1,51
1,51
1,52
1,52
1,52
1,52
1,52
1,53
1,53
1,53
1,53
1,54
1,54
1,55
1,56
1,55
1,56
1,56
1,56
1,56
1,57
1,56
1,57
1,58
1,58
1,58
1,6
1,61
1,61
1,61
1,6
1,59
1,56
1,57
1,55
1,59
1,62
1,63
1,62
1,56
1,56
1,54
1,54
1,52
1,56
1,59




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163434&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163434&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.543833333333330.00560514123695848275.431656057799
Geometric Mean1.54323056996337
Harmonic Mean1.54262531723763
Quadratic Mean1.54443355311907
Winsorized Mean ( 1 / 20 )1.543833333333330.00551367927374363280.000568891472
Winsorized Mean ( 2 / 20 )1.543833333333330.00551367927374363280.000568891472
Winsorized Mean ( 3 / 20 )1.544333333333330.00513306918390006300.859637383645
Winsorized Mean ( 4 / 20 )1.545666666666670.00483844459918265319.455278443774
Winsorized Mean ( 5 / 20 )1.54650.00468695147449745329.958611352131
Winsorized Mean ( 6 / 20 )1.54550.00446850244760969345.865313518341
Winsorized Mean ( 7 / 20 )1.54550.00446850244760969345.865313518341
Winsorized Mean ( 8 / 20 )1.544166666666670.0042071479843189367.034074489931
Winsorized Mean ( 9 / 20 )1.544166666666670.0042071479843189367.034074489931
Winsorized Mean ( 10 / 20 )1.544166666666670.0042071479843189367.034074489931
Winsorized Mean ( 11 / 20 )1.544166666666670.00356768030371686432.820918695527
Winsorized Mean ( 12 / 20 )1.544166666666670.00356768030371686432.820918695527
Winsorized Mean ( 13 / 20 )1.544166666666670.00356768030371686432.820918695527
Winsorized Mean ( 14 / 20 )1.541833333333330.00319331634875117482.831378086392
Winsorized Mean ( 15 / 20 )1.544333333333330.00279594810402065552.346923432713
Winsorized Mean ( 16 / 20 )1.544333333333330.00279594810402065552.346923432713
Winsorized Mean ( 17 / 20 )1.54150.00238669807131439645.871389652179
Winsorized Mean ( 18 / 20 )1.54150.00238669807131439645.871389652179
Winsorized Mean ( 19 / 20 )1.54150.00238669807131439645.871389652179
Winsorized Mean ( 20 / 20 )1.54150.00238669807131439645.871389652179
Trimmed Mean ( 1 / 20 )1.544137931034480.00530403219990735291.12529351942
Trimmed Mean ( 2 / 20 )1.544464285714290.00504473264487387306.153842916467
Trimmed Mean ( 3 / 20 )1.544814814814810.00471953240009257327.323701556645
Trimmed Mean ( 4 / 20 )1.5450.00450824617335586342.705331650053
Trimmed Mean ( 5 / 20 )1.54480.00436348484585429354.028959552295
Trimmed Mean ( 6 / 20 )1.5443750.00423077891743672365.033255137729
Trimmed Mean ( 7 / 20 )1.544130434782610.0041304347826087373.842105263158
Trimmed Mean ( 8 / 20 )1.543863636363640.00399809559701172386.149755277877
Trimmed Mean ( 9 / 20 )1.543809523809520.00389991484097116395.857239648106
Trimmed Mean ( 10 / 20 )1.543750.00376705523296449409.802857810806
Trimmed Mean ( 11 / 20 )1.543684210526320.00358638671212033430.428822778474
Trimmed Mean ( 12 / 20 )1.543611111111110.00352210204591938438.26416469094
Trimmed Mean ( 13 / 20 )1.543529411764710.00342691332355021450.41390488559
Trimmed Mean ( 14 / 20 )1.54343750.00328760425444897469.471803947003
Trimmed Mean ( 15 / 20 )1.543666666666670.00319782013875808482.724668581946
Trimmed Mean ( 16 / 20 )1.543571428571430.00317955962285875485.467049422271
Trimmed Mean ( 17 / 20 )1.543461538461540.00313502828804844492.327786752555
Trimmed Mean ( 18 / 20 )1.543750.00317442794116093486.308093493983
Trimmed Mean ( 19 / 20 )1.544090909090910.00320031728061081482.480571050195
Trimmed Mean ( 20 / 20 )1.54450.00320156211871643482.420750473904
Median1.545
Midrange1.535
Midmean - Weighted Average at Xnp1.54057142857143
Midmean - Weighted Average at X(n+1)p1.54451612903226
Midmean - Empirical Distribution Function1.54057142857143
Midmean - Empirical Distribution Function - Averaging1.54451612903226
Midmean - Empirical Distribution Function - Interpolation1.54451612903226
Midmean - Closest Observation1.54057142857143
Midmean - True Basic - Statistics Graphics Toolkit1.54451612903226
Midmean - MS Excel (old versions)1.54057142857143
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.54383333333333 & 0.00560514123695848 & 275.431656057799 \tabularnewline
Geometric Mean & 1.54323056996337 &  &  \tabularnewline
Harmonic Mean & 1.54262531723763 &  &  \tabularnewline
Quadratic Mean & 1.54443355311907 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.54383333333333 & 0.00551367927374363 & 280.000568891472 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.54383333333333 & 0.00551367927374363 & 280.000568891472 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.54433333333333 & 0.00513306918390006 & 300.859637383645 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.54566666666667 & 0.00483844459918265 & 319.455278443774 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.5465 & 0.00468695147449745 & 329.958611352131 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.5455 & 0.00446850244760969 & 345.865313518341 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.5455 & 0.00446850244760969 & 345.865313518341 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.54416666666667 & 0.0042071479843189 & 367.034074489931 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.54416666666667 & 0.0042071479843189 & 367.034074489931 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.54416666666667 & 0.0042071479843189 & 367.034074489931 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.54416666666667 & 0.00356768030371686 & 432.820918695527 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.54416666666667 & 0.00356768030371686 & 432.820918695527 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.54416666666667 & 0.00356768030371686 & 432.820918695527 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.54183333333333 & 0.00319331634875117 & 482.831378086392 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.54433333333333 & 0.00279594810402065 & 552.346923432713 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.54433333333333 & 0.00279594810402065 & 552.346923432713 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.5415 & 0.00238669807131439 & 645.871389652179 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.5415 & 0.00238669807131439 & 645.871389652179 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.5415 & 0.00238669807131439 & 645.871389652179 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.5415 & 0.00238669807131439 & 645.871389652179 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.54413793103448 & 0.00530403219990735 & 291.12529351942 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.54446428571429 & 0.00504473264487387 & 306.153842916467 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.54481481481481 & 0.00471953240009257 & 327.323701556645 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.545 & 0.00450824617335586 & 342.705331650053 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.5448 & 0.00436348484585429 & 354.028959552295 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.544375 & 0.00423077891743672 & 365.033255137729 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.54413043478261 & 0.0041304347826087 & 373.842105263158 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.54386363636364 & 0.00399809559701172 & 386.149755277877 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.54380952380952 & 0.00389991484097116 & 395.857239648106 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.54375 & 0.00376705523296449 & 409.802857810806 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.54368421052632 & 0.00358638671212033 & 430.428822778474 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.54361111111111 & 0.00352210204591938 & 438.26416469094 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.54352941176471 & 0.00342691332355021 & 450.41390488559 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.5434375 & 0.00328760425444897 & 469.471803947003 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.54366666666667 & 0.00319782013875808 & 482.724668581946 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.54357142857143 & 0.00317955962285875 & 485.467049422271 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.54346153846154 & 0.00313502828804844 & 492.327786752555 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.54375 & 0.00317442794116093 & 486.308093493983 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.54409090909091 & 0.00320031728061081 & 482.480571050195 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.5445 & 0.00320156211871643 & 482.420750473904 \tabularnewline
Median & 1.545 &  &  \tabularnewline
Midrange & 1.535 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.54057142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.54451612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.54057142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.54451612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.54451612903226 &  &  \tabularnewline
Midmean - Closest Observation & 1.54057142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.54451612903226 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.54057142857143 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163434&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]1.54383333333333[/C][C]0.00560514123695848[/C][C]275.431656057799[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.54323056996337[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.54262531723763[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.54443355311907[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.54383333333333[/C][C]0.00551367927374363[/C][C]280.000568891472[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.54383333333333[/C][C]0.00551367927374363[/C][C]280.000568891472[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.54433333333333[/C][C]0.00513306918390006[/C][C]300.859637383645[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.54566666666667[/C][C]0.00483844459918265[/C][C]319.455278443774[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.5465[/C][C]0.00468695147449745[/C][C]329.958611352131[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.5455[/C][C]0.00446850244760969[/C][C]345.865313518341[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.5455[/C][C]0.00446850244760969[/C][C]345.865313518341[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.54416666666667[/C][C]0.0042071479843189[/C][C]367.034074489931[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.54416666666667[/C][C]0.0042071479843189[/C][C]367.034074489931[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.54416666666667[/C][C]0.0042071479843189[/C][C]367.034074489931[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.54416666666667[/C][C]0.00356768030371686[/C][C]432.820918695527[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.54416666666667[/C][C]0.00356768030371686[/C][C]432.820918695527[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.54416666666667[/C][C]0.00356768030371686[/C][C]432.820918695527[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.54183333333333[/C][C]0.00319331634875117[/C][C]482.831378086392[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.54433333333333[/C][C]0.00279594810402065[/C][C]552.346923432713[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.54433333333333[/C][C]0.00279594810402065[/C][C]552.346923432713[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.5415[/C][C]0.00238669807131439[/C][C]645.871389652179[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.5415[/C][C]0.00238669807131439[/C][C]645.871389652179[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.5415[/C][C]0.00238669807131439[/C][C]645.871389652179[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.5415[/C][C]0.00238669807131439[/C][C]645.871389652179[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.54413793103448[/C][C]0.00530403219990735[/C][C]291.12529351942[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.54446428571429[/C][C]0.00504473264487387[/C][C]306.153842916467[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.54481481481481[/C][C]0.00471953240009257[/C][C]327.323701556645[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.545[/C][C]0.00450824617335586[/C][C]342.705331650053[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.5448[/C][C]0.00436348484585429[/C][C]354.028959552295[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.544375[/C][C]0.00423077891743672[/C][C]365.033255137729[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.54413043478261[/C][C]0.0041304347826087[/C][C]373.842105263158[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.54386363636364[/C][C]0.00399809559701172[/C][C]386.149755277877[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.54380952380952[/C][C]0.00389991484097116[/C][C]395.857239648106[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.54375[/C][C]0.00376705523296449[/C][C]409.802857810806[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.54368421052632[/C][C]0.00358638671212033[/C][C]430.428822778474[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.54361111111111[/C][C]0.00352210204591938[/C][C]438.26416469094[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.54352941176471[/C][C]0.00342691332355021[/C][C]450.41390488559[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.5434375[/C][C]0.00328760425444897[/C][C]469.471803947003[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.54366666666667[/C][C]0.00319782013875808[/C][C]482.724668581946[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.54357142857143[/C][C]0.00317955962285875[/C][C]485.467049422271[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.54346153846154[/C][C]0.00313502828804844[/C][C]492.327786752555[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.54375[/C][C]0.00317442794116093[/C][C]486.308093493983[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.54409090909091[/C][C]0.00320031728061081[/C][C]482.480571050195[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.5445[/C][C]0.00320156211871643[/C][C]482.420750473904[/C][/ROW]
[ROW][C]Median[/C][C]1.545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.535[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.54057142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.54451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.54057142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.54451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.54451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.54057142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.54451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.54057142857143[/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=163434&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163434&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 Mean1.543833333333330.00560514123695848275.431656057799
Geometric Mean1.54323056996337
Harmonic Mean1.54262531723763
Quadratic Mean1.54443355311907
Winsorized Mean ( 1 / 20 )1.543833333333330.00551367927374363280.000568891472
Winsorized Mean ( 2 / 20 )1.543833333333330.00551367927374363280.000568891472
Winsorized Mean ( 3 / 20 )1.544333333333330.00513306918390006300.859637383645
Winsorized Mean ( 4 / 20 )1.545666666666670.00483844459918265319.455278443774
Winsorized Mean ( 5 / 20 )1.54650.00468695147449745329.958611352131
Winsorized Mean ( 6 / 20 )1.54550.00446850244760969345.865313518341
Winsorized Mean ( 7 / 20 )1.54550.00446850244760969345.865313518341
Winsorized Mean ( 8 / 20 )1.544166666666670.0042071479843189367.034074489931
Winsorized Mean ( 9 / 20 )1.544166666666670.0042071479843189367.034074489931
Winsorized Mean ( 10 / 20 )1.544166666666670.0042071479843189367.034074489931
Winsorized Mean ( 11 / 20 )1.544166666666670.00356768030371686432.820918695527
Winsorized Mean ( 12 / 20 )1.544166666666670.00356768030371686432.820918695527
Winsorized Mean ( 13 / 20 )1.544166666666670.00356768030371686432.820918695527
Winsorized Mean ( 14 / 20 )1.541833333333330.00319331634875117482.831378086392
Winsorized Mean ( 15 / 20 )1.544333333333330.00279594810402065552.346923432713
Winsorized Mean ( 16 / 20 )1.544333333333330.00279594810402065552.346923432713
Winsorized Mean ( 17 / 20 )1.54150.00238669807131439645.871389652179
Winsorized Mean ( 18 / 20 )1.54150.00238669807131439645.871389652179
Winsorized Mean ( 19 / 20 )1.54150.00238669807131439645.871389652179
Winsorized Mean ( 20 / 20 )1.54150.00238669807131439645.871389652179
Trimmed Mean ( 1 / 20 )1.544137931034480.00530403219990735291.12529351942
Trimmed Mean ( 2 / 20 )1.544464285714290.00504473264487387306.153842916467
Trimmed Mean ( 3 / 20 )1.544814814814810.00471953240009257327.323701556645
Trimmed Mean ( 4 / 20 )1.5450.00450824617335586342.705331650053
Trimmed Mean ( 5 / 20 )1.54480.00436348484585429354.028959552295
Trimmed Mean ( 6 / 20 )1.5443750.00423077891743672365.033255137729
Trimmed Mean ( 7 / 20 )1.544130434782610.0041304347826087373.842105263158
Trimmed Mean ( 8 / 20 )1.543863636363640.00399809559701172386.149755277877
Trimmed Mean ( 9 / 20 )1.543809523809520.00389991484097116395.857239648106
Trimmed Mean ( 10 / 20 )1.543750.00376705523296449409.802857810806
Trimmed Mean ( 11 / 20 )1.543684210526320.00358638671212033430.428822778474
Trimmed Mean ( 12 / 20 )1.543611111111110.00352210204591938438.26416469094
Trimmed Mean ( 13 / 20 )1.543529411764710.00342691332355021450.41390488559
Trimmed Mean ( 14 / 20 )1.54343750.00328760425444897469.471803947003
Trimmed Mean ( 15 / 20 )1.543666666666670.00319782013875808482.724668581946
Trimmed Mean ( 16 / 20 )1.543571428571430.00317955962285875485.467049422271
Trimmed Mean ( 17 / 20 )1.543461538461540.00313502828804844492.327786752555
Trimmed Mean ( 18 / 20 )1.543750.00317442794116093486.308093493983
Trimmed Mean ( 19 / 20 )1.544090909090910.00320031728061081482.480571050195
Trimmed Mean ( 20 / 20 )1.54450.00320156211871643482.420750473904
Median1.545
Midrange1.535
Midmean - Weighted Average at Xnp1.54057142857143
Midmean - Weighted Average at X(n+1)p1.54451612903226
Midmean - Empirical Distribution Function1.54057142857143
Midmean - Empirical Distribution Function - Averaging1.54451612903226
Midmean - Empirical Distribution Function - Interpolation1.54451612903226
Midmean - Closest Observation1.54057142857143
Midmean - True Basic - Statistics Graphics Toolkit1.54451612903226
Midmean - MS Excel (old versions)1.54057142857143
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')