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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 02 May 2013 19:37:56 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/02/t1367538080tj4nu6q67tocqgo.htm/, Retrieved Fri, 03 May 2024 23:29:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208676, Retrieved Fri, 03 May 2024 23:29:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-05-02 23:37:56] [1f4ca98ed28755372cdf3133ccb2c2d2] [Current]
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Dataseries X:
9,11	
9,06	
9,11	
9,13	
9,13	
9,19	
9,2	
9,23	
9,24	
9,28	
9,32	
9,32	
9,32	
9,36	
9,37	
9,38	
9,41	
9,44	
9,44	
9,44	
9,47	
9,48	
9,56	
9,58	
9,56	
9,58	
9,7	
9,74	
9,76	
9,78	
9,84	
9,88	
9,96	
9,97	
9,96	
9,96	
9,96	
10,02	
10,08	
10,09	
10,12	
10,14	
10,17	
10,22	
10,25	
10,25	
10,26	
10,34	
10,33	
10,3	
10,33	
10,33	
10,37	
10,44	
10,45	
10,45	
10,44	
10,43	
10,4	
10,43	
10,47	
10,52	
10,55	
10,5	
10,44	
10,47	
10,5	
10,54	
10,55	
10,53	
10,54	
10,54	




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208676&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208676&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208676&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.916805555555560.0583651242643645169.909782263761
Geometric Mean9.90449660026593
Harmonic Mean9.89208728994763
Quadratic Mean9.92899254987914
Winsorized Mean ( 1 / 24 )9.91750.0582255039602415170.329139731827
Winsorized Mean ( 2 / 24 )9.917222222222220.0581833155552958170.447870279877
Winsorized Mean ( 3 / 24 )9.918055555555560.0580221879234795170.935566384288
Winsorized Mean ( 4 / 24 )9.918055555555550.0580221879234795170.935566384288
Winsorized Mean ( 5 / 24 )9.921527777777780.0571433484663995173.625243253144
Winsorized Mean ( 6 / 24 )9.921527777777780.0568695139479437174.461272640023
Winsorized Mean ( 7 / 24 )9.92250.0560700259414661176.966210259266
Winsorized Mean ( 8 / 24 )9.923611111111110.0558776558556842177.595336796893
Winsorized Mean ( 9 / 24 )9.924861111111110.0544933245454332182.129851571753
Winsorized Mean ( 10 / 24 )9.930416666666670.0535845161560174185.322503197624
Winsorized Mean ( 11 / 24 )9.927361111111110.0531562468837691186.758127089337
Winsorized Mean ( 12 / 24 )9.927361111111110.0531562468837691186.758127089337
Winsorized Mean ( 13 / 24 )9.932777777777780.0517624518077037191.891562916645
Winsorized Mean ( 14 / 24 )9.934722222222220.0514606570714126193.054709900724
Winsorized Mean ( 15 / 24 )9.936805555555560.0511399114908905194.306272065519
Winsorized Mean ( 16 / 24 )9.941250.0498204669982617199.541485637757
Winsorized Mean ( 17 / 24 )9.948333333333330.0487684799049332203.991048167302
Winsorized Mean ( 18 / 24 )9.940833333333330.0477386722628622208.234390738736
Winsorized Mean ( 19 / 24 )9.932916666666670.0466802618945923212.786224059667
Winsorized Mean ( 20 / 24 )9.932916666666670.0443596578538871223.917792589473
Winsorized Mean ( 21 / 24 )9.932916666666670.0435559636320748228.049521543636
Winsorized Mean ( 22 / 24 )9.957361111111110.0400547322415652248.593875276945
Winsorized Mean ( 23 / 24 )9.957361111111110.0400547322415652248.593875276945
Winsorized Mean ( 24 / 24 )9.954027777777780.0378250956483499263.159355109576
Trimmed Mean ( 1 / 24 )9.920.058053662617196170.876384930477
Trimmed Mean ( 2 / 24 )9.922647058823530.0578073218880999171.650350418087
Trimmed Mean ( 3 / 24 )9.925606060606060.0574975944719801172.626457711079
Trimmed Mean ( 4 / 24 )9.92843750.0571557234554014173.708543952683
Trimmed Mean ( 5 / 24 )9.931451612903230.0567019944091318175.151715850471
Trimmed Mean ( 6 / 24 )9.933833333333330.0563765045356085176.205201354031
Trimmed Mean ( 7 / 24 )9.936379310344830.0560030345927542177.425730276952
Trimmed Mean ( 8 / 24 )9.938928571428570.0556885346749994178.473515768238
Trimmed Mean ( 9 / 24 )9.941481481481480.0552868179922142179.816488676948
Trimmed Mean ( 10 / 24 )9.944038461538460.0550293077100065180.704407802867
Trimmed Mean ( 11 / 24 )9.9460.0548266284178908181.408200485924
Trimmed Mean ( 12 / 24 )9.948541666666670.0545711760999688182.30396296466
Trimmed Mean ( 13 / 24 )9.951304347826090.0541581230235594183.745369895799
Trimmed Mean ( 14 / 24 )9.953636363636360.0538321042216967184.90149154572
Trimmed Mean ( 15 / 24 )9.955952380952380.0533729449920157186.535563710073
Trimmed Mean ( 16 / 24 )9.958250.052740155844115188.817227416502
Trimmed Mean ( 17 / 24 )9.960263157894740.0520961563661186191.189981231946
Trimmed Mean ( 18 / 24 )9.961666666666670.0513662541314048193.93406887687
Trimmed Mean ( 19 / 24 )9.964117647058820.0504880241126385197.356062594744
Trimmed Mean ( 20 / 24 )9.96781250.0493929568714818201.806353200028
Trimmed Mean ( 21 / 24 )9.9720.0483435978002865206.273435444246
Trimmed Mean ( 22 / 24 )9.976785714285710.0468930268939573212.756274762279
Trimmed Mean ( 23 / 24 )9.979230769230770.0458053509703265217.861681175535
Trimmed Mean ( 24 / 24 )9.982083333333330.043920131590618227.278083462429
Median9.965
Midrange9.805
Midmean - Weighted Average at Xnp9.94756756756757
Midmean - Weighted Average at X(n+1)p9.94756756756757
Midmean - Empirical Distribution Function9.94756756756757
Midmean - Empirical Distribution Function - Averaging9.94756756756757
Midmean - Empirical Distribution Function - Interpolation9.94756756756757
Midmean - Closest Observation9.94756756756757
Midmean - True Basic - Statistics Graphics Toolkit9.94756756756757
Midmean - MS Excel (old versions)9.97230769230769
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.91680555555556 & 0.0583651242643645 & 169.909782263761 \tabularnewline
Geometric Mean & 9.90449660026593 &  &  \tabularnewline
Harmonic Mean & 9.89208728994763 &  &  \tabularnewline
Quadratic Mean & 9.92899254987914 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 9.9175 & 0.0582255039602415 & 170.329139731827 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 9.91722222222222 & 0.0581833155552958 & 170.447870279877 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 9.91805555555556 & 0.0580221879234795 & 170.935566384288 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 9.91805555555555 & 0.0580221879234795 & 170.935566384288 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 9.92152777777778 & 0.0571433484663995 & 173.625243253144 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 9.92152777777778 & 0.0568695139479437 & 174.461272640023 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 9.9225 & 0.0560700259414661 & 176.966210259266 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 9.92361111111111 & 0.0558776558556842 & 177.595336796893 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 9.92486111111111 & 0.0544933245454332 & 182.129851571753 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 9.93041666666667 & 0.0535845161560174 & 185.322503197624 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 9.92736111111111 & 0.0531562468837691 & 186.758127089337 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 9.92736111111111 & 0.0531562468837691 & 186.758127089337 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9.93277777777778 & 0.0517624518077037 & 191.891562916645 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 9.93472222222222 & 0.0514606570714126 & 193.054709900724 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9.93680555555556 & 0.0511399114908905 & 194.306272065519 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 9.94125 & 0.0498204669982617 & 199.541485637757 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 9.94833333333333 & 0.0487684799049332 & 203.991048167302 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9.94083333333333 & 0.0477386722628622 & 208.234390738736 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 9.93291666666667 & 0.0466802618945923 & 212.786224059667 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 9.93291666666667 & 0.0443596578538871 & 223.917792589473 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 9.93291666666667 & 0.0435559636320748 & 228.049521543636 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 9.95736111111111 & 0.0400547322415652 & 248.593875276945 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 9.95736111111111 & 0.0400547322415652 & 248.593875276945 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 9.95402777777778 & 0.0378250956483499 & 263.159355109576 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 9.92 & 0.058053662617196 & 170.876384930477 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 9.92264705882353 & 0.0578073218880999 & 171.650350418087 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 9.92560606060606 & 0.0574975944719801 & 172.626457711079 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 9.9284375 & 0.0571557234554014 & 173.708543952683 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 9.93145161290323 & 0.0567019944091318 & 175.151715850471 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 9.93383333333333 & 0.0563765045356085 & 176.205201354031 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 9.93637931034483 & 0.0560030345927542 & 177.425730276952 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 9.93892857142857 & 0.0556885346749994 & 178.473515768238 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 9.94148148148148 & 0.0552868179922142 & 179.816488676948 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 9.94403846153846 & 0.0550293077100065 & 180.704407802867 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 9.946 & 0.0548266284178908 & 181.408200485924 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 9.94854166666667 & 0.0545711760999688 & 182.30396296466 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 9.95130434782609 & 0.0541581230235594 & 183.745369895799 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 9.95363636363636 & 0.0538321042216967 & 184.90149154572 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 9.95595238095238 & 0.0533729449920157 & 186.535563710073 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 9.95825 & 0.052740155844115 & 188.817227416502 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 9.96026315789474 & 0.0520961563661186 & 191.189981231946 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 9.96166666666667 & 0.0513662541314048 & 193.93406887687 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 9.96411764705882 & 0.0504880241126385 & 197.356062594744 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 9.9678125 & 0.0493929568714818 & 201.806353200028 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 9.972 & 0.0483435978002865 & 206.273435444246 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 9.97678571428571 & 0.0468930268939573 & 212.756274762279 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 9.97923076923077 & 0.0458053509703265 & 217.861681175535 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 9.98208333333333 & 0.043920131590618 & 227.278083462429 \tabularnewline
Median & 9.965 &  &  \tabularnewline
Midrange & 9.805 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.94756756756757 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.94756756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.94756756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.94756756756757 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.94756756756757 &  &  \tabularnewline
Midmean - Closest Observation & 9.94756756756757 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.94756756756757 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.97230769230769 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208676&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]9.91680555555556[/C][C]0.0583651242643645[/C][C]169.909782263761[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.90449660026593[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.89208728994763[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.92899254987914[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]9.9175[/C][C]0.0582255039602415[/C][C]170.329139731827[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]9.91722222222222[/C][C]0.0581833155552958[/C][C]170.447870279877[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]9.91805555555556[/C][C]0.0580221879234795[/C][C]170.935566384288[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]9.91805555555555[/C][C]0.0580221879234795[/C][C]170.935566384288[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]9.92152777777778[/C][C]0.0571433484663995[/C][C]173.625243253144[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]9.92152777777778[/C][C]0.0568695139479437[/C][C]174.461272640023[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]9.9225[/C][C]0.0560700259414661[/C][C]176.966210259266[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]9.92361111111111[/C][C]0.0558776558556842[/C][C]177.595336796893[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]9.92486111111111[/C][C]0.0544933245454332[/C][C]182.129851571753[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]9.93041666666667[/C][C]0.0535845161560174[/C][C]185.322503197624[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]9.92736111111111[/C][C]0.0531562468837691[/C][C]186.758127089337[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]9.92736111111111[/C][C]0.0531562468837691[/C][C]186.758127089337[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9.93277777777778[/C][C]0.0517624518077037[/C][C]191.891562916645[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]9.93472222222222[/C][C]0.0514606570714126[/C][C]193.054709900724[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9.93680555555556[/C][C]0.0511399114908905[/C][C]194.306272065519[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]9.94125[/C][C]0.0498204669982617[/C][C]199.541485637757[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]9.94833333333333[/C][C]0.0487684799049332[/C][C]203.991048167302[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9.94083333333333[/C][C]0.0477386722628622[/C][C]208.234390738736[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]9.93291666666667[/C][C]0.0466802618945923[/C][C]212.786224059667[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]9.93291666666667[/C][C]0.0443596578538871[/C][C]223.917792589473[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]9.93291666666667[/C][C]0.0435559636320748[/C][C]228.049521543636[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]9.95736111111111[/C][C]0.0400547322415652[/C][C]248.593875276945[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]9.95736111111111[/C][C]0.0400547322415652[/C][C]248.593875276945[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]9.95402777777778[/C][C]0.0378250956483499[/C][C]263.159355109576[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]9.92[/C][C]0.058053662617196[/C][C]170.876384930477[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]9.92264705882353[/C][C]0.0578073218880999[/C][C]171.650350418087[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]9.92560606060606[/C][C]0.0574975944719801[/C][C]172.626457711079[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]9.9284375[/C][C]0.0571557234554014[/C][C]173.708543952683[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]9.93145161290323[/C][C]0.0567019944091318[/C][C]175.151715850471[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]9.93383333333333[/C][C]0.0563765045356085[/C][C]176.205201354031[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]9.93637931034483[/C][C]0.0560030345927542[/C][C]177.425730276952[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]9.93892857142857[/C][C]0.0556885346749994[/C][C]178.473515768238[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]9.94148148148148[/C][C]0.0552868179922142[/C][C]179.816488676948[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]9.94403846153846[/C][C]0.0550293077100065[/C][C]180.704407802867[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]9.946[/C][C]0.0548266284178908[/C][C]181.408200485924[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]9.94854166666667[/C][C]0.0545711760999688[/C][C]182.30396296466[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]9.95130434782609[/C][C]0.0541581230235594[/C][C]183.745369895799[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]9.95363636363636[/C][C]0.0538321042216967[/C][C]184.90149154572[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]9.95595238095238[/C][C]0.0533729449920157[/C][C]186.535563710073[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]9.95825[/C][C]0.052740155844115[/C][C]188.817227416502[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]9.96026315789474[/C][C]0.0520961563661186[/C][C]191.189981231946[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]9.96166666666667[/C][C]0.0513662541314048[/C][C]193.93406887687[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]9.96411764705882[/C][C]0.0504880241126385[/C][C]197.356062594744[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]9.9678125[/C][C]0.0493929568714818[/C][C]201.806353200028[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]9.972[/C][C]0.0483435978002865[/C][C]206.273435444246[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]9.97678571428571[/C][C]0.0468930268939573[/C][C]212.756274762279[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]9.97923076923077[/C][C]0.0458053509703265[/C][C]217.861681175535[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]9.98208333333333[/C][C]0.043920131590618[/C][C]227.278083462429[/C][/ROW]
[ROW][C]Median[/C][C]9.965[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9.805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.94756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.94756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.94756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.94756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.94756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.94756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.94756756756757[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.97230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208676&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208676&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 Mean9.916805555555560.0583651242643645169.909782263761
Geometric Mean9.90449660026593
Harmonic Mean9.89208728994763
Quadratic Mean9.92899254987914
Winsorized Mean ( 1 / 24 )9.91750.0582255039602415170.329139731827
Winsorized Mean ( 2 / 24 )9.917222222222220.0581833155552958170.447870279877
Winsorized Mean ( 3 / 24 )9.918055555555560.0580221879234795170.935566384288
Winsorized Mean ( 4 / 24 )9.918055555555550.0580221879234795170.935566384288
Winsorized Mean ( 5 / 24 )9.921527777777780.0571433484663995173.625243253144
Winsorized Mean ( 6 / 24 )9.921527777777780.0568695139479437174.461272640023
Winsorized Mean ( 7 / 24 )9.92250.0560700259414661176.966210259266
Winsorized Mean ( 8 / 24 )9.923611111111110.0558776558556842177.595336796893
Winsorized Mean ( 9 / 24 )9.924861111111110.0544933245454332182.129851571753
Winsorized Mean ( 10 / 24 )9.930416666666670.0535845161560174185.322503197624
Winsorized Mean ( 11 / 24 )9.927361111111110.0531562468837691186.758127089337
Winsorized Mean ( 12 / 24 )9.927361111111110.0531562468837691186.758127089337
Winsorized Mean ( 13 / 24 )9.932777777777780.0517624518077037191.891562916645
Winsorized Mean ( 14 / 24 )9.934722222222220.0514606570714126193.054709900724
Winsorized Mean ( 15 / 24 )9.936805555555560.0511399114908905194.306272065519
Winsorized Mean ( 16 / 24 )9.941250.0498204669982617199.541485637757
Winsorized Mean ( 17 / 24 )9.948333333333330.0487684799049332203.991048167302
Winsorized Mean ( 18 / 24 )9.940833333333330.0477386722628622208.234390738736
Winsorized Mean ( 19 / 24 )9.932916666666670.0466802618945923212.786224059667
Winsorized Mean ( 20 / 24 )9.932916666666670.0443596578538871223.917792589473
Winsorized Mean ( 21 / 24 )9.932916666666670.0435559636320748228.049521543636
Winsorized Mean ( 22 / 24 )9.957361111111110.0400547322415652248.593875276945
Winsorized Mean ( 23 / 24 )9.957361111111110.0400547322415652248.593875276945
Winsorized Mean ( 24 / 24 )9.954027777777780.0378250956483499263.159355109576
Trimmed Mean ( 1 / 24 )9.920.058053662617196170.876384930477
Trimmed Mean ( 2 / 24 )9.922647058823530.0578073218880999171.650350418087
Trimmed Mean ( 3 / 24 )9.925606060606060.0574975944719801172.626457711079
Trimmed Mean ( 4 / 24 )9.92843750.0571557234554014173.708543952683
Trimmed Mean ( 5 / 24 )9.931451612903230.0567019944091318175.151715850471
Trimmed Mean ( 6 / 24 )9.933833333333330.0563765045356085176.205201354031
Trimmed Mean ( 7 / 24 )9.936379310344830.0560030345927542177.425730276952
Trimmed Mean ( 8 / 24 )9.938928571428570.0556885346749994178.473515768238
Trimmed Mean ( 9 / 24 )9.941481481481480.0552868179922142179.816488676948
Trimmed Mean ( 10 / 24 )9.944038461538460.0550293077100065180.704407802867
Trimmed Mean ( 11 / 24 )9.9460.0548266284178908181.408200485924
Trimmed Mean ( 12 / 24 )9.948541666666670.0545711760999688182.30396296466
Trimmed Mean ( 13 / 24 )9.951304347826090.0541581230235594183.745369895799
Trimmed Mean ( 14 / 24 )9.953636363636360.0538321042216967184.90149154572
Trimmed Mean ( 15 / 24 )9.955952380952380.0533729449920157186.535563710073
Trimmed Mean ( 16 / 24 )9.958250.052740155844115188.817227416502
Trimmed Mean ( 17 / 24 )9.960263157894740.0520961563661186191.189981231946
Trimmed Mean ( 18 / 24 )9.961666666666670.0513662541314048193.93406887687
Trimmed Mean ( 19 / 24 )9.964117647058820.0504880241126385197.356062594744
Trimmed Mean ( 20 / 24 )9.96781250.0493929568714818201.806353200028
Trimmed Mean ( 21 / 24 )9.9720.0483435978002865206.273435444246
Trimmed Mean ( 22 / 24 )9.976785714285710.0468930268939573212.756274762279
Trimmed Mean ( 23 / 24 )9.979230769230770.0458053509703265217.861681175535
Trimmed Mean ( 24 / 24 )9.982083333333330.043920131590618227.278083462429
Median9.965
Midrange9.805
Midmean - Weighted Average at Xnp9.94756756756757
Midmean - Weighted Average at X(n+1)p9.94756756756757
Midmean - Empirical Distribution Function9.94756756756757
Midmean - Empirical Distribution Function - Averaging9.94756756756757
Midmean - Empirical Distribution Function - Interpolation9.94756756756757
Midmean - Closest Observation9.94756756756757
Midmean - True Basic - Statistics Graphics Toolkit9.94756756756757
Midmean - MS Excel (old versions)9.97230769230769
Number of observations72



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