Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Dec 2007 05:14:59 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/17/t1197893268wdosjk1xhfjm5dw.htm/, Retrieved Fri, 03 May 2024 15:53:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4363, Retrieved Fri, 03 May 2024 15:53:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Brent olie CT] [2007-12-17 12:14:59] [5ac741e139b03fb8a6fb673aeace8af7] [Current]
Feedback Forum

Post a new message
Dataseries X:
25.62
27.5
24.5
25.66
28.31
27.85
24.61
25.68
25.62
20.54
18.8
18.71
19.46
20.12
23.54
25.6
25.39
24.09
25.69
26.56
28.33
27.5
24.23
28.23
31.29
32.72
30.46
24.89
25.68
27.52
28.4
29.71
26.85
29.62
28.69
29.76
31.3
30.86
33.46
33.15
37.99
35.24
38.24
43.16
43.33
49.67
43.17
39.56
44.36
45.22
53.1
52.1
48.52
54.84
57.57
64.14
62.85
58.75
55.33
57.03
63.18
60.19
62.12
70.12
69.75
68.56
73.77
73.23
61.96
57.81
58.76
62.47
53.68
57.56
62.05
67.49
67.21
71.05
76.93
70.76




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4363&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4363&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4363&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean41.99151.9544554997832321.4850120684034
Geometric Mean38.5124325932502
Harmonic Mean35.4065157967637
Quadratic Mean45.4429079175178
Winsorized Mean ( 1 / 26 )41.9531251.9457279770208721.5616599521970
Winsorized Mean ( 2 / 26 )41.9561251.9405003717701821.6212919154076
Winsorized Mean ( 3 / 26 )41.8991251.9207140615227821.8143480278275
Winsorized Mean ( 4 / 26 )41.9056251.9149483322817221.8834233245699
Winsorized Mean ( 5 / 26 )42.0531251.8824338759357722.3397621226377
Winsorized Mean ( 6 / 26 )42.0666251.8721434099948222.4697663519893
Winsorized Mean ( 7 / 26 )41.974751.8514463980984322.6713287746873
Winsorized Mean ( 8 / 26 )41.894751.8289803738885822.9060686479253
Winsorized Mean ( 9 / 26 )41.8756251.8219309624034222.9841996563686
Winsorized Mean ( 10 / 26 )41.5268751.7525703419833623.6948406607204
Winsorized Mean ( 11 / 26 )41.4636251.7230690186863224.0638213271411
Winsorized Mean ( 12 / 26 )41.4456251.7114966694346124.2160126514833
Winsorized Mean ( 13 / 26 )41.3871251.7013848342549124.3255518485474
Winsorized Mean ( 14 / 26 )41.3258751.6918163100695724.4269278845649
Winsorized Mean ( 15 / 26 )41.320251.6888948709984324.4658508410133
Winsorized Mean ( 16 / 26 )41.306251.6856312190997824.5049151510494
Winsorized Mean ( 17 / 26 )40.9301251.6282876916455025.1369123589193
Winsorized Mean ( 18 / 26 )40.6106251.5805384171520025.694171403424
Winsorized Mean ( 19 / 26 )40.8148751.5558625146069926.2329573576171
Winsorized Mean ( 20 / 26 )40.6523751.5134627832626826.8605052265394
Winsorized Mean ( 21 / 26 )40.761.4849349813154027.4490132651421
Winsorized Mean ( 22 / 26 )40.757251.4845409508167527.4544464250559
Winsorized Mean ( 23 / 26 )40.6106251.4621440965169727.7747077711014
Winsorized Mean ( 24 / 26 )40.1996251.3792421607873529.1461689200770
Winsorized Mean ( 25 / 26 )40.165251.3446314606730129.8708242181813
Winsorized Mean ( 26 / 26 )39.814251.2900077123579730.8635751698140
Trimmed Mean ( 1 / 26 )41.84205128205131.9302383510525221.6771422343959
Trimmed Mean ( 2 / 26 )41.72513157894741.9114569853351921.8289670649483
Trimmed Mean ( 3 / 26 )41.60027027027031.8919567077806021.9879609819775
Trimmed Mean ( 4 / 26 )41.48958333333331.8768256259605322.1062536441550
Trimmed Mean ( 5 / 26 )41.37071428571431.8600216980571522.2420600409808
Trimmed Mean ( 6 / 26 )41.21014705882351.8482871135964022.2963990581727
Trimmed Mean ( 7 / 26 )41.03712121212121.8355750452180122.3565477854092
Trimmed Mean ( 8 / 26 )40.86968751.8238844705578222.4080462111180
Trimmed Mean ( 9 / 26 )40.70435483870971.8132223044573722.4486290173289
Trimmed Mean ( 10 / 26 )40.53083333333331.800108397421422.5157737119567
Trimmed Mean ( 11 / 26 )40.39344827586211.7963344331578622.4865968887834
Trimmed Mean ( 12 / 26 )40.25446428571431.7948742118433922.4274570441188
Trimmed Mean ( 13 / 26 )40.10740740740741.7925194778939822.3748795491636
Trimmed Mean ( 14 / 26 )39.95596153846151.7886861264052222.3381626036102
Trimmed Mean ( 15 / 26 )39.79941.7827762896043722.3243938300482
Trimmed Mean ( 16 / 26 )39.63041666666671.7728287078880022.3543405464587
Trimmed Mean ( 17 / 26 )39.44826086956521.7577544497836122.4424184358751
Trimmed Mean ( 18 / 26 )39.28977272727271.7470589145209822.489094329166
Trimmed Mean ( 19 / 26 )39.151.7393990177901822.5077740067591
Trimmed Mean ( 20 / 26 )38.974751.7294637151403822.5357431085719
Trimmed Mean ( 21 / 26 )38.79815789473681.7207355127601222.5474267294589
Trimmed Mean ( 22 / 26 )38.59055555555561.7093316685437122.5764000432013
Trimmed Mean ( 23 / 26 )38.35882352941181.6879621379320022.7249312454407
Trimmed Mean ( 24 / 26 )38.11406251.6585587444359522.9802306537909
Trimmed Mean ( 25 / 26 )37.88233333333331.6349136631123.1708463805190
Trimmed Mean ( 26 / 26 )37.62142857142861.6030824073757123.4681812976889
Median34.35
Midrange47.82
Midmean - Weighted Average at Xnp38.6719512195122
Midmean - Weighted Average at X(n+1)p38.97475
Midmean - Empirical Distribution Function38.6719512195122
Midmean - Empirical Distribution Function - Averaging38.97475
Midmean - Empirical Distribution Function - Interpolation38.97475
Midmean - Closest Observation38.6719512195122
Midmean - True Basic - Statistics Graphics Toolkit38.97475
Midmean - MS Excel (old versions)39.15
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 41.9915 & 1.95445549978323 & 21.4850120684034 \tabularnewline
Geometric Mean & 38.5124325932502 &  &  \tabularnewline
Harmonic Mean & 35.4065157967637 &  &  \tabularnewline
Quadratic Mean & 45.4429079175178 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 41.953125 & 1.94572797702087 & 21.5616599521970 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 41.956125 & 1.94050037177018 & 21.6212919154076 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 41.899125 & 1.92071406152278 & 21.8143480278275 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 41.905625 & 1.91494833228172 & 21.8834233245699 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 42.053125 & 1.88243387593577 & 22.3397621226377 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 42.066625 & 1.87214340999482 & 22.4697663519893 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 41.97475 & 1.85144639809843 & 22.6713287746873 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 41.89475 & 1.82898037388858 & 22.9060686479253 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 41.875625 & 1.82193096240342 & 22.9841996563686 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 41.526875 & 1.75257034198336 & 23.6948406607204 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 41.463625 & 1.72306901868632 & 24.0638213271411 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 41.445625 & 1.71149666943461 & 24.2160126514833 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 41.387125 & 1.70138483425491 & 24.3255518485474 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 41.325875 & 1.69181631006957 & 24.4269278845649 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 41.32025 & 1.68889487099843 & 24.4658508410133 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 41.30625 & 1.68563121909978 & 24.5049151510494 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 40.930125 & 1.62828769164550 & 25.1369123589193 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 40.610625 & 1.58053841715200 & 25.694171403424 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 40.814875 & 1.55586251460699 & 26.2329573576171 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 40.652375 & 1.51346278326268 & 26.8605052265394 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 40.76 & 1.48493498131540 & 27.4490132651421 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 40.75725 & 1.48454095081675 & 27.4544464250559 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 40.610625 & 1.46214409651697 & 27.7747077711014 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 40.199625 & 1.37924216078735 & 29.1461689200770 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 40.16525 & 1.34463146067301 & 29.8708242181813 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 39.81425 & 1.29000771235797 & 30.8635751698140 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 41.8420512820513 & 1.93023835105252 & 21.6771422343959 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 41.7251315789474 & 1.91145698533519 & 21.8289670649483 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 41.6002702702703 & 1.89195670778060 & 21.9879609819775 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 41.4895833333333 & 1.87682562596053 & 22.1062536441550 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 41.3707142857143 & 1.86002169805715 & 22.2420600409808 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 41.2101470588235 & 1.84828711359640 & 22.2963990581727 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 41.0371212121212 & 1.83557504521801 & 22.3565477854092 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 40.8696875 & 1.82388447055782 & 22.4080462111180 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 40.7043548387097 & 1.81322230445737 & 22.4486290173289 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 40.5308333333333 & 1.8001083974214 & 22.5157737119567 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 40.3934482758621 & 1.79633443315786 & 22.4865968887834 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 40.2544642857143 & 1.79487421184339 & 22.4274570441188 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 40.1074074074074 & 1.79251947789398 & 22.3748795491636 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 39.9559615384615 & 1.78868612640522 & 22.3381626036102 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 39.7994 & 1.78277628960437 & 22.3243938300482 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 39.6304166666667 & 1.77282870788800 & 22.3543405464587 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 39.4482608695652 & 1.75775444978361 & 22.4424184358751 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 39.2897727272727 & 1.74705891452098 & 22.489094329166 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 39.15 & 1.73939901779018 & 22.5077740067591 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 38.97475 & 1.72946371514038 & 22.5357431085719 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 38.7981578947368 & 1.72073551276012 & 22.5474267294589 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 38.5905555555556 & 1.70933166854371 & 22.5764000432013 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 38.3588235294118 & 1.68796213793200 & 22.7249312454407 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 38.1140625 & 1.65855874443595 & 22.9802306537909 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 37.8823333333333 & 1.63491366311 & 23.1708463805190 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 37.6214285714286 & 1.60308240737571 & 23.4681812976889 \tabularnewline
Median & 34.35 &  &  \tabularnewline
Midrange & 47.82 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 38.6719512195122 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 38.97475 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 38.6719512195122 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 38.97475 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 38.97475 &  &  \tabularnewline
Midmean - Closest Observation & 38.6719512195122 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 38.97475 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 39.15 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4363&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]41.9915[/C][C]1.95445549978323[/C][C]21.4850120684034[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]38.5124325932502[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]35.4065157967637[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]45.4429079175178[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]41.953125[/C][C]1.94572797702087[/C][C]21.5616599521970[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]41.956125[/C][C]1.94050037177018[/C][C]21.6212919154076[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]41.899125[/C][C]1.92071406152278[/C][C]21.8143480278275[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]41.905625[/C][C]1.91494833228172[/C][C]21.8834233245699[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]42.053125[/C][C]1.88243387593577[/C][C]22.3397621226377[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]42.066625[/C][C]1.87214340999482[/C][C]22.4697663519893[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]41.97475[/C][C]1.85144639809843[/C][C]22.6713287746873[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]41.89475[/C][C]1.82898037388858[/C][C]22.9060686479253[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]41.875625[/C][C]1.82193096240342[/C][C]22.9841996563686[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]41.526875[/C][C]1.75257034198336[/C][C]23.6948406607204[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]41.463625[/C][C]1.72306901868632[/C][C]24.0638213271411[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]41.445625[/C][C]1.71149666943461[/C][C]24.2160126514833[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]41.387125[/C][C]1.70138483425491[/C][C]24.3255518485474[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]41.325875[/C][C]1.69181631006957[/C][C]24.4269278845649[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]41.32025[/C][C]1.68889487099843[/C][C]24.4658508410133[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]41.30625[/C][C]1.68563121909978[/C][C]24.5049151510494[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]40.930125[/C][C]1.62828769164550[/C][C]25.1369123589193[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]40.610625[/C][C]1.58053841715200[/C][C]25.694171403424[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]40.814875[/C][C]1.55586251460699[/C][C]26.2329573576171[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]40.652375[/C][C]1.51346278326268[/C][C]26.8605052265394[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]40.76[/C][C]1.48493498131540[/C][C]27.4490132651421[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]40.75725[/C][C]1.48454095081675[/C][C]27.4544464250559[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]40.610625[/C][C]1.46214409651697[/C][C]27.7747077711014[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]40.199625[/C][C]1.37924216078735[/C][C]29.1461689200770[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]40.16525[/C][C]1.34463146067301[/C][C]29.8708242181813[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]39.81425[/C][C]1.29000771235797[/C][C]30.8635751698140[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]41.8420512820513[/C][C]1.93023835105252[/C][C]21.6771422343959[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]41.7251315789474[/C][C]1.91145698533519[/C][C]21.8289670649483[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]41.6002702702703[/C][C]1.89195670778060[/C][C]21.9879609819775[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]41.4895833333333[/C][C]1.87682562596053[/C][C]22.1062536441550[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]41.3707142857143[/C][C]1.86002169805715[/C][C]22.2420600409808[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]41.2101470588235[/C][C]1.84828711359640[/C][C]22.2963990581727[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]41.0371212121212[/C][C]1.83557504521801[/C][C]22.3565477854092[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]40.8696875[/C][C]1.82388447055782[/C][C]22.4080462111180[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]40.7043548387097[/C][C]1.81322230445737[/C][C]22.4486290173289[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]40.5308333333333[/C][C]1.8001083974214[/C][C]22.5157737119567[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]40.3934482758621[/C][C]1.79633443315786[/C][C]22.4865968887834[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]40.2544642857143[/C][C]1.79487421184339[/C][C]22.4274570441188[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]40.1074074074074[/C][C]1.79251947789398[/C][C]22.3748795491636[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]39.9559615384615[/C][C]1.78868612640522[/C][C]22.3381626036102[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]39.7994[/C][C]1.78277628960437[/C][C]22.3243938300482[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]39.6304166666667[/C][C]1.77282870788800[/C][C]22.3543405464587[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]39.4482608695652[/C][C]1.75775444978361[/C][C]22.4424184358751[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]39.2897727272727[/C][C]1.74705891452098[/C][C]22.489094329166[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]39.15[/C][C]1.73939901779018[/C][C]22.5077740067591[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]38.97475[/C][C]1.72946371514038[/C][C]22.5357431085719[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]38.7981578947368[/C][C]1.72073551276012[/C][C]22.5474267294589[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]38.5905555555556[/C][C]1.70933166854371[/C][C]22.5764000432013[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]38.3588235294118[/C][C]1.68796213793200[/C][C]22.7249312454407[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]38.1140625[/C][C]1.65855874443595[/C][C]22.9802306537909[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]37.8823333333333[/C][C]1.63491366311[/C][C]23.1708463805190[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]37.6214285714286[/C][C]1.60308240737571[/C][C]23.4681812976889[/C][/ROW]
[ROW][C]Median[/C][C]34.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]47.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]38.6719512195122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]38.97475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]38.6719512195122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]38.97475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]38.97475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]38.6719512195122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]38.97475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]39.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4363&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4363&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 Mean41.99151.9544554997832321.4850120684034
Geometric Mean38.5124325932502
Harmonic Mean35.4065157967637
Quadratic Mean45.4429079175178
Winsorized Mean ( 1 / 26 )41.9531251.9457279770208721.5616599521970
Winsorized Mean ( 2 / 26 )41.9561251.9405003717701821.6212919154076
Winsorized Mean ( 3 / 26 )41.8991251.9207140615227821.8143480278275
Winsorized Mean ( 4 / 26 )41.9056251.9149483322817221.8834233245699
Winsorized Mean ( 5 / 26 )42.0531251.8824338759357722.3397621226377
Winsorized Mean ( 6 / 26 )42.0666251.8721434099948222.4697663519893
Winsorized Mean ( 7 / 26 )41.974751.8514463980984322.6713287746873
Winsorized Mean ( 8 / 26 )41.894751.8289803738885822.9060686479253
Winsorized Mean ( 9 / 26 )41.8756251.8219309624034222.9841996563686
Winsorized Mean ( 10 / 26 )41.5268751.7525703419833623.6948406607204
Winsorized Mean ( 11 / 26 )41.4636251.7230690186863224.0638213271411
Winsorized Mean ( 12 / 26 )41.4456251.7114966694346124.2160126514833
Winsorized Mean ( 13 / 26 )41.3871251.7013848342549124.3255518485474
Winsorized Mean ( 14 / 26 )41.3258751.6918163100695724.4269278845649
Winsorized Mean ( 15 / 26 )41.320251.6888948709984324.4658508410133
Winsorized Mean ( 16 / 26 )41.306251.6856312190997824.5049151510494
Winsorized Mean ( 17 / 26 )40.9301251.6282876916455025.1369123589193
Winsorized Mean ( 18 / 26 )40.6106251.5805384171520025.694171403424
Winsorized Mean ( 19 / 26 )40.8148751.5558625146069926.2329573576171
Winsorized Mean ( 20 / 26 )40.6523751.5134627832626826.8605052265394
Winsorized Mean ( 21 / 26 )40.761.4849349813154027.4490132651421
Winsorized Mean ( 22 / 26 )40.757251.4845409508167527.4544464250559
Winsorized Mean ( 23 / 26 )40.6106251.4621440965169727.7747077711014
Winsorized Mean ( 24 / 26 )40.1996251.3792421607873529.1461689200770
Winsorized Mean ( 25 / 26 )40.165251.3446314606730129.8708242181813
Winsorized Mean ( 26 / 26 )39.814251.2900077123579730.8635751698140
Trimmed Mean ( 1 / 26 )41.84205128205131.9302383510525221.6771422343959
Trimmed Mean ( 2 / 26 )41.72513157894741.9114569853351921.8289670649483
Trimmed Mean ( 3 / 26 )41.60027027027031.8919567077806021.9879609819775
Trimmed Mean ( 4 / 26 )41.48958333333331.8768256259605322.1062536441550
Trimmed Mean ( 5 / 26 )41.37071428571431.8600216980571522.2420600409808
Trimmed Mean ( 6 / 26 )41.21014705882351.8482871135964022.2963990581727
Trimmed Mean ( 7 / 26 )41.03712121212121.8355750452180122.3565477854092
Trimmed Mean ( 8 / 26 )40.86968751.8238844705578222.4080462111180
Trimmed Mean ( 9 / 26 )40.70435483870971.8132223044573722.4486290173289
Trimmed Mean ( 10 / 26 )40.53083333333331.800108397421422.5157737119567
Trimmed Mean ( 11 / 26 )40.39344827586211.7963344331578622.4865968887834
Trimmed Mean ( 12 / 26 )40.25446428571431.7948742118433922.4274570441188
Trimmed Mean ( 13 / 26 )40.10740740740741.7925194778939822.3748795491636
Trimmed Mean ( 14 / 26 )39.95596153846151.7886861264052222.3381626036102
Trimmed Mean ( 15 / 26 )39.79941.7827762896043722.3243938300482
Trimmed Mean ( 16 / 26 )39.63041666666671.7728287078880022.3543405464587
Trimmed Mean ( 17 / 26 )39.44826086956521.7577544497836122.4424184358751
Trimmed Mean ( 18 / 26 )39.28977272727271.7470589145209822.489094329166
Trimmed Mean ( 19 / 26 )39.151.7393990177901822.5077740067591
Trimmed Mean ( 20 / 26 )38.974751.7294637151403822.5357431085719
Trimmed Mean ( 21 / 26 )38.79815789473681.7207355127601222.5474267294589
Trimmed Mean ( 22 / 26 )38.59055555555561.7093316685437122.5764000432013
Trimmed Mean ( 23 / 26 )38.35882352941181.6879621379320022.7249312454407
Trimmed Mean ( 24 / 26 )38.11406251.6585587444359522.9802306537909
Trimmed Mean ( 25 / 26 )37.88233333333331.6349136631123.1708463805190
Trimmed Mean ( 26 / 26 )37.62142857142861.6030824073757123.4681812976889
Median34.35
Midrange47.82
Midmean - Weighted Average at Xnp38.6719512195122
Midmean - Weighted Average at X(n+1)p38.97475
Midmean - Empirical Distribution Function38.6719512195122
Midmean - Empirical Distribution Function - Averaging38.97475
Midmean - Empirical Distribution Function - Interpolation38.97475
Midmean - Closest Observation38.6719512195122
Midmean - True Basic - Statistics Graphics Toolkit38.97475
Midmean - MS Excel (old versions)39.15
Number of observations80



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')