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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 01 Mar 2016 09:51:26 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/01/t1456826142ondkxy2humss8ka.htm/, Retrieved Tue, 07 May 2024 14:19:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293101, Retrieved Tue, 07 May 2024 14:19:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-01 09:51:26] [409a9d71664281dd1fd3bb0995266dd0] [Current]
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Dataseries X:
100,57
100,27
100,27
100,18
100,16
100,18
100,18
100,59
100,69
101,06
101,15
101,16
101,16
100,81
100,94
101,13
101,29
101,34
101,35
101,7
102,05
102,48
102,66
102,72
102,73
102,18
102,22
102,37
102,53
102,61
102,62
103
103,17
103,52
103,69
103,73
99,57
99,09
99,14
99,36
99,6
99,65
99,8
100,15
100,45
100,89
101,13
101,17
101,21
101,1
101,17
101,11
101,2
101,15
100,92
101,1
101,22
101,25
101,39
101,43
101,95
101,92
102,05
102,07
102,1
102,16
101,63
101,43
101,4
101,6
101,72
101,73





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net
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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \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=293101&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/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=293101&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293101&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'Sir Maurice George Kendall' @ kendall.wessa.net
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 Mean101.3398611111110.12384450171355818.28308652336
Geometric Mean101.334490273946
Harmonic Mean101.32912132628
Quadratic Mean101.34523377901
Winsorized Mean ( 1 / 24 )101.340.123518608457867820.443180709634
Winsorized Mean ( 2 / 24 )101.3413888888890.120812861396042838.829473268387
Winsorized Mean ( 3 / 24 )101.3355555555560.115367665805185878.37051090793
Winsorized Mean ( 4 / 24 )101.3277777777780.112965645999761896.978695434471
Winsorized Mean ( 5 / 24 )101.31250.108533356331681933.468782540787
Winsorized Mean ( 6 / 24 )101.3241666666670.105761222707011958.046475572277
Winsorized Mean ( 7 / 24 )101.3523611111110.09826796049616821031.3876526934
Winsorized Mean ( 8 / 24 )101.3490277777780.09725097802997411042.13890524104
Winsorized Mean ( 9 / 24 )101.3502777777780.09659256756526661049.25544824447
Winsorized Mean ( 10 / 24 )101.3391666666670.0945866036331491071.39026853853
Winsorized Mean ( 11 / 24 )101.3315277777780.09324666073775021086.70409187913
Winsorized Mean ( 12 / 24 )101.3281944444440.08753589167497941157.56168704691
Winsorized Mean ( 13 / 24 )101.3011111111110.08315416315249281218.23258476355
Winsorized Mean ( 14 / 24 )101.3283333333330.07602224573528061332.87740125663
Winsorized Mean ( 15 / 24 )101.3491666666670.07140161435206761419.42402264091
Winsorized Mean ( 16 / 24 )101.3402777777780.06861130118516651477.02019969397
Winsorized Mean ( 17 / 24 )101.3568055555560.06394773222350641584.99452648765
Winsorized Mean ( 18 / 24 )101.3818055555560.05889545603312121721.38586546543
Winsorized Mean ( 19 / 24 )101.4029166666670.05609049720899061807.84485273582
Winsorized Mean ( 20 / 24 )101.3834722222220.05056417223082952005.04562320132
Winsorized Mean ( 21 / 24 )101.3805555555560.04843719167255672093.03124427412
Winsorized Mean ( 22 / 24 )101.3591666666670.03492600606773572902.1115804106
Winsorized Mean ( 23 / 24 )101.368750.03294132017872663077.25220027652
Winsorized Mean ( 24 / 24 )101.3620833333330.03194401493213363173.11657750854
Trimmed Mean ( 1 / 24 )101.3378571428570.118330500568049856.396758708718
Trimmed Mean ( 2 / 24 )101.3355882352940.112113815232452903.863524982977
Trimmed Mean ( 3 / 24 )101.3324242424240.106426826938155952.132344425796
Trimmed Mean ( 4 / 24 )101.331250.102193817762568991.559491743701
Trimmed Mean ( 5 / 24 )101.3322580645160.09800560624453581033.94348494391
Trimmed Mean ( 6 / 24 )101.3370.09439288611517571073.56607230286
Trimmed Mean ( 7 / 24 )101.3396551724140.090815344689371115.88691887964
Trimmed Mean ( 8 / 24 )101.3373214285710.08847022063781211145.43990845729
Trimmed Mean ( 9 / 24 )101.335370370370.08581329291722341180.88196974471
Trimmed Mean ( 10 / 24 )101.3330769230770.08264962594162771226.0560863838
Trimmed Mean ( 11 / 24 )101.33220.07916260197227231280.05140654034
Trimmed Mean ( 12 / 24 )101.3322916666670.0750544953219061350.11622198052
Trimmed Mean ( 13 / 24 )101.3328260869570.07123185457118241422.57739457975
Trimmed Mean ( 14 / 24 )101.3368181818180.06736412424607841504.31434114157
Trimmed Mean ( 15 / 24 )101.3378571428570.0641585721678061579.49052977378
Trimmed Mean ( 16 / 24 )101.33650.06109424203848021658.691500521
Trimmed Mean ( 17 / 24 )101.3360526315790.05770940528684251755.97118230368
Trimmed Mean ( 18 / 24 )101.3336111111110.05438130044181091863.39072967812
Trimmed Mean ( 19 / 24 )101.3279411764710.05116952951474351980.23984463791
Trimmed Mean ( 20 / 24 )101.31906250.04732855173651332140.75983275511
Trimmed Mean ( 21 / 24 )101.3113333333330.04371993767369282317.2799121874
Trimmed Mean ( 22 / 24 )101.3028571428570.0390456832659932594.47008399741
Trimmed Mean ( 23 / 24 )101.2957692307690.03741317364418832707.48935105387
Trimmed Mean ( 24 / 24 )101.286250.03533900265564472866.13210301852
Median101.215
Midrange101.41
Midmean - Weighted Average at Xnp101.316216216216
Midmean - Weighted Average at X(n+1)p101.333611111111
Midmean - Empirical Distribution Function101.316216216216
Midmean - Empirical Distribution Function - Averaging101.333611111111
Midmean - Empirical Distribution Function - Interpolation101.333611111111
Midmean - Closest Observation101.316216216216
Midmean - True Basic - Statistics Graphics Toolkit101.333611111111
Midmean - MS Excel (old versions)101.336052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.339861111111 & 0.12384450171355 & 818.28308652336 \tabularnewline
Geometric Mean & 101.334490273946 &  &  \tabularnewline
Harmonic Mean & 101.32912132628 &  &  \tabularnewline
Quadratic Mean & 101.34523377901 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 101.34 & 0.123518608457867 & 820.443180709634 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 101.341388888889 & 0.120812861396042 & 838.829473268387 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 101.335555555556 & 0.115367665805185 & 878.37051090793 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 101.327777777778 & 0.112965645999761 & 896.978695434471 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 101.3125 & 0.108533356331681 & 933.468782540787 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 101.324166666667 & 0.105761222707011 & 958.046475572277 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 101.352361111111 & 0.0982679604961682 & 1031.3876526934 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 101.349027777778 & 0.0972509780299741 & 1042.13890524104 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 101.350277777778 & 0.0965925675652666 & 1049.25544824447 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 101.339166666667 & 0.094586603633149 & 1071.39026853853 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 101.331527777778 & 0.0932466607377502 & 1086.70409187913 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 101.328194444444 & 0.0875358916749794 & 1157.56168704691 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 101.301111111111 & 0.0831541631524928 & 1218.23258476355 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 101.328333333333 & 0.0760222457352806 & 1332.87740125663 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 101.349166666667 & 0.0714016143520676 & 1419.42402264091 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 101.340277777778 & 0.0686113011851665 & 1477.02019969397 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 101.356805555556 & 0.0639477322235064 & 1584.99452648765 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 101.381805555556 & 0.0588954560331212 & 1721.38586546543 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 101.402916666667 & 0.0560904972089906 & 1807.84485273582 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.383472222222 & 0.0505641722308295 & 2005.04562320132 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 101.380555555556 & 0.0484371916725567 & 2093.03124427412 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 101.359166666667 & 0.0349260060677357 & 2902.1115804106 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 101.36875 & 0.0329413201787266 & 3077.25220027652 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 101.362083333333 & 0.0319440149321336 & 3173.11657750854 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 101.337857142857 & 0.118330500568049 & 856.396758708718 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 101.335588235294 & 0.112113815232452 & 903.863524982977 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 101.332424242424 & 0.106426826938155 & 952.132344425796 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 101.33125 & 0.102193817762568 & 991.559491743701 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 101.332258064516 & 0.0980056062445358 & 1033.94348494391 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 101.337 & 0.0943928861151757 & 1073.56607230286 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 101.339655172414 & 0.09081534468937 & 1115.88691887964 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.337321428571 & 0.0884702206378121 & 1145.43990845729 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.33537037037 & 0.0858132929172234 & 1180.88196974471 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.333076923077 & 0.0826496259416277 & 1226.0560863838 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.3322 & 0.0791626019722723 & 1280.05140654034 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.332291666667 & 0.075054495321906 & 1350.11622198052 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.332826086957 & 0.0712318545711824 & 1422.57739457975 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.336818181818 & 0.0673641242460784 & 1504.31434114157 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.337857142857 & 0.064158572167806 & 1579.49052977378 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.3365 & 0.0610942420384802 & 1658.691500521 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.336052631579 & 0.0577094052868425 & 1755.97118230368 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.333611111111 & 0.0543813004418109 & 1863.39072967812 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.327941176471 & 0.0511695295147435 & 1980.23984463791 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.3190625 & 0.0473285517365133 & 2140.75983275511 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 101.311333333333 & 0.0437199376736928 & 2317.2799121874 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 101.302857142857 & 0.039045683265993 & 2594.47008399741 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 101.295769230769 & 0.0374131736441883 & 2707.48935105387 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 101.28625 & 0.0353390026556447 & 2866.13210301852 \tabularnewline
Median & 101.215 &  &  \tabularnewline
Midrange & 101.41 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.316216216216 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.333611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.316216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.333611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.333611111111 &  &  \tabularnewline
Midmean - Closest Observation & 101.316216216216 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.333611111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.336052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293101&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]101.339861111111[/C][C]0.12384450171355[/C][C]818.28308652336[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.334490273946[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.32912132628[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.34523377901[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]101.34[/C][C]0.123518608457867[/C][C]820.443180709634[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]101.341388888889[/C][C]0.120812861396042[/C][C]838.829473268387[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]101.335555555556[/C][C]0.115367665805185[/C][C]878.37051090793[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]101.327777777778[/C][C]0.112965645999761[/C][C]896.978695434471[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]101.3125[/C][C]0.108533356331681[/C][C]933.468782540787[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]101.324166666667[/C][C]0.105761222707011[/C][C]958.046475572277[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]101.352361111111[/C][C]0.0982679604961682[/C][C]1031.3876526934[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]101.349027777778[/C][C]0.0972509780299741[/C][C]1042.13890524104[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]101.350277777778[/C][C]0.0965925675652666[/C][C]1049.25544824447[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]101.339166666667[/C][C]0.094586603633149[/C][C]1071.39026853853[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]101.331527777778[/C][C]0.0932466607377502[/C][C]1086.70409187913[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]101.328194444444[/C][C]0.0875358916749794[/C][C]1157.56168704691[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]101.301111111111[/C][C]0.0831541631524928[/C][C]1218.23258476355[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]101.328333333333[/C][C]0.0760222457352806[/C][C]1332.87740125663[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]101.349166666667[/C][C]0.0714016143520676[/C][C]1419.42402264091[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]101.340277777778[/C][C]0.0686113011851665[/C][C]1477.02019969397[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]101.356805555556[/C][C]0.0639477322235064[/C][C]1584.99452648765[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]101.381805555556[/C][C]0.0588954560331212[/C][C]1721.38586546543[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]101.402916666667[/C][C]0.0560904972089906[/C][C]1807.84485273582[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.383472222222[/C][C]0.0505641722308295[/C][C]2005.04562320132[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]101.380555555556[/C][C]0.0484371916725567[/C][C]2093.03124427412[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]101.359166666667[/C][C]0.0349260060677357[/C][C]2902.1115804106[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]101.36875[/C][C]0.0329413201787266[/C][C]3077.25220027652[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]101.362083333333[/C][C]0.0319440149321336[/C][C]3173.11657750854[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]101.337857142857[/C][C]0.118330500568049[/C][C]856.396758708718[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]101.335588235294[/C][C]0.112113815232452[/C][C]903.863524982977[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]101.332424242424[/C][C]0.106426826938155[/C][C]952.132344425796[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]101.33125[/C][C]0.102193817762568[/C][C]991.559491743701[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]101.332258064516[/C][C]0.0980056062445358[/C][C]1033.94348494391[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]101.337[/C][C]0.0943928861151757[/C][C]1073.56607230286[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]101.339655172414[/C][C]0.09081534468937[/C][C]1115.88691887964[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.337321428571[/C][C]0.0884702206378121[/C][C]1145.43990845729[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.33537037037[/C][C]0.0858132929172234[/C][C]1180.88196974471[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.333076923077[/C][C]0.0826496259416277[/C][C]1226.0560863838[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.3322[/C][C]0.0791626019722723[/C][C]1280.05140654034[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.332291666667[/C][C]0.075054495321906[/C][C]1350.11622198052[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.332826086957[/C][C]0.0712318545711824[/C][C]1422.57739457975[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.336818181818[/C][C]0.0673641242460784[/C][C]1504.31434114157[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.337857142857[/C][C]0.064158572167806[/C][C]1579.49052977378[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.3365[/C][C]0.0610942420384802[/C][C]1658.691500521[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.336052631579[/C][C]0.0577094052868425[/C][C]1755.97118230368[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.333611111111[/C][C]0.0543813004418109[/C][C]1863.39072967812[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.327941176471[/C][C]0.0511695295147435[/C][C]1980.23984463791[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.3190625[/C][C]0.0473285517365133[/C][C]2140.75983275511[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]101.311333333333[/C][C]0.0437199376736928[/C][C]2317.2799121874[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]101.302857142857[/C][C]0.039045683265993[/C][C]2594.47008399741[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]101.295769230769[/C][C]0.0374131736441883[/C][C]2707.48935105387[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]101.28625[/C][C]0.0353390026556447[/C][C]2866.13210301852[/C][/ROW]
[ROW][C]Median[/C][C]101.215[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.316216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.333611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.316216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.333611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.333611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.316216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.333611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.336052631579[/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=293101&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293101&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.3398611111110.12384450171355818.28308652336
Geometric Mean101.334490273946
Harmonic Mean101.32912132628
Quadratic Mean101.34523377901
Winsorized Mean ( 1 / 24 )101.340.123518608457867820.443180709634
Winsorized Mean ( 2 / 24 )101.3413888888890.120812861396042838.829473268387
Winsorized Mean ( 3 / 24 )101.3355555555560.115367665805185878.37051090793
Winsorized Mean ( 4 / 24 )101.3277777777780.112965645999761896.978695434471
Winsorized Mean ( 5 / 24 )101.31250.108533356331681933.468782540787
Winsorized Mean ( 6 / 24 )101.3241666666670.105761222707011958.046475572277
Winsorized Mean ( 7 / 24 )101.3523611111110.09826796049616821031.3876526934
Winsorized Mean ( 8 / 24 )101.3490277777780.09725097802997411042.13890524104
Winsorized Mean ( 9 / 24 )101.3502777777780.09659256756526661049.25544824447
Winsorized Mean ( 10 / 24 )101.3391666666670.0945866036331491071.39026853853
Winsorized Mean ( 11 / 24 )101.3315277777780.09324666073775021086.70409187913
Winsorized Mean ( 12 / 24 )101.3281944444440.08753589167497941157.56168704691
Winsorized Mean ( 13 / 24 )101.3011111111110.08315416315249281218.23258476355
Winsorized Mean ( 14 / 24 )101.3283333333330.07602224573528061332.87740125663
Winsorized Mean ( 15 / 24 )101.3491666666670.07140161435206761419.42402264091
Winsorized Mean ( 16 / 24 )101.3402777777780.06861130118516651477.02019969397
Winsorized Mean ( 17 / 24 )101.3568055555560.06394773222350641584.99452648765
Winsorized Mean ( 18 / 24 )101.3818055555560.05889545603312121721.38586546543
Winsorized Mean ( 19 / 24 )101.4029166666670.05609049720899061807.84485273582
Winsorized Mean ( 20 / 24 )101.3834722222220.05056417223082952005.04562320132
Winsorized Mean ( 21 / 24 )101.3805555555560.04843719167255672093.03124427412
Winsorized Mean ( 22 / 24 )101.3591666666670.03492600606773572902.1115804106
Winsorized Mean ( 23 / 24 )101.368750.03294132017872663077.25220027652
Winsorized Mean ( 24 / 24 )101.3620833333330.03194401493213363173.11657750854
Trimmed Mean ( 1 / 24 )101.3378571428570.118330500568049856.396758708718
Trimmed Mean ( 2 / 24 )101.3355882352940.112113815232452903.863524982977
Trimmed Mean ( 3 / 24 )101.3324242424240.106426826938155952.132344425796
Trimmed Mean ( 4 / 24 )101.331250.102193817762568991.559491743701
Trimmed Mean ( 5 / 24 )101.3322580645160.09800560624453581033.94348494391
Trimmed Mean ( 6 / 24 )101.3370.09439288611517571073.56607230286
Trimmed Mean ( 7 / 24 )101.3396551724140.090815344689371115.88691887964
Trimmed Mean ( 8 / 24 )101.3373214285710.08847022063781211145.43990845729
Trimmed Mean ( 9 / 24 )101.335370370370.08581329291722341180.88196974471
Trimmed Mean ( 10 / 24 )101.3330769230770.08264962594162771226.0560863838
Trimmed Mean ( 11 / 24 )101.33220.07916260197227231280.05140654034
Trimmed Mean ( 12 / 24 )101.3322916666670.0750544953219061350.11622198052
Trimmed Mean ( 13 / 24 )101.3328260869570.07123185457118241422.57739457975
Trimmed Mean ( 14 / 24 )101.3368181818180.06736412424607841504.31434114157
Trimmed Mean ( 15 / 24 )101.3378571428570.0641585721678061579.49052977378
Trimmed Mean ( 16 / 24 )101.33650.06109424203848021658.691500521
Trimmed Mean ( 17 / 24 )101.3360526315790.05770940528684251755.97118230368
Trimmed Mean ( 18 / 24 )101.3336111111110.05438130044181091863.39072967812
Trimmed Mean ( 19 / 24 )101.3279411764710.05116952951474351980.23984463791
Trimmed Mean ( 20 / 24 )101.31906250.04732855173651332140.75983275511
Trimmed Mean ( 21 / 24 )101.3113333333330.04371993767369282317.2799121874
Trimmed Mean ( 22 / 24 )101.3028571428570.0390456832659932594.47008399741
Trimmed Mean ( 23 / 24 )101.2957692307690.03741317364418832707.48935105387
Trimmed Mean ( 24 / 24 )101.286250.03533900265564472866.13210301852
Median101.215
Midrange101.41
Midmean - Weighted Average at Xnp101.316216216216
Midmean - Weighted Average at X(n+1)p101.333611111111
Midmean - Empirical Distribution Function101.316216216216
Midmean - Empirical Distribution Function - Averaging101.333611111111
Midmean - Empirical Distribution Function - Interpolation101.333611111111
Midmean - Closest Observation101.316216216216
Midmean - True Basic - Statistics Graphics Toolkit101.333611111111
Midmean - MS Excel (old versions)101.336052631579
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')