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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Dec 2014 18:21:02 +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/2014/Dec/15/t14186676710b7i06c9g5hdh7h.htm/, Retrieved Thu, 16 May 2024 12:24:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268849, Retrieved Thu, 16 May 2024 12:24:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2014-11-04 10:08:09] [32b17a345b130fdf5cc88718ed94a974]
- R  D  [Central Tendency] [] [2014-12-15 18:08:27] [6656361aa4da5489a6a45e803df0211c]
-   PD    [Central Tendency] [] [2014-12-15 18:18:47] [eee95947b6243a1febfcd5f41483d733]
-    D        [Central Tendency] [] [2014-12-15 18:21:02] [ef562ec391a3ad5a7cbe41e167f467b9] [Current]
-   PD          [Central Tendency] [] [2014-12-17 15:55:10] [6656361aa4da5489a6a45e803df0211c]
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Dataseries X:
12,9
12,8
7,4
6,7
12,6
14,8
13,3
11,1
8,2
11,4
6,4
12,0
6,3
11,9
9,3
10,0
13,8
10,8
11,7
10,9
9,9
11,5
8,3
11,7
9,0
10,8
10,4
11,8
13,0
10,8
11,3
10,9
13,3
10,1
14,3
9,3
12,5
7,6
9,2
14,5
12,3
12,6
13,0
13,2
7,7
4,35
12,7
18,1
17,85
17,1
19,1
16,1
13,35
18,4
14,7
10,6
12,6
16,2
13,6
14,1
14,5
16,15
14,75
14,8
12,45
12,65
17,35
8,6
18,4
16,1
17,75
15,25
17,65
16,35
17,65
13,6
14,35
14,75
18,25
9,9
16
18,25
16,85
18,95
15,6
17,1
16,1
15,4
15,4
13,35
19,1
7,6
19,1
14,75
19,25
13,6
12,75
9,85
15,25
11,9
16,35
12,4
18,15
17,75
12,35
15,6
19,3
17,1
18,4
19,05
18,55
19,1
12,85
9,5
4,5
13,6
11,7
13,35
17,6
14,05
16,1
13,35
11,85
11,95
13,2
7,7
14,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268849&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268849&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.46102362204720.31018413266727743.3968801250268
Geometric Mean12.9429741405818
Harmonic Mean12.327947384786
Quadratic Mean13.9040334316806
Winsorized Mean ( 1 / 42 )13.4618110236220.30985231023790343.445895282453
Winsorized Mean ( 2 / 42 )13.48779527559060.30358115262281144.4289612812317
Winsorized Mean ( 3 / 42 )13.4901574803150.30313996449394544.5014153868993
Winsorized Mean ( 4 / 42 )13.49960629921260.30141704661512844.7871361318523
Winsorized Mean ( 5 / 42 )13.52716535433070.29668983486666445.593625950852
Winsorized Mean ( 6 / 42 )13.53425196850390.29480922634149545.908508822673
Winsorized Mean ( 7 / 42 )13.52874015748030.29399667624969746.0166432153475
Winsorized Mean ( 8 / 42 )13.5098425196850.28940485121566546.6814653000322
Winsorized Mean ( 9 / 42 )13.49921259842520.28795226256369446.8800365666139
Winsorized Mean ( 10 / 42 )13.53858267716540.2818446017004448.0356288376064
Winsorized Mean ( 11 / 42 )13.54724409448820.28055069929997948.288042511713
Winsorized Mean ( 12 / 42 )13.56141732283460.27447908246217949.4078353846994
Winsorized Mean ( 13 / 42 )13.60236220472440.2687581195848950.6119116539955
Winsorized Mean ( 14 / 42 )13.61338582677170.26429121537631551.5090363763624
Winsorized Mean ( 15 / 42 )13.61929133858270.26193248402118151.9954269493407
Winsorized Mean ( 16 / 42 )13.58779527559060.25772693111303952.7216741258248
Winsorized Mean ( 17 / 42 )13.60118110236220.25248203258859453.8698970493659
Winsorized Mean ( 18 / 42 )13.65078740157480.24624411781410255.4359938533851
Winsorized Mean ( 19 / 42 )13.64330708661420.24336358593595456.061415409143
Winsorized Mean ( 20 / 42 )13.64330708661420.24336358593595456.061415409143
Winsorized Mean ( 21 / 42 )13.65157480314960.24027773230447456.8158134015127
Winsorized Mean ( 22 / 42 )13.62559055118110.23261436862053558.5758765977547
Winsorized Mean ( 23 / 42 )13.63464566929130.22047892999360261.8410370083301
Winsorized Mean ( 24 / 42 )13.67244094488190.21614594391997963.2555980321502
Winsorized Mean ( 25 / 42 )13.7118110236220.21177635388193764.7466573688686
Winsorized Mean ( 26 / 42 )13.66062992125980.20537143100321866.5167002758323
Winsorized Mean ( 27 / 42 )13.55433070866140.19268673763269870.3438694078616
Winsorized Mean ( 28 / 42 )13.57637795275590.19020495163293971.377626272085
Winsorized Mean ( 29 / 42 )13.5421259842520.1862831720700872.6964536504531
Winsorized Mean ( 30 / 42 )13.57755905511810.17969835146573575.5575048094253
Winsorized Mean ( 31 / 42 )13.61417322834650.17304616404286478.6736493331004
Winsorized Mean ( 32 / 42 )13.63937007874020.17039477707044680.045705116309
Winsorized Mean ( 33 / 42 )13.66535433070870.16770813691811881.4829535515061
Winsorized Mean ( 34 / 42 )13.71889763779530.16232046809486384.5173612349227
Winsorized Mean ( 35 / 42 )13.69133858267720.15912943396953586.0390076250654
Winsorized Mean ( 36 / 42 )13.57795275590550.14637290085265392.7627496402074
Winsorized Mean ( 37 / 42 )13.60708661417320.14343279700628394.867330890697
Winsorized Mean ( 38 / 42 )13.56220472440940.135409543420199100.156934155842
Winsorized Mean ( 39 / 42 )13.57755905511810.133875571420312101.419242592739
Winsorized Mean ( 40 / 42 )13.53031496062990.128819786505894105.032893840504
Winsorized Mean ( 41 / 42 )13.54645669291340.127205184444737106.49296058211
Winsorized Mean ( 42 / 42 )13.41417322834650.110168965056877121.760000390502
Trimmed Mean ( 1 / 42 )13.48720.30293505319063544.5217542768568
Trimmed Mean ( 2 / 42 )13.51341463414630.29527865132922345.7649565023225
Trimmed Mean ( 3 / 42 )13.52685950413220.29047081172875546.568739294755
Trimmed Mean ( 4 / 42 )13.53991596638660.28533294759161247.453040669407
Trimmed Mean ( 5 / 42 )13.55085470085470.28019336121273848.3625116676699
Trimmed Mean ( 6 / 42 )13.55608695652170.27575369833553249.160127455578
Trimmed Mean ( 7 / 42 )13.56017699115040.27125594548882349.9903401811673
Trimmed Mean ( 8 / 42 )13.56531531531530.26641813212930950.9173876676354
Trimmed Mean ( 9 / 42 )13.57339449541280.26188903853473251.8287995990818
Trimmed Mean ( 10 / 42 )13.58317757009350.25707922936976652.8365422729515
Trimmed Mean ( 11 / 42 )13.58857142857140.25271534278577253.7702668891399
Trimmed Mean ( 12 / 42 )13.59320388349510.24802383675323754.8060382479256
Trimmed Mean ( 13 / 42 )13.59653465346530.24366554888969155.7999877923679
Trimmed Mean ( 14 / 42 )13.59595959595960.23958051531528356.7490205873694
Trimmed Mean ( 15 / 42 )13.59432989690720.23558515048173657.7045279344173
Trimmed Mean ( 16 / 42 )13.59210526315790.23137850176784458.7440283315329
Trimmed Mean ( 17 / 42 )13.59247311827960.22716537154426759.8351457613374
Trimmed Mean ( 18 / 42 )13.59175824175820.2230577050131460.9338208736506
Trimmed Mean ( 19 / 42 )13.58707865168540.21916524951430661.9946760802448
Trimmed Mean ( 20 / 42 )13.58275862068970.21507417702123763.1538328255392
Trimmed Mean ( 21 / 42 )13.57823529411760.21037089938320764.5442660269462
Trimmed Mean ( 22 / 42 )13.57289156626510.20535245463247266.0955896074241
Trimmed Mean ( 23 / 42 )13.56913580246910.20056934374970567.6530896935196
Trimmed Mean ( 24 / 42 )13.56455696202530.19659787310346868.9964583436077
Trimmed Mean ( 25 / 42 )13.55714285714290.19250905271546270.4234043329951
Trimmed Mean ( 26 / 42 )13.54666666666670.18826455732172171.9554804121579
Trimmed Mean ( 27 / 42 )13.53904109589040.18415715324749373.5189530090909
Trimmed Mean ( 28 / 42 )13.53802816901410.18101398055306874.7899589172625
Trimmed Mean ( 29 / 42 )13.53550724637680.17759194108289676.2169001805026
Trimmed Mean ( 30 / 42 )13.53507462686570.17403547899259877.7719273404092
Trimmed Mean ( 31 / 42 )13.53230769230770.17066551987603279.2913981812923
Trimmed Mean ( 32 / 42 )13.52698412698410.16750108098490980.7575930104169
Trimmed Mean ( 33 / 42 )13.51967213114750.16400169384922982.4361737603549
Trimmed Mean ( 34 / 42 )13.51016949152540.16008736866597484.3924764589937
Trimmed Mean ( 35 / 42 )13.49649122807020.15602388224670286.5027265936748
Trimmed Mean ( 36 / 42 )13.48363636363640.15153565517833688.9799588602962
Trimmed Mean ( 37 / 42 )13.4773584905660.14820874124973290.9349770932653
Trimmed Mean ( 38 / 42 )13.46862745098040.14445951182763393.234618341027
Trimmed Mean ( 39 / 42 )13.46224489795920.14115451600985595.37239954136
Trimmed Mean ( 40 / 42 )13.45425531914890.13714437475318998.102859438178
Trimmed Mean ( 41 / 42 )13.44888888888890.132996628734603101.122028557027
Trimmed Mean ( 42 / 42 )13.44186046511630.127870477023141105.120906545799
Median13.35
Midrange11.825
Midmean - Weighted Average at Xnp13.5323076923077
Midmean - Weighted Average at X(n+1)p13.5323076923077
Midmean - Empirical Distribution Function13.5323076923077
Midmean - Empirical Distribution Function - Averaging13.5323076923077
Midmean - Empirical Distribution Function - Interpolation13.5671875
Midmean - Closest Observation13.5323076923077
Midmean - True Basic - Statistics Graphics Toolkit13.5323076923077
Midmean - MS Excel (old versions)13.5323076923077
Number of observations127

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.4610236220472 & 0.310184132667277 & 43.3968801250268 \tabularnewline
Geometric Mean & 12.9429741405818 &  &  \tabularnewline
Harmonic Mean & 12.327947384786 &  &  \tabularnewline
Quadratic Mean & 13.9040334316806 &  &  \tabularnewline
Winsorized Mean ( 1 / 42 ) & 13.461811023622 & 0.309852310237903 & 43.445895282453 \tabularnewline
Winsorized Mean ( 2 / 42 ) & 13.4877952755906 & 0.303581152622811 & 44.4289612812317 \tabularnewline
Winsorized Mean ( 3 / 42 ) & 13.490157480315 & 0.303139964493945 & 44.5014153868993 \tabularnewline
Winsorized Mean ( 4 / 42 ) & 13.4996062992126 & 0.301417046615128 & 44.7871361318523 \tabularnewline
Winsorized Mean ( 5 / 42 ) & 13.5271653543307 & 0.296689834866664 & 45.593625950852 \tabularnewline
Winsorized Mean ( 6 / 42 ) & 13.5342519685039 & 0.294809226341495 & 45.908508822673 \tabularnewline
Winsorized Mean ( 7 / 42 ) & 13.5287401574803 & 0.293996676249697 & 46.0166432153475 \tabularnewline
Winsorized Mean ( 8 / 42 ) & 13.509842519685 & 0.289404851215665 & 46.6814653000322 \tabularnewline
Winsorized Mean ( 9 / 42 ) & 13.4992125984252 & 0.287952262563694 & 46.8800365666139 \tabularnewline
Winsorized Mean ( 10 / 42 ) & 13.5385826771654 & 0.28184460170044 & 48.0356288376064 \tabularnewline
Winsorized Mean ( 11 / 42 ) & 13.5472440944882 & 0.280550699299979 & 48.288042511713 \tabularnewline
Winsorized Mean ( 12 / 42 ) & 13.5614173228346 & 0.274479082462179 & 49.4078353846994 \tabularnewline
Winsorized Mean ( 13 / 42 ) & 13.6023622047244 & 0.26875811958489 & 50.6119116539955 \tabularnewline
Winsorized Mean ( 14 / 42 ) & 13.6133858267717 & 0.264291215376315 & 51.5090363763624 \tabularnewline
Winsorized Mean ( 15 / 42 ) & 13.6192913385827 & 0.261932484021181 & 51.9954269493407 \tabularnewline
Winsorized Mean ( 16 / 42 ) & 13.5877952755906 & 0.257726931113039 & 52.7216741258248 \tabularnewline
Winsorized Mean ( 17 / 42 ) & 13.6011811023622 & 0.252482032588594 & 53.8698970493659 \tabularnewline
Winsorized Mean ( 18 / 42 ) & 13.6507874015748 & 0.246244117814102 & 55.4359938533851 \tabularnewline
Winsorized Mean ( 19 / 42 ) & 13.6433070866142 & 0.243363585935954 & 56.061415409143 \tabularnewline
Winsorized Mean ( 20 / 42 ) & 13.6433070866142 & 0.243363585935954 & 56.061415409143 \tabularnewline
Winsorized Mean ( 21 / 42 ) & 13.6515748031496 & 0.240277732304474 & 56.8158134015127 \tabularnewline
Winsorized Mean ( 22 / 42 ) & 13.6255905511811 & 0.232614368620535 & 58.5758765977547 \tabularnewline
Winsorized Mean ( 23 / 42 ) & 13.6346456692913 & 0.220478929993602 & 61.8410370083301 \tabularnewline
Winsorized Mean ( 24 / 42 ) & 13.6724409448819 & 0.216145943919979 & 63.2555980321502 \tabularnewline
Winsorized Mean ( 25 / 42 ) & 13.711811023622 & 0.211776353881937 & 64.7466573688686 \tabularnewline
Winsorized Mean ( 26 / 42 ) & 13.6606299212598 & 0.205371431003218 & 66.5167002758323 \tabularnewline
Winsorized Mean ( 27 / 42 ) & 13.5543307086614 & 0.192686737632698 & 70.3438694078616 \tabularnewline
Winsorized Mean ( 28 / 42 ) & 13.5763779527559 & 0.190204951632939 & 71.377626272085 \tabularnewline
Winsorized Mean ( 29 / 42 ) & 13.542125984252 & 0.18628317207008 & 72.6964536504531 \tabularnewline
Winsorized Mean ( 30 / 42 ) & 13.5775590551181 & 0.179698351465735 & 75.5575048094253 \tabularnewline
Winsorized Mean ( 31 / 42 ) & 13.6141732283465 & 0.173046164042864 & 78.6736493331004 \tabularnewline
Winsorized Mean ( 32 / 42 ) & 13.6393700787402 & 0.170394777070446 & 80.045705116309 \tabularnewline
Winsorized Mean ( 33 / 42 ) & 13.6653543307087 & 0.167708136918118 & 81.4829535515061 \tabularnewline
Winsorized Mean ( 34 / 42 ) & 13.7188976377953 & 0.162320468094863 & 84.5173612349227 \tabularnewline
Winsorized Mean ( 35 / 42 ) & 13.6913385826772 & 0.159129433969535 & 86.0390076250654 \tabularnewline
Winsorized Mean ( 36 / 42 ) & 13.5779527559055 & 0.146372900852653 & 92.7627496402074 \tabularnewline
Winsorized Mean ( 37 / 42 ) & 13.6070866141732 & 0.143432797006283 & 94.867330890697 \tabularnewline
Winsorized Mean ( 38 / 42 ) & 13.5622047244094 & 0.135409543420199 & 100.156934155842 \tabularnewline
Winsorized Mean ( 39 / 42 ) & 13.5775590551181 & 0.133875571420312 & 101.419242592739 \tabularnewline
Winsorized Mean ( 40 / 42 ) & 13.5303149606299 & 0.128819786505894 & 105.032893840504 \tabularnewline
Winsorized Mean ( 41 / 42 ) & 13.5464566929134 & 0.127205184444737 & 106.49296058211 \tabularnewline
Winsorized Mean ( 42 / 42 ) & 13.4141732283465 & 0.110168965056877 & 121.760000390502 \tabularnewline
Trimmed Mean ( 1 / 42 ) & 13.4872 & 0.302935053190635 & 44.5217542768568 \tabularnewline
Trimmed Mean ( 2 / 42 ) & 13.5134146341463 & 0.295278651329223 & 45.7649565023225 \tabularnewline
Trimmed Mean ( 3 / 42 ) & 13.5268595041322 & 0.290470811728755 & 46.568739294755 \tabularnewline
Trimmed Mean ( 4 / 42 ) & 13.5399159663866 & 0.285332947591612 & 47.453040669407 \tabularnewline
Trimmed Mean ( 5 / 42 ) & 13.5508547008547 & 0.280193361212738 & 48.3625116676699 \tabularnewline
Trimmed Mean ( 6 / 42 ) & 13.5560869565217 & 0.275753698335532 & 49.160127455578 \tabularnewline
Trimmed Mean ( 7 / 42 ) & 13.5601769911504 & 0.271255945488823 & 49.9903401811673 \tabularnewline
Trimmed Mean ( 8 / 42 ) & 13.5653153153153 & 0.266418132129309 & 50.9173876676354 \tabularnewline
Trimmed Mean ( 9 / 42 ) & 13.5733944954128 & 0.261889038534732 & 51.8287995990818 \tabularnewline
Trimmed Mean ( 10 / 42 ) & 13.5831775700935 & 0.257079229369766 & 52.8365422729515 \tabularnewline
Trimmed Mean ( 11 / 42 ) & 13.5885714285714 & 0.252715342785772 & 53.7702668891399 \tabularnewline
Trimmed Mean ( 12 / 42 ) & 13.5932038834951 & 0.248023836753237 & 54.8060382479256 \tabularnewline
Trimmed Mean ( 13 / 42 ) & 13.5965346534653 & 0.243665548889691 & 55.7999877923679 \tabularnewline
Trimmed Mean ( 14 / 42 ) & 13.5959595959596 & 0.239580515315283 & 56.7490205873694 \tabularnewline
Trimmed Mean ( 15 / 42 ) & 13.5943298969072 & 0.235585150481736 & 57.7045279344173 \tabularnewline
Trimmed Mean ( 16 / 42 ) & 13.5921052631579 & 0.231378501767844 & 58.7440283315329 \tabularnewline
Trimmed Mean ( 17 / 42 ) & 13.5924731182796 & 0.227165371544267 & 59.8351457613374 \tabularnewline
Trimmed Mean ( 18 / 42 ) & 13.5917582417582 & 0.22305770501314 & 60.9338208736506 \tabularnewline
Trimmed Mean ( 19 / 42 ) & 13.5870786516854 & 0.219165249514306 & 61.9946760802448 \tabularnewline
Trimmed Mean ( 20 / 42 ) & 13.5827586206897 & 0.215074177021237 & 63.1538328255392 \tabularnewline
Trimmed Mean ( 21 / 42 ) & 13.5782352941176 & 0.210370899383207 & 64.5442660269462 \tabularnewline
Trimmed Mean ( 22 / 42 ) & 13.5728915662651 & 0.205352454632472 & 66.0955896074241 \tabularnewline
Trimmed Mean ( 23 / 42 ) & 13.5691358024691 & 0.200569343749705 & 67.6530896935196 \tabularnewline
Trimmed Mean ( 24 / 42 ) & 13.5645569620253 & 0.196597873103468 & 68.9964583436077 \tabularnewline
Trimmed Mean ( 25 / 42 ) & 13.5571428571429 & 0.192509052715462 & 70.4234043329951 \tabularnewline
Trimmed Mean ( 26 / 42 ) & 13.5466666666667 & 0.188264557321721 & 71.9554804121579 \tabularnewline
Trimmed Mean ( 27 / 42 ) & 13.5390410958904 & 0.184157153247493 & 73.5189530090909 \tabularnewline
Trimmed Mean ( 28 / 42 ) & 13.5380281690141 & 0.181013980553068 & 74.7899589172625 \tabularnewline
Trimmed Mean ( 29 / 42 ) & 13.5355072463768 & 0.177591941082896 & 76.2169001805026 \tabularnewline
Trimmed Mean ( 30 / 42 ) & 13.5350746268657 & 0.174035478992598 & 77.7719273404092 \tabularnewline
Trimmed Mean ( 31 / 42 ) & 13.5323076923077 & 0.170665519876032 & 79.2913981812923 \tabularnewline
Trimmed Mean ( 32 / 42 ) & 13.5269841269841 & 0.167501080984909 & 80.7575930104169 \tabularnewline
Trimmed Mean ( 33 / 42 ) & 13.5196721311475 & 0.164001693849229 & 82.4361737603549 \tabularnewline
Trimmed Mean ( 34 / 42 ) & 13.5101694915254 & 0.160087368665974 & 84.3924764589937 \tabularnewline
Trimmed Mean ( 35 / 42 ) & 13.4964912280702 & 0.156023882246702 & 86.5027265936748 \tabularnewline
Trimmed Mean ( 36 / 42 ) & 13.4836363636364 & 0.151535655178336 & 88.9799588602962 \tabularnewline
Trimmed Mean ( 37 / 42 ) & 13.477358490566 & 0.148208741249732 & 90.9349770932653 \tabularnewline
Trimmed Mean ( 38 / 42 ) & 13.4686274509804 & 0.144459511827633 & 93.234618341027 \tabularnewline
Trimmed Mean ( 39 / 42 ) & 13.4622448979592 & 0.141154516009855 & 95.37239954136 \tabularnewline
Trimmed Mean ( 40 / 42 ) & 13.4542553191489 & 0.137144374753189 & 98.102859438178 \tabularnewline
Trimmed Mean ( 41 / 42 ) & 13.4488888888889 & 0.132996628734603 & 101.122028557027 \tabularnewline
Trimmed Mean ( 42 / 42 ) & 13.4418604651163 & 0.127870477023141 & 105.120906545799 \tabularnewline
Median & 13.35 &  &  \tabularnewline
Midrange & 11.825 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.5323076923077 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.5323076923077 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.5323076923077 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.5323076923077 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.5671875 &  &  \tabularnewline
Midmean - Closest Observation & 13.5323076923077 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.5323076923077 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.5323076923077 &  &  \tabularnewline
Number of observations & 127 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268849&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]13.4610236220472[/C][C]0.310184132667277[/C][C]43.3968801250268[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12.9429741405818[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12.327947384786[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.9040334316806[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 42 )[/C][C]13.461811023622[/C][C]0.309852310237903[/C][C]43.445895282453[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 42 )[/C][C]13.4877952755906[/C][C]0.303581152622811[/C][C]44.4289612812317[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 42 )[/C][C]13.490157480315[/C][C]0.303139964493945[/C][C]44.5014153868993[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 42 )[/C][C]13.4996062992126[/C][C]0.301417046615128[/C][C]44.7871361318523[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 42 )[/C][C]13.5271653543307[/C][C]0.296689834866664[/C][C]45.593625950852[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 42 )[/C][C]13.5342519685039[/C][C]0.294809226341495[/C][C]45.908508822673[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 42 )[/C][C]13.5287401574803[/C][C]0.293996676249697[/C][C]46.0166432153475[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 42 )[/C][C]13.509842519685[/C][C]0.289404851215665[/C][C]46.6814653000322[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 42 )[/C][C]13.4992125984252[/C][C]0.287952262563694[/C][C]46.8800365666139[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 42 )[/C][C]13.5385826771654[/C][C]0.28184460170044[/C][C]48.0356288376064[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 42 )[/C][C]13.5472440944882[/C][C]0.280550699299979[/C][C]48.288042511713[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 42 )[/C][C]13.5614173228346[/C][C]0.274479082462179[/C][C]49.4078353846994[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 42 )[/C][C]13.6023622047244[/C][C]0.26875811958489[/C][C]50.6119116539955[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 42 )[/C][C]13.6133858267717[/C][C]0.264291215376315[/C][C]51.5090363763624[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 42 )[/C][C]13.6192913385827[/C][C]0.261932484021181[/C][C]51.9954269493407[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 42 )[/C][C]13.5877952755906[/C][C]0.257726931113039[/C][C]52.7216741258248[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 42 )[/C][C]13.6011811023622[/C][C]0.252482032588594[/C][C]53.8698970493659[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 42 )[/C][C]13.6507874015748[/C][C]0.246244117814102[/C][C]55.4359938533851[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 42 )[/C][C]13.6433070866142[/C][C]0.243363585935954[/C][C]56.061415409143[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 42 )[/C][C]13.6433070866142[/C][C]0.243363585935954[/C][C]56.061415409143[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 42 )[/C][C]13.6515748031496[/C][C]0.240277732304474[/C][C]56.8158134015127[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 42 )[/C][C]13.6255905511811[/C][C]0.232614368620535[/C][C]58.5758765977547[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 42 )[/C][C]13.6346456692913[/C][C]0.220478929993602[/C][C]61.8410370083301[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 42 )[/C][C]13.6724409448819[/C][C]0.216145943919979[/C][C]63.2555980321502[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 42 )[/C][C]13.711811023622[/C][C]0.211776353881937[/C][C]64.7466573688686[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 42 )[/C][C]13.6606299212598[/C][C]0.205371431003218[/C][C]66.5167002758323[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 42 )[/C][C]13.5543307086614[/C][C]0.192686737632698[/C][C]70.3438694078616[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 42 )[/C][C]13.5763779527559[/C][C]0.190204951632939[/C][C]71.377626272085[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 42 )[/C][C]13.542125984252[/C][C]0.18628317207008[/C][C]72.6964536504531[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 42 )[/C][C]13.5775590551181[/C][C]0.179698351465735[/C][C]75.5575048094253[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 42 )[/C][C]13.6141732283465[/C][C]0.173046164042864[/C][C]78.6736493331004[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 42 )[/C][C]13.6393700787402[/C][C]0.170394777070446[/C][C]80.045705116309[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 42 )[/C][C]13.6653543307087[/C][C]0.167708136918118[/C][C]81.4829535515061[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 42 )[/C][C]13.7188976377953[/C][C]0.162320468094863[/C][C]84.5173612349227[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 42 )[/C][C]13.6913385826772[/C][C]0.159129433969535[/C][C]86.0390076250654[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 42 )[/C][C]13.5779527559055[/C][C]0.146372900852653[/C][C]92.7627496402074[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 42 )[/C][C]13.6070866141732[/C][C]0.143432797006283[/C][C]94.867330890697[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 42 )[/C][C]13.5622047244094[/C][C]0.135409543420199[/C][C]100.156934155842[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 42 )[/C][C]13.5775590551181[/C][C]0.133875571420312[/C][C]101.419242592739[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 42 )[/C][C]13.5303149606299[/C][C]0.128819786505894[/C][C]105.032893840504[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 42 )[/C][C]13.5464566929134[/C][C]0.127205184444737[/C][C]106.49296058211[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 42 )[/C][C]13.4141732283465[/C][C]0.110168965056877[/C][C]121.760000390502[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 42 )[/C][C]13.4872[/C][C]0.302935053190635[/C][C]44.5217542768568[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 42 )[/C][C]13.5134146341463[/C][C]0.295278651329223[/C][C]45.7649565023225[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 42 )[/C][C]13.5268595041322[/C][C]0.290470811728755[/C][C]46.568739294755[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 42 )[/C][C]13.5399159663866[/C][C]0.285332947591612[/C][C]47.453040669407[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 42 )[/C][C]13.5508547008547[/C][C]0.280193361212738[/C][C]48.3625116676699[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 42 )[/C][C]13.5560869565217[/C][C]0.275753698335532[/C][C]49.160127455578[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 42 )[/C][C]13.5601769911504[/C][C]0.271255945488823[/C][C]49.9903401811673[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 42 )[/C][C]13.5653153153153[/C][C]0.266418132129309[/C][C]50.9173876676354[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 42 )[/C][C]13.5733944954128[/C][C]0.261889038534732[/C][C]51.8287995990818[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 42 )[/C][C]13.5831775700935[/C][C]0.257079229369766[/C][C]52.8365422729515[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 42 )[/C][C]13.5885714285714[/C][C]0.252715342785772[/C][C]53.7702668891399[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 42 )[/C][C]13.5932038834951[/C][C]0.248023836753237[/C][C]54.8060382479256[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 42 )[/C][C]13.5965346534653[/C][C]0.243665548889691[/C][C]55.7999877923679[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 42 )[/C][C]13.5959595959596[/C][C]0.239580515315283[/C][C]56.7490205873694[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 42 )[/C][C]13.5943298969072[/C][C]0.235585150481736[/C][C]57.7045279344173[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 42 )[/C][C]13.5921052631579[/C][C]0.231378501767844[/C][C]58.7440283315329[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 42 )[/C][C]13.5924731182796[/C][C]0.227165371544267[/C][C]59.8351457613374[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 42 )[/C][C]13.5917582417582[/C][C]0.22305770501314[/C][C]60.9338208736506[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 42 )[/C][C]13.5870786516854[/C][C]0.219165249514306[/C][C]61.9946760802448[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 42 )[/C][C]13.5827586206897[/C][C]0.215074177021237[/C][C]63.1538328255392[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 42 )[/C][C]13.5782352941176[/C][C]0.210370899383207[/C][C]64.5442660269462[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 42 )[/C][C]13.5728915662651[/C][C]0.205352454632472[/C][C]66.0955896074241[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 42 )[/C][C]13.5691358024691[/C][C]0.200569343749705[/C][C]67.6530896935196[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 42 )[/C][C]13.5645569620253[/C][C]0.196597873103468[/C][C]68.9964583436077[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 42 )[/C][C]13.5571428571429[/C][C]0.192509052715462[/C][C]70.4234043329951[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 42 )[/C][C]13.5466666666667[/C][C]0.188264557321721[/C][C]71.9554804121579[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 42 )[/C][C]13.5390410958904[/C][C]0.184157153247493[/C][C]73.5189530090909[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 42 )[/C][C]13.5380281690141[/C][C]0.181013980553068[/C][C]74.7899589172625[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 42 )[/C][C]13.5355072463768[/C][C]0.177591941082896[/C][C]76.2169001805026[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 42 )[/C][C]13.5350746268657[/C][C]0.174035478992598[/C][C]77.7719273404092[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 42 )[/C][C]13.5323076923077[/C][C]0.170665519876032[/C][C]79.2913981812923[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 42 )[/C][C]13.5269841269841[/C][C]0.167501080984909[/C][C]80.7575930104169[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 42 )[/C][C]13.5196721311475[/C][C]0.164001693849229[/C][C]82.4361737603549[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 42 )[/C][C]13.5101694915254[/C][C]0.160087368665974[/C][C]84.3924764589937[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 42 )[/C][C]13.4964912280702[/C][C]0.156023882246702[/C][C]86.5027265936748[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 42 )[/C][C]13.4836363636364[/C][C]0.151535655178336[/C][C]88.9799588602962[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 42 )[/C][C]13.477358490566[/C][C]0.148208741249732[/C][C]90.9349770932653[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 42 )[/C][C]13.4686274509804[/C][C]0.144459511827633[/C][C]93.234618341027[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 42 )[/C][C]13.4622448979592[/C][C]0.141154516009855[/C][C]95.37239954136[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 42 )[/C][C]13.4542553191489[/C][C]0.137144374753189[/C][C]98.102859438178[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 42 )[/C][C]13.4488888888889[/C][C]0.132996628734603[/C][C]101.122028557027[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 42 )[/C][C]13.4418604651163[/C][C]0.127870477023141[/C][C]105.120906545799[/C][/ROW]
[ROW][C]Median[/C][C]13.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11.825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.5323076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.5323076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.5323076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.5323076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.5671875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.5323076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.5323076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.5323076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]127[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268849&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 Mean13.46102362204720.31018413266727743.3968801250268
Geometric Mean12.9429741405818
Harmonic Mean12.327947384786
Quadratic Mean13.9040334316806
Winsorized Mean ( 1 / 42 )13.4618110236220.30985231023790343.445895282453
Winsorized Mean ( 2 / 42 )13.48779527559060.30358115262281144.4289612812317
Winsorized Mean ( 3 / 42 )13.4901574803150.30313996449394544.5014153868993
Winsorized Mean ( 4 / 42 )13.49960629921260.30141704661512844.7871361318523
Winsorized Mean ( 5 / 42 )13.52716535433070.29668983486666445.593625950852
Winsorized Mean ( 6 / 42 )13.53425196850390.29480922634149545.908508822673
Winsorized Mean ( 7 / 42 )13.52874015748030.29399667624969746.0166432153475
Winsorized Mean ( 8 / 42 )13.5098425196850.28940485121566546.6814653000322
Winsorized Mean ( 9 / 42 )13.49921259842520.28795226256369446.8800365666139
Winsorized Mean ( 10 / 42 )13.53858267716540.2818446017004448.0356288376064
Winsorized Mean ( 11 / 42 )13.54724409448820.28055069929997948.288042511713
Winsorized Mean ( 12 / 42 )13.56141732283460.27447908246217949.4078353846994
Winsorized Mean ( 13 / 42 )13.60236220472440.2687581195848950.6119116539955
Winsorized Mean ( 14 / 42 )13.61338582677170.26429121537631551.5090363763624
Winsorized Mean ( 15 / 42 )13.61929133858270.26193248402118151.9954269493407
Winsorized Mean ( 16 / 42 )13.58779527559060.25772693111303952.7216741258248
Winsorized Mean ( 17 / 42 )13.60118110236220.25248203258859453.8698970493659
Winsorized Mean ( 18 / 42 )13.65078740157480.24624411781410255.4359938533851
Winsorized Mean ( 19 / 42 )13.64330708661420.24336358593595456.061415409143
Winsorized Mean ( 20 / 42 )13.64330708661420.24336358593595456.061415409143
Winsorized Mean ( 21 / 42 )13.65157480314960.24027773230447456.8158134015127
Winsorized Mean ( 22 / 42 )13.62559055118110.23261436862053558.5758765977547
Winsorized Mean ( 23 / 42 )13.63464566929130.22047892999360261.8410370083301
Winsorized Mean ( 24 / 42 )13.67244094488190.21614594391997963.2555980321502
Winsorized Mean ( 25 / 42 )13.7118110236220.21177635388193764.7466573688686
Winsorized Mean ( 26 / 42 )13.66062992125980.20537143100321866.5167002758323
Winsorized Mean ( 27 / 42 )13.55433070866140.19268673763269870.3438694078616
Winsorized Mean ( 28 / 42 )13.57637795275590.19020495163293971.377626272085
Winsorized Mean ( 29 / 42 )13.5421259842520.1862831720700872.6964536504531
Winsorized Mean ( 30 / 42 )13.57755905511810.17969835146573575.5575048094253
Winsorized Mean ( 31 / 42 )13.61417322834650.17304616404286478.6736493331004
Winsorized Mean ( 32 / 42 )13.63937007874020.17039477707044680.045705116309
Winsorized Mean ( 33 / 42 )13.66535433070870.16770813691811881.4829535515061
Winsorized Mean ( 34 / 42 )13.71889763779530.16232046809486384.5173612349227
Winsorized Mean ( 35 / 42 )13.69133858267720.15912943396953586.0390076250654
Winsorized Mean ( 36 / 42 )13.57795275590550.14637290085265392.7627496402074
Winsorized Mean ( 37 / 42 )13.60708661417320.14343279700628394.867330890697
Winsorized Mean ( 38 / 42 )13.56220472440940.135409543420199100.156934155842
Winsorized Mean ( 39 / 42 )13.57755905511810.133875571420312101.419242592739
Winsorized Mean ( 40 / 42 )13.53031496062990.128819786505894105.032893840504
Winsorized Mean ( 41 / 42 )13.54645669291340.127205184444737106.49296058211
Winsorized Mean ( 42 / 42 )13.41417322834650.110168965056877121.760000390502
Trimmed Mean ( 1 / 42 )13.48720.30293505319063544.5217542768568
Trimmed Mean ( 2 / 42 )13.51341463414630.29527865132922345.7649565023225
Trimmed Mean ( 3 / 42 )13.52685950413220.29047081172875546.568739294755
Trimmed Mean ( 4 / 42 )13.53991596638660.28533294759161247.453040669407
Trimmed Mean ( 5 / 42 )13.55085470085470.28019336121273848.3625116676699
Trimmed Mean ( 6 / 42 )13.55608695652170.27575369833553249.160127455578
Trimmed Mean ( 7 / 42 )13.56017699115040.27125594548882349.9903401811673
Trimmed Mean ( 8 / 42 )13.56531531531530.26641813212930950.9173876676354
Trimmed Mean ( 9 / 42 )13.57339449541280.26188903853473251.8287995990818
Trimmed Mean ( 10 / 42 )13.58317757009350.25707922936976652.8365422729515
Trimmed Mean ( 11 / 42 )13.58857142857140.25271534278577253.7702668891399
Trimmed Mean ( 12 / 42 )13.59320388349510.24802383675323754.8060382479256
Trimmed Mean ( 13 / 42 )13.59653465346530.24366554888969155.7999877923679
Trimmed Mean ( 14 / 42 )13.59595959595960.23958051531528356.7490205873694
Trimmed Mean ( 15 / 42 )13.59432989690720.23558515048173657.7045279344173
Trimmed Mean ( 16 / 42 )13.59210526315790.23137850176784458.7440283315329
Trimmed Mean ( 17 / 42 )13.59247311827960.22716537154426759.8351457613374
Trimmed Mean ( 18 / 42 )13.59175824175820.2230577050131460.9338208736506
Trimmed Mean ( 19 / 42 )13.58707865168540.21916524951430661.9946760802448
Trimmed Mean ( 20 / 42 )13.58275862068970.21507417702123763.1538328255392
Trimmed Mean ( 21 / 42 )13.57823529411760.21037089938320764.5442660269462
Trimmed Mean ( 22 / 42 )13.57289156626510.20535245463247266.0955896074241
Trimmed Mean ( 23 / 42 )13.56913580246910.20056934374970567.6530896935196
Trimmed Mean ( 24 / 42 )13.56455696202530.19659787310346868.9964583436077
Trimmed Mean ( 25 / 42 )13.55714285714290.19250905271546270.4234043329951
Trimmed Mean ( 26 / 42 )13.54666666666670.18826455732172171.9554804121579
Trimmed Mean ( 27 / 42 )13.53904109589040.18415715324749373.5189530090909
Trimmed Mean ( 28 / 42 )13.53802816901410.18101398055306874.7899589172625
Trimmed Mean ( 29 / 42 )13.53550724637680.17759194108289676.2169001805026
Trimmed Mean ( 30 / 42 )13.53507462686570.17403547899259877.7719273404092
Trimmed Mean ( 31 / 42 )13.53230769230770.17066551987603279.2913981812923
Trimmed Mean ( 32 / 42 )13.52698412698410.16750108098490980.7575930104169
Trimmed Mean ( 33 / 42 )13.51967213114750.16400169384922982.4361737603549
Trimmed Mean ( 34 / 42 )13.51016949152540.16008736866597484.3924764589937
Trimmed Mean ( 35 / 42 )13.49649122807020.15602388224670286.5027265936748
Trimmed Mean ( 36 / 42 )13.48363636363640.15153565517833688.9799588602962
Trimmed Mean ( 37 / 42 )13.4773584905660.14820874124973290.9349770932653
Trimmed Mean ( 38 / 42 )13.46862745098040.14445951182763393.234618341027
Trimmed Mean ( 39 / 42 )13.46224489795920.14115451600985595.37239954136
Trimmed Mean ( 40 / 42 )13.45425531914890.13714437475318998.102859438178
Trimmed Mean ( 41 / 42 )13.44888888888890.132996628734603101.122028557027
Trimmed Mean ( 42 / 42 )13.44186046511630.127870477023141105.120906545799
Median13.35
Midrange11.825
Midmean - Weighted Average at Xnp13.5323076923077
Midmean - Weighted Average at X(n+1)p13.5323076923077
Midmean - Empirical Distribution Function13.5323076923077
Midmean - Empirical Distribution Function - Averaging13.5323076923077
Midmean - Empirical Distribution Function - Interpolation13.5671875
Midmean - Closest Observation13.5323076923077
Midmean - True Basic - Statistics Graphics Toolkit13.5323076923077
Midmean - MS Excel (old versions)13.5323076923077
Number of observations127



Parameters (Session):
par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')