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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 16 Oct 2010 13:03:12 +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/2010/Oct/16/t128723499037bepw1ui8cne2g.htm/, Retrieved Sat, 27 Apr 2024 17:30:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=83762, Retrieved Sat, 27 Apr 2024 17:30:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52 - Sofie Baert
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-10-16 13:03:12] [1ce81d942cb901782da36327f25f651a] [Current]
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Dataseries X:
6,59
6,59
6,59
6,59
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,63
6,79
6,79
6,79
6,81
6,80
6,80
6,85
6,85
6,85
6,85
6,85
6,85
6,86
6,86
6,88
6,88
6,88
6,91
6,91
6,91
6,91
6,99
6,99
6,99
7,02
7,02
7,05
7,05
7,05
7,05
7,10
7,10
7,10
7,10
7,12
7,13
7,18
7,24
7,24
7,24
7,27
7,27
7,27
7,27
7,30
7,30
7,57
7,76
7,94
7,94
7,96




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=83762&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=83762&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83762&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 Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.952222222222220.0387703312417367179.318102259030
Geometric Mean6.9448252907669
Harmonic Mean6.93769223527144
Quadratic Mean6.95989343788155
Winsorized Mean ( 1 / 24 )6.951944444444440.0386694990913017179.778497467225
Winsorized Mean ( 2 / 24 )6.951944444444440.0386694990913017179.778497467225
Winsorized Mean ( 3 / 24 )6.944444444444440.0361221242385148192.249060398281
Winsorized Mean ( 4 / 24 )6.936111111111110.0326901297573241212.177533787767
Winsorized Mean ( 5 / 24 )6.917361111111110.02828772430687244.535793550248
Winsorized Mean ( 6 / 24 )6.917361111111110.02828772430687244.535793550248
Winsorized Mean ( 7 / 24 )6.914444444444450.0277465395556234249.200244613678
Winsorized Mean ( 8 / 24 )6.914444444444450.0277465395556234249.200244613678
Winsorized Mean ( 9 / 24 )6.914444444444450.0277465395556234249.200244613678
Winsorized Mean ( 10 / 24 )6.914444444444440.0277465395556234249.200244613678
Winsorized Mean ( 11 / 24 )6.909861111111110.0269370775063582256.518588903347
Winsorized Mean ( 12 / 24 )6.909861111111110.0269370775063582256.518588903347
Winsorized Mean ( 13 / 24 )6.909861111111110.0269370775063582256.518588903347
Winsorized Mean ( 14 / 24 )6.898194444444440.0250010378414380275.91632348202
Winsorized Mean ( 15 / 24 )6.887777777777780.0234130280719629294.185688267546
Winsorized Mean ( 16 / 24 )6.885555555555560.0230922224786163298.176390857643
Winsorized Mean ( 17 / 24 )6.880833333333330.0224294669110858306.776498996170
Winsorized Mean ( 18 / 24 )6.880833333333330.0224294669110858306.77649899617
Winsorized Mean ( 19 / 24 )6.880833333333330.0224294669110858306.776498996170
Winsorized Mean ( 20 / 24 )6.880833333333330.0224294669110858306.776498996170
Winsorized Mean ( 21 / 24 )6.912916666666670.0135738827690249509.280710928321
Winsorized Mean ( 22 / 24 )6.912916666666670.0135738827690249509.280710928321
Winsorized Mean ( 23 / 24 )6.912916666666670.0135738827690249509.280710928321
Winsorized Mean ( 24 / 24 )6.916250.0131537755577667525.799605567717
Trimmed Mean ( 1 / 24 )6.9430.0367726775427708188.808660776048
Trimmed Mean ( 2 / 24 )6.93352941176470.0344483458190664201.273217825372
Trimmed Mean ( 3 / 24 )6.923484848484850.0315449081770642219.480266343549
Trimmed Mean ( 4 / 24 )6.9156250.0292684236849202236.282796588157
Trimmed Mean ( 5 / 24 )6.909677419354840.0278907437624417247.740880566246
Trimmed Mean ( 6 / 24 )6.907833333333330.027674553024799249.609571910458
Trimmed Mean ( 7 / 24 )6.905862068965520.0273889270735582252.140657077165
Trimmed Mean ( 8 / 24 )6.904285714285710.0271549870367259254.254796916234
Trimmed Mean ( 9 / 24 )6.902592592592590.0268419100128257257.157280882559
Trimmed Mean ( 10 / 24 )6.900769230769230.0264302008482968261.094089688461
Trimmed Mean ( 11 / 24 )6.89880.0258940383967004266.424259295108
Trimmed Mean ( 12 / 24 )6.897291666666670.0253866196945432271.690037888315
Trimmed Mean ( 13 / 24 )6.895652173913040.0247199818916984278.950535001353
Trimmed Mean ( 14 / 24 )6.893863636363640.0238436944765001289.127326436686
Trimmed Mean ( 15 / 24 )6.893333333333330.0231659835793644297.562730704589
Trimmed Mean ( 16 / 24 )6.8940.0226279835828480304.667005557916
Trimmed Mean ( 17 / 24 )6.8950.0219586770842135313.998879511596
Trimmed Mean ( 18 / 24 )6.896666666666670.0211869981094276325.514102141627
Trimmed Mean ( 19 / 24 )6.89852941176470.0200939520212588343.31371969368
Trimmed Mean ( 20 / 24 )6.9006250.0185183948435237372.636238632384
Trimmed Mean ( 21 / 24 )6.9030.0161540714059492427.322612766078
Trimmed Mean ( 22 / 24 )6.901785714285710.0159617065847454432.396478261399
Trimmed Mean ( 23 / 24 )6.900384615384620.0155956677340538442.455221094339
Trimmed Mean ( 24 / 24 )6.898750.0149553986665472461.288271467572
Median6.88
Midrange7.275
Midmean - Weighted Average at Xnp6.82745098039216
Midmean - Weighted Average at X(n+1)p6.82745098039216
Midmean - Empirical Distribution Function6.82745098039216
Midmean - Empirical Distribution Function - Averaging6.82745098039216
Midmean - Empirical Distribution Function - Interpolation6.82745098039216
Midmean - Closest Observation6.82745098039216
Midmean - True Basic - Statistics Graphics Toolkit6.82745098039216
Midmean - MS Excel (old versions)6.82745098039216
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.95222222222222 & 0.0387703312417367 & 179.318102259030 \tabularnewline
Geometric Mean & 6.9448252907669 &  &  \tabularnewline
Harmonic Mean & 6.93769223527144 &  &  \tabularnewline
Quadratic Mean & 6.95989343788155 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 6.95194444444444 & 0.0386694990913017 & 179.778497467225 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6.95194444444444 & 0.0386694990913017 & 179.778497467225 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 6.94444444444444 & 0.0361221242385148 & 192.249060398281 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 6.93611111111111 & 0.0326901297573241 & 212.177533787767 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 6.91736111111111 & 0.02828772430687 & 244.535793550248 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 6.91736111111111 & 0.02828772430687 & 244.535793550248 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 6.91444444444445 & 0.0277465395556234 & 249.200244613678 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 6.91444444444445 & 0.0277465395556234 & 249.200244613678 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 6.91444444444445 & 0.0277465395556234 & 249.200244613678 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 6.91444444444444 & 0.0277465395556234 & 249.200244613678 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6.90986111111111 & 0.0269370775063582 & 256.518588903347 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 6.90986111111111 & 0.0269370775063582 & 256.518588903347 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 6.90986111111111 & 0.0269370775063582 & 256.518588903347 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 6.89819444444444 & 0.0250010378414380 & 275.91632348202 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 6.88777777777778 & 0.0234130280719629 & 294.185688267546 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 6.88555555555556 & 0.0230922224786163 & 298.176390857643 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 6.88083333333333 & 0.0224294669110858 & 306.776498996170 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 6.88083333333333 & 0.0224294669110858 & 306.77649899617 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 6.88083333333333 & 0.0224294669110858 & 306.776498996170 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 6.88083333333333 & 0.0224294669110858 & 306.776498996170 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 6.91291666666667 & 0.0135738827690249 & 509.280710928321 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 6.91291666666667 & 0.0135738827690249 & 509.280710928321 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 6.91291666666667 & 0.0135738827690249 & 509.280710928321 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 6.91625 & 0.0131537755577667 & 525.799605567717 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 6.943 & 0.0367726775427708 & 188.808660776048 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 6.9335294117647 & 0.0344483458190664 & 201.273217825372 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 6.92348484848485 & 0.0315449081770642 & 219.480266343549 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 6.915625 & 0.0292684236849202 & 236.282796588157 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 6.90967741935484 & 0.0278907437624417 & 247.740880566246 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 6.90783333333333 & 0.027674553024799 & 249.609571910458 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 6.90586206896552 & 0.0273889270735582 & 252.140657077165 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 6.90428571428571 & 0.0271549870367259 & 254.254796916234 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 6.90259259259259 & 0.0268419100128257 & 257.157280882559 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 6.90076923076923 & 0.0264302008482968 & 261.094089688461 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 6.8988 & 0.0258940383967004 & 266.424259295108 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 6.89729166666667 & 0.0253866196945432 & 271.690037888315 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 6.89565217391304 & 0.0247199818916984 & 278.950535001353 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 6.89386363636364 & 0.0238436944765001 & 289.127326436686 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 6.89333333333333 & 0.0231659835793644 & 297.562730704589 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 6.894 & 0.0226279835828480 & 304.667005557916 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 6.895 & 0.0219586770842135 & 313.998879511596 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 6.89666666666667 & 0.0211869981094276 & 325.514102141627 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 6.8985294117647 & 0.0200939520212588 & 343.31371969368 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 6.900625 & 0.0185183948435237 & 372.636238632384 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 6.903 & 0.0161540714059492 & 427.322612766078 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 6.90178571428571 & 0.0159617065847454 & 432.396478261399 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 6.90038461538462 & 0.0155956677340538 & 442.455221094339 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 6.89875 & 0.0149553986665472 & 461.288271467572 \tabularnewline
Median & 6.88 &  &  \tabularnewline
Midrange & 7.275 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.82745098039216 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.82745098039216 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.82745098039216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.82745098039216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.82745098039216 &  &  \tabularnewline
Midmean - Closest Observation & 6.82745098039216 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.82745098039216 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.82745098039216 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=83762&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]6.95222222222222[/C][C]0.0387703312417367[/C][C]179.318102259030[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.9448252907669[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.93769223527144[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.95989343788155[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]6.95194444444444[/C][C]0.0386694990913017[/C][C]179.778497467225[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6.95194444444444[/C][C]0.0386694990913017[/C][C]179.778497467225[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]6.94444444444444[/C][C]0.0361221242385148[/C][C]192.249060398281[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]6.93611111111111[/C][C]0.0326901297573241[/C][C]212.177533787767[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]6.91736111111111[/C][C]0.02828772430687[/C][C]244.535793550248[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]6.91736111111111[/C][C]0.02828772430687[/C][C]244.535793550248[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]6.91444444444445[/C][C]0.0277465395556234[/C][C]249.200244613678[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]6.91444444444445[/C][C]0.0277465395556234[/C][C]249.200244613678[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]6.91444444444445[/C][C]0.0277465395556234[/C][C]249.200244613678[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]6.91444444444444[/C][C]0.0277465395556234[/C][C]249.200244613678[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6.90986111111111[/C][C]0.0269370775063582[/C][C]256.518588903347[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]6.90986111111111[/C][C]0.0269370775063582[/C][C]256.518588903347[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]6.90986111111111[/C][C]0.0269370775063582[/C][C]256.518588903347[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]6.89819444444444[/C][C]0.0250010378414380[/C][C]275.91632348202[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]6.88777777777778[/C][C]0.0234130280719629[/C][C]294.185688267546[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]6.88555555555556[/C][C]0.0230922224786163[/C][C]298.176390857643[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]6.88083333333333[/C][C]0.0224294669110858[/C][C]306.776498996170[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]6.88083333333333[/C][C]0.0224294669110858[/C][C]306.77649899617[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]6.88083333333333[/C][C]0.0224294669110858[/C][C]306.776498996170[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]6.88083333333333[/C][C]0.0224294669110858[/C][C]306.776498996170[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]6.91291666666667[/C][C]0.0135738827690249[/C][C]509.280710928321[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]6.91291666666667[/C][C]0.0135738827690249[/C][C]509.280710928321[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]6.91291666666667[/C][C]0.0135738827690249[/C][C]509.280710928321[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]6.91625[/C][C]0.0131537755577667[/C][C]525.799605567717[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]6.943[/C][C]0.0367726775427708[/C][C]188.808660776048[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]6.9335294117647[/C][C]0.0344483458190664[/C][C]201.273217825372[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]6.92348484848485[/C][C]0.0315449081770642[/C][C]219.480266343549[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]6.915625[/C][C]0.0292684236849202[/C][C]236.282796588157[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]6.90967741935484[/C][C]0.0278907437624417[/C][C]247.740880566246[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]6.90783333333333[/C][C]0.027674553024799[/C][C]249.609571910458[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]6.90586206896552[/C][C]0.0273889270735582[/C][C]252.140657077165[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]6.90428571428571[/C][C]0.0271549870367259[/C][C]254.254796916234[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]6.90259259259259[/C][C]0.0268419100128257[/C][C]257.157280882559[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]6.90076923076923[/C][C]0.0264302008482968[/C][C]261.094089688461[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]6.8988[/C][C]0.0258940383967004[/C][C]266.424259295108[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]6.89729166666667[/C][C]0.0253866196945432[/C][C]271.690037888315[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]6.89565217391304[/C][C]0.0247199818916984[/C][C]278.950535001353[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]6.89386363636364[/C][C]0.0238436944765001[/C][C]289.127326436686[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]6.89333333333333[/C][C]0.0231659835793644[/C][C]297.562730704589[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]6.894[/C][C]0.0226279835828480[/C][C]304.667005557916[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]6.895[/C][C]0.0219586770842135[/C][C]313.998879511596[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]6.89666666666667[/C][C]0.0211869981094276[/C][C]325.514102141627[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]6.8985294117647[/C][C]0.0200939520212588[/C][C]343.31371969368[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]6.900625[/C][C]0.0185183948435237[/C][C]372.636238632384[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]6.903[/C][C]0.0161540714059492[/C][C]427.322612766078[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]6.90178571428571[/C][C]0.0159617065847454[/C][C]432.396478261399[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]6.90038461538462[/C][C]0.0155956677340538[/C][C]442.455221094339[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]6.89875[/C][C]0.0149553986665472[/C][C]461.288271467572[/C][/ROW]
[ROW][C]Median[/C][C]6.88[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.82745098039216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.82745098039216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.82745098039216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.82745098039216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.82745098039216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.82745098039216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.82745098039216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.82745098039216[/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=83762&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=83762&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 Mean6.952222222222220.0387703312417367179.318102259030
Geometric Mean6.9448252907669
Harmonic Mean6.93769223527144
Quadratic Mean6.95989343788155
Winsorized Mean ( 1 / 24 )6.951944444444440.0386694990913017179.778497467225
Winsorized Mean ( 2 / 24 )6.951944444444440.0386694990913017179.778497467225
Winsorized Mean ( 3 / 24 )6.944444444444440.0361221242385148192.249060398281
Winsorized Mean ( 4 / 24 )6.936111111111110.0326901297573241212.177533787767
Winsorized Mean ( 5 / 24 )6.917361111111110.02828772430687244.535793550248
Winsorized Mean ( 6 / 24 )6.917361111111110.02828772430687244.535793550248
Winsorized Mean ( 7 / 24 )6.914444444444450.0277465395556234249.200244613678
Winsorized Mean ( 8 / 24 )6.914444444444450.0277465395556234249.200244613678
Winsorized Mean ( 9 / 24 )6.914444444444450.0277465395556234249.200244613678
Winsorized Mean ( 10 / 24 )6.914444444444440.0277465395556234249.200244613678
Winsorized Mean ( 11 / 24 )6.909861111111110.0269370775063582256.518588903347
Winsorized Mean ( 12 / 24 )6.909861111111110.0269370775063582256.518588903347
Winsorized Mean ( 13 / 24 )6.909861111111110.0269370775063582256.518588903347
Winsorized Mean ( 14 / 24 )6.898194444444440.0250010378414380275.91632348202
Winsorized Mean ( 15 / 24 )6.887777777777780.0234130280719629294.185688267546
Winsorized Mean ( 16 / 24 )6.885555555555560.0230922224786163298.176390857643
Winsorized Mean ( 17 / 24 )6.880833333333330.0224294669110858306.776498996170
Winsorized Mean ( 18 / 24 )6.880833333333330.0224294669110858306.77649899617
Winsorized Mean ( 19 / 24 )6.880833333333330.0224294669110858306.776498996170
Winsorized Mean ( 20 / 24 )6.880833333333330.0224294669110858306.776498996170
Winsorized Mean ( 21 / 24 )6.912916666666670.0135738827690249509.280710928321
Winsorized Mean ( 22 / 24 )6.912916666666670.0135738827690249509.280710928321
Winsorized Mean ( 23 / 24 )6.912916666666670.0135738827690249509.280710928321
Winsorized Mean ( 24 / 24 )6.916250.0131537755577667525.799605567717
Trimmed Mean ( 1 / 24 )6.9430.0367726775427708188.808660776048
Trimmed Mean ( 2 / 24 )6.93352941176470.0344483458190664201.273217825372
Trimmed Mean ( 3 / 24 )6.923484848484850.0315449081770642219.480266343549
Trimmed Mean ( 4 / 24 )6.9156250.0292684236849202236.282796588157
Trimmed Mean ( 5 / 24 )6.909677419354840.0278907437624417247.740880566246
Trimmed Mean ( 6 / 24 )6.907833333333330.027674553024799249.609571910458
Trimmed Mean ( 7 / 24 )6.905862068965520.0273889270735582252.140657077165
Trimmed Mean ( 8 / 24 )6.904285714285710.0271549870367259254.254796916234
Trimmed Mean ( 9 / 24 )6.902592592592590.0268419100128257257.157280882559
Trimmed Mean ( 10 / 24 )6.900769230769230.0264302008482968261.094089688461
Trimmed Mean ( 11 / 24 )6.89880.0258940383967004266.424259295108
Trimmed Mean ( 12 / 24 )6.897291666666670.0253866196945432271.690037888315
Trimmed Mean ( 13 / 24 )6.895652173913040.0247199818916984278.950535001353
Trimmed Mean ( 14 / 24 )6.893863636363640.0238436944765001289.127326436686
Trimmed Mean ( 15 / 24 )6.893333333333330.0231659835793644297.562730704589
Trimmed Mean ( 16 / 24 )6.8940.0226279835828480304.667005557916
Trimmed Mean ( 17 / 24 )6.8950.0219586770842135313.998879511596
Trimmed Mean ( 18 / 24 )6.896666666666670.0211869981094276325.514102141627
Trimmed Mean ( 19 / 24 )6.89852941176470.0200939520212588343.31371969368
Trimmed Mean ( 20 / 24 )6.9006250.0185183948435237372.636238632384
Trimmed Mean ( 21 / 24 )6.9030.0161540714059492427.322612766078
Trimmed Mean ( 22 / 24 )6.901785714285710.0159617065847454432.396478261399
Trimmed Mean ( 23 / 24 )6.900384615384620.0155956677340538442.455221094339
Trimmed Mean ( 24 / 24 )6.898750.0149553986665472461.288271467572
Median6.88
Midrange7.275
Midmean - Weighted Average at Xnp6.82745098039216
Midmean - Weighted Average at X(n+1)p6.82745098039216
Midmean - Empirical Distribution Function6.82745098039216
Midmean - Empirical Distribution Function - Averaging6.82745098039216
Midmean - Empirical Distribution Function - Interpolation6.82745098039216
Midmean - Closest Observation6.82745098039216
Midmean - True Basic - Statistics Graphics Toolkit6.82745098039216
Midmean - MS Excel (old versions)6.82745098039216
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')