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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 15:25:00 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t12560740456wfleq65ng4q65l.htm/, Retrieved Thu, 02 May 2024 20:22:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49193, Retrieved Thu, 02 May 2024 20:22:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Y[t]/X[t]=c+e[t]] [2009-10-20 21:25:00] [fe64bd97bfa4d92f47365386639c265d] [Current]
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Dataseries X:
1.973	   
1.954	   
1.961	   
1.939	   
1.929	   
1.978	   
1.912	   
2.036	   
1.933	   
1.933	   
1.954	   
2.012	   
1.981	   
1.988	   
1.963	   
1.949	   
1.959	   
1.984	   
1.926	   
2.040	   
1.943	   
1.949	   
1.990	   
2.056	   
2.034	   
2.000	   
2.019	   
1.994	   
1.964	   
1.960	   
1.932	   
2.043	   
1.954	   
1.970	   
1.970	   
2.017	   
1.984	   
1.973	   
1.953	   
1.973	   
1.990	   
1.957	   
1.980	   
2.006	   
1.970	   
1.991	   
2.019	   
2.089	   
2.062	   
1.986	   
2.037	   
2.022	   
2.009	   
2.017	   
2.018	   
2.109	   
2.039	   
2.045	   
2.101	   
2.098	   
2.081	 






Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49193&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49193&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.993573770491800.00602868638857585330.681286435725
Geometric Mean1.99303198494807
Harmonic Mean1.99249531242666
Quadratic Mean1.9941206287402
Winsorized Mean ( 1 / 20 )1.993672131147540.00594030970616666335.617540122176
Winsorized Mean ( 2 / 20 )1.993672131147540.00589265177818512338.331910011756
Winsorized Mean ( 3 / 20 )1.993377049180330.00573919340567765347.327038536169
Winsorized Mean ( 4 / 20 )1.992918032786890.00558566153637053356.791764021178
Winsorized Mean ( 5 / 20 )1.991360655737710.0052038254522126382.672453952314
Winsorized Mean ( 6 / 20 )1.991360655737700.00496589641514482401.007288364800
Winsorized Mean ( 7 / 20 )1.990557377049180.00462498114544459430.392538791168
Winsorized Mean ( 8 / 20 )1.991081967213110.0044440846102356448.029716317115
Winsorized Mean ( 9 / 20 )1.990639344262300.00435921439674259456.650938240109
Winsorized Mean ( 10 / 20 )1.991131147540980.00422673480469263471.080216655745
Winsorized Mean ( 11 / 20 )1.990950819672130.00413220235471082481.81348558654
Winsorized Mean ( 12 / 20 )1.990754098360660.00409582325823274486.044922558407
Winsorized Mean ( 13 / 20 )1.990327868852460.00401797337052782495.35616225127
Winsorized Mean ( 14 / 20 )1.988262295081970.00343733134821998578.431955974098
Winsorized Mean ( 15 / 20 )1.988016393442620.00324428811251142612.774305024251
Winsorized Mean ( 16 / 20 )1.988278688524590.00320545395432552620.279909446697
Winsorized Mean ( 17 / 20 )1.988278688524590.00312027839128071637.211953292573
Winsorized Mean ( 18 / 20 )1.988573770491800.00298836167045406665.439458065882
Winsorized Mean ( 19 / 20 )1.988885245901640.00294420783232454675.524745252565
Winsorized Mean ( 20 / 20 )1.98921311475410.00241490304075104823.723802234085
Trimmed Mean ( 1 / 20 )1.9930.00574710559123435346.783257826301
Trimmed Mean ( 2 / 20 )1.992280701754390.0055081253711211361.698503124101
Trimmed Mean ( 3 / 20 )1.991509090909090.00524259122756182379.871137089451
Trimmed Mean ( 4 / 20 )1.990792452830190.00498752860394371399.154092320601
Trimmed Mean ( 5 / 20 )1.99015686274510.00473032540844911420.723035077114
Trimmed Mean ( 6 / 20 )1.989857142857140.00454690221226399437.629192352117
Trimmed Mean ( 7 / 20 )1.989531914893620.00438965345025647453.232114434313
Trimmed Mean ( 8 / 20 )1.989333333333330.00428858009041678463.867595192796
Trimmed Mean ( 9 / 20 )1.989023255813950.00420310600387823473.227002597287
Trimmed Mean ( 10 / 20 )1.988756097560980.0041098899884103483.895214511624
Trimmed Mean ( 11 / 20 )1.988384615384620.00401525689943268495.207321769512
Trimmed Mean ( 12 / 20 )1.9880.00390791143346055508.711631225372
Trimmed Mean ( 13 / 20 )1.98760.00376587954394398527.791708897412
Trimmed Mean ( 14 / 20 )1.987212121212120.00358731920032151553.954641402978
Trimmed Mean ( 15 / 20 )1.987064516129030.00351125241384053565.913321496481
Trimmed Mean ( 16 / 20 )1.986931034482760.00344875612419096576.129758942833
Trimmed Mean ( 17 / 20 )1.986740740740740.00335530901026936592.118560365099
Trimmed Mean ( 18 / 20 )1.986520.00323064493045377614.898895658267
Trimmed Mean ( 19 / 20 )1.986217391304350.00307286769910487646.37256979301
Trimmed Mean ( 20 / 20 )1.985809523809520.00281714060336688704.902524721771
Median1.984
Midrange2.0105
Midmean - Weighted Average at Xnp1.98706451612903
Midmean - Weighted Average at X(n+1)p1.98706451612903
Midmean - Empirical Distribution Function1.98706451612903
Midmean - Empirical Distribution Function - Averaging1.98706451612903
Midmean - Empirical Distribution Function - Interpolation1.98706451612903
Midmean - Closest Observation1.986125
Midmean - True Basic - Statistics Graphics Toolkit1.98706451612903
Midmean - MS Excel (old versions)1.98706451612903
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.99357377049180 & 0.00602868638857585 & 330.681286435725 \tabularnewline
Geometric Mean & 1.99303198494807 &  &  \tabularnewline
Harmonic Mean & 1.99249531242666 &  &  \tabularnewline
Quadratic Mean & 1.9941206287402 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.99367213114754 & 0.00594030970616666 & 335.617540122176 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.99367213114754 & 0.00589265177818512 & 338.331910011756 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.99337704918033 & 0.00573919340567765 & 347.327038536169 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.99291803278689 & 0.00558566153637053 & 356.791764021178 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.99136065573771 & 0.0052038254522126 & 382.672453952314 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.99136065573770 & 0.00496589641514482 & 401.007288364800 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.99055737704918 & 0.00462498114544459 & 430.392538791168 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.99108196721311 & 0.0044440846102356 & 448.029716317115 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.99063934426230 & 0.00435921439674259 & 456.650938240109 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.99113114754098 & 0.00422673480469263 & 471.080216655745 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.99095081967213 & 0.00413220235471082 & 481.81348558654 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.99075409836066 & 0.00409582325823274 & 486.044922558407 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.99032786885246 & 0.00401797337052782 & 495.35616225127 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.98826229508197 & 0.00343733134821998 & 578.431955974098 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.98801639344262 & 0.00324428811251142 & 612.774305024251 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.98827868852459 & 0.00320545395432552 & 620.279909446697 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.98827868852459 & 0.00312027839128071 & 637.211953292573 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.98857377049180 & 0.00298836167045406 & 665.439458065882 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.98888524590164 & 0.00294420783232454 & 675.524745252565 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.9892131147541 & 0.00241490304075104 & 823.723802234085 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.993 & 0.00574710559123435 & 346.783257826301 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.99228070175439 & 0.0055081253711211 & 361.698503124101 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.99150909090909 & 0.00524259122756182 & 379.871137089451 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.99079245283019 & 0.00498752860394371 & 399.154092320601 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.9901568627451 & 0.00473032540844911 & 420.723035077114 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.98985714285714 & 0.00454690221226399 & 437.629192352117 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.98953191489362 & 0.00438965345025647 & 453.232114434313 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.98933333333333 & 0.00428858009041678 & 463.867595192796 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.98902325581395 & 0.00420310600387823 & 473.227002597287 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.98875609756098 & 0.0041098899884103 & 483.895214511624 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.98838461538462 & 0.00401525689943268 & 495.207321769512 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.988 & 0.00390791143346055 & 508.711631225372 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.9876 & 0.00376587954394398 & 527.791708897412 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.98721212121212 & 0.00358731920032151 & 553.954641402978 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.98706451612903 & 0.00351125241384053 & 565.913321496481 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.98693103448276 & 0.00344875612419096 & 576.129758942833 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.98674074074074 & 0.00335530901026936 & 592.118560365099 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.98652 & 0.00323064493045377 & 614.898895658267 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.98621739130435 & 0.00307286769910487 & 646.37256979301 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.98580952380952 & 0.00281714060336688 & 704.902524721771 \tabularnewline
Median & 1.984 &  &  \tabularnewline
Midrange & 2.0105 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.98706451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.98706451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.98706451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.98706451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.98706451612903 &  &  \tabularnewline
Midmean - Closest Observation & 1.986125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.98706451612903 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.98706451612903 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49193&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]1.99357377049180[/C][C]0.00602868638857585[/C][C]330.681286435725[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.99303198494807[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.99249531242666[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.9941206287402[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.99367213114754[/C][C]0.00594030970616666[/C][C]335.617540122176[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.99367213114754[/C][C]0.00589265177818512[/C][C]338.331910011756[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.99337704918033[/C][C]0.00573919340567765[/C][C]347.327038536169[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.99291803278689[/C][C]0.00558566153637053[/C][C]356.791764021178[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.99136065573771[/C][C]0.0052038254522126[/C][C]382.672453952314[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.99136065573770[/C][C]0.00496589641514482[/C][C]401.007288364800[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.99055737704918[/C][C]0.00462498114544459[/C][C]430.392538791168[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.99108196721311[/C][C]0.0044440846102356[/C][C]448.029716317115[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.99063934426230[/C][C]0.00435921439674259[/C][C]456.650938240109[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.99113114754098[/C][C]0.00422673480469263[/C][C]471.080216655745[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.99095081967213[/C][C]0.00413220235471082[/C][C]481.81348558654[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.99075409836066[/C][C]0.00409582325823274[/C][C]486.044922558407[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.99032786885246[/C][C]0.00401797337052782[/C][C]495.35616225127[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.98826229508197[/C][C]0.00343733134821998[/C][C]578.431955974098[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.98801639344262[/C][C]0.00324428811251142[/C][C]612.774305024251[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.98827868852459[/C][C]0.00320545395432552[/C][C]620.279909446697[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.98827868852459[/C][C]0.00312027839128071[/C][C]637.211953292573[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.98857377049180[/C][C]0.00298836167045406[/C][C]665.439458065882[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.98888524590164[/C][C]0.00294420783232454[/C][C]675.524745252565[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.9892131147541[/C][C]0.00241490304075104[/C][C]823.723802234085[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.993[/C][C]0.00574710559123435[/C][C]346.783257826301[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.99228070175439[/C][C]0.0055081253711211[/C][C]361.698503124101[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.99150909090909[/C][C]0.00524259122756182[/C][C]379.871137089451[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.99079245283019[/C][C]0.00498752860394371[/C][C]399.154092320601[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.9901568627451[/C][C]0.00473032540844911[/C][C]420.723035077114[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.98985714285714[/C][C]0.00454690221226399[/C][C]437.629192352117[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.98953191489362[/C][C]0.00438965345025647[/C][C]453.232114434313[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.98933333333333[/C][C]0.00428858009041678[/C][C]463.867595192796[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.98902325581395[/C][C]0.00420310600387823[/C][C]473.227002597287[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.98875609756098[/C][C]0.0041098899884103[/C][C]483.895214511624[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.98838461538462[/C][C]0.00401525689943268[/C][C]495.207321769512[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.988[/C][C]0.00390791143346055[/C][C]508.711631225372[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.9876[/C][C]0.00376587954394398[/C][C]527.791708897412[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.98721212121212[/C][C]0.00358731920032151[/C][C]553.954641402978[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.98706451612903[/C][C]0.00351125241384053[/C][C]565.913321496481[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.98693103448276[/C][C]0.00344875612419096[/C][C]576.129758942833[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.98674074074074[/C][C]0.00335530901026936[/C][C]592.118560365099[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.98652[/C][C]0.00323064493045377[/C][C]614.898895658267[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.98621739130435[/C][C]0.00307286769910487[/C][C]646.37256979301[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.98580952380952[/C][C]0.00281714060336688[/C][C]704.902524721771[/C][/ROW]
[ROW][C]Median[/C][C]1.984[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.0105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.98706451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.98706451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.98706451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.98706451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.98706451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.986125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.98706451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.98706451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49193&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 Mean1.993573770491800.00602868638857585330.681286435725
Geometric Mean1.99303198494807
Harmonic Mean1.99249531242666
Quadratic Mean1.9941206287402
Winsorized Mean ( 1 / 20 )1.993672131147540.00594030970616666335.617540122176
Winsorized Mean ( 2 / 20 )1.993672131147540.00589265177818512338.331910011756
Winsorized Mean ( 3 / 20 )1.993377049180330.00573919340567765347.327038536169
Winsorized Mean ( 4 / 20 )1.992918032786890.00558566153637053356.791764021178
Winsorized Mean ( 5 / 20 )1.991360655737710.0052038254522126382.672453952314
Winsorized Mean ( 6 / 20 )1.991360655737700.00496589641514482401.007288364800
Winsorized Mean ( 7 / 20 )1.990557377049180.00462498114544459430.392538791168
Winsorized Mean ( 8 / 20 )1.991081967213110.0044440846102356448.029716317115
Winsorized Mean ( 9 / 20 )1.990639344262300.00435921439674259456.650938240109
Winsorized Mean ( 10 / 20 )1.991131147540980.00422673480469263471.080216655745
Winsorized Mean ( 11 / 20 )1.990950819672130.00413220235471082481.81348558654
Winsorized Mean ( 12 / 20 )1.990754098360660.00409582325823274486.044922558407
Winsorized Mean ( 13 / 20 )1.990327868852460.00401797337052782495.35616225127
Winsorized Mean ( 14 / 20 )1.988262295081970.00343733134821998578.431955974098
Winsorized Mean ( 15 / 20 )1.988016393442620.00324428811251142612.774305024251
Winsorized Mean ( 16 / 20 )1.988278688524590.00320545395432552620.279909446697
Winsorized Mean ( 17 / 20 )1.988278688524590.00312027839128071637.211953292573
Winsorized Mean ( 18 / 20 )1.988573770491800.00298836167045406665.439458065882
Winsorized Mean ( 19 / 20 )1.988885245901640.00294420783232454675.524745252565
Winsorized Mean ( 20 / 20 )1.98921311475410.00241490304075104823.723802234085
Trimmed Mean ( 1 / 20 )1.9930.00574710559123435346.783257826301
Trimmed Mean ( 2 / 20 )1.992280701754390.0055081253711211361.698503124101
Trimmed Mean ( 3 / 20 )1.991509090909090.00524259122756182379.871137089451
Trimmed Mean ( 4 / 20 )1.990792452830190.00498752860394371399.154092320601
Trimmed Mean ( 5 / 20 )1.99015686274510.00473032540844911420.723035077114
Trimmed Mean ( 6 / 20 )1.989857142857140.00454690221226399437.629192352117
Trimmed Mean ( 7 / 20 )1.989531914893620.00438965345025647453.232114434313
Trimmed Mean ( 8 / 20 )1.989333333333330.00428858009041678463.867595192796
Trimmed Mean ( 9 / 20 )1.989023255813950.00420310600387823473.227002597287
Trimmed Mean ( 10 / 20 )1.988756097560980.0041098899884103483.895214511624
Trimmed Mean ( 11 / 20 )1.988384615384620.00401525689943268495.207321769512
Trimmed Mean ( 12 / 20 )1.9880.00390791143346055508.711631225372
Trimmed Mean ( 13 / 20 )1.98760.00376587954394398527.791708897412
Trimmed Mean ( 14 / 20 )1.987212121212120.00358731920032151553.954641402978
Trimmed Mean ( 15 / 20 )1.987064516129030.00351125241384053565.913321496481
Trimmed Mean ( 16 / 20 )1.986931034482760.00344875612419096576.129758942833
Trimmed Mean ( 17 / 20 )1.986740740740740.00335530901026936592.118560365099
Trimmed Mean ( 18 / 20 )1.986520.00323064493045377614.898895658267
Trimmed Mean ( 19 / 20 )1.986217391304350.00307286769910487646.37256979301
Trimmed Mean ( 20 / 20 )1.985809523809520.00281714060336688704.902524721771
Median1.984
Midrange2.0105
Midmean - Weighted Average at Xnp1.98706451612903
Midmean - Weighted Average at X(n+1)p1.98706451612903
Midmean - Empirical Distribution Function1.98706451612903
Midmean - Empirical Distribution Function - Averaging1.98706451612903
Midmean - Empirical Distribution Function - Interpolation1.98706451612903
Midmean - Closest Observation1.986125
Midmean - True Basic - Statistics Graphics Toolkit1.98706451612903
Midmean - MS Excel (old versions)1.98706451612903
Number of observations61



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')