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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 16:27:20 +0100
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/Oct/10/t141295487901nrdcosek62gw9.htm/, Retrieved Sun, 12 May 2024 17:36:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240345, Retrieved Sun, 12 May 2024 17:36:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 15:27:20] [96e2dc230ff7f688e72ca2986234e864] [Current]
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Dataseries X:
105,86
105,97
106,08
106,04
106,65
106,85
106,85
106,95
107,29
107,65
107,87
107,98
107,98
107,83
108,69
108,91
109,67
109,72
109,72
109,72
109,74
109,78
110,49
110,37
110,37
110,41
110,64
110,88
110,91
110,99
110,99
110,99
111,28
112,37
112,35
112,24
112,24
112,21
112,35
112,71
113,08
113,26
113,26
113,27
113,85
114,92
115,24
115,21
115,21
115,18
115,24
116,24
116,68
116,77
116,77
116,84
116,94
117,83
118,16
118,27
113,62
113,72
113,53
113,69
114,61
114,46
114,68
114,72
115,62
115,4
115,43
115,44




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240345&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240345&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240345&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112.0240277777780.403137473286532277.880463119726
Geometric Mean111.972366856062
Harmonic Mean111.920559039095
Quadratic Mean112.075517874978
Winsorized Mean ( 1 / 24 )112.0240277777780.402480409019923278.334113331297
Winsorized Mean ( 2 / 24 )112.0168055555560.400147802622015279.938574750511
Winsorized Mean ( 3 / 24 )111.9813888888890.392700030543507285.157576213844
Winsorized Mean ( 4 / 24 )112.00750.38526045241782290.731891366121
Winsorized Mean ( 5 / 24 )112.0165277777780.381720589898981293.451625984918
Winsorized Mean ( 6 / 24 )112.0165277777780.381720589898981293.451625984918
Winsorized Mean ( 7 / 24 )112.01750.378350124237025296.068357915549
Winsorized Mean ( 8 / 24 )112.0063888888890.363066583043428308.500958556936
Winsorized Mean ( 9 / 24 )111.9738888888890.342763015739939326.680195198906
Winsorized Mean ( 10 / 24 )111.9738888888890.334664861415386334.585138144834
Winsorized Mean ( 11 / 24 )111.9784722222220.333378791484972335.889609904204
Winsorized Mean ( 12 / 24 )111.9918055555560.329486804349684339.897695680398
Winsorized Mean ( 13 / 24 )111.9629166666670.325332767974332344.148907482632
Winsorized Mean ( 14 / 24 )112.1009722222220.302430824726913370.666489844236
Winsorized Mean ( 15 / 24 )112.1405555555560.294330616968155381.002006215645
Winsorized Mean ( 16 / 24 )112.3094444444440.269568998203076416.625966609995
Winsorized Mean ( 17 / 24 )112.3141666666670.266874387260936420.850302718828
Winsorized Mean ( 18 / 24 )112.2491666666670.257202564592923436.423201472833
Winsorized Mean ( 19 / 24 )112.1963888888890.249583401369688449.534657646168
Winsorized Mean ( 20 / 24 )112.1908333333330.247228356643486453.794357801429
Winsorized Mean ( 21 / 24 )112.1820833333330.242714817610696462.197093847268
Winsorized Mean ( 22 / 24 )112.3165277777780.21193821623499529.949387010246
Winsorized Mean ( 23 / 24 )112.1216666666670.185179775612172605.474686941443
Winsorized Mean ( 24 / 24 )112.0916666666670.177758606165012630.5836273413
Trimmed Mean ( 1 / 24 )112.0228571428570.3950505978473283.565846383449
Trimmed Mean ( 2 / 24 )112.0216176470590.386189405366234290.069111400986
Trimmed Mean ( 3 / 24 )112.0242424242420.377074560625188297.087775527754
Trimmed Mean ( 4 / 24 )112.04031250.369489738830044303.229834892751
Trimmed Mean ( 5 / 24 )112.0498387096770.363003984484667308.673853453006
Trimmed Mean ( 6 / 24 )112.0578333333330.356156197218756314.631148379276
Trimmed Mean ( 7 / 24 )112.0663793103450.347712662236341322.295939956806
Trimmed Mean ( 8 / 24 )112.0753571428570.338177695191517331.40966638674
Trimmed Mean ( 9 / 24 )112.0868518518520.330168711936797339.483566429844
Trimmed Mean ( 10 / 24 )112.1042307692310.324819284500238345.128002303536
Trimmed Mean ( 11 / 24 )112.1230.319688655936825350.725613554949
Trimmed Mean ( 12 / 24 )112.1427083333330.313234348460159358.015360973725
Trimmed Mean ( 13 / 24 )112.1623913043480.305657789889377366.954139611299
Trimmed Mean ( 14 / 24 )112.18750.296563674804469378.291441370788
Trimmed Mean ( 15 / 24 )112.1980952380950.290026279015837386.854927832138
Trimmed Mean ( 16 / 24 )112.2050.283025549268015396.448307547478
Trimmed Mean ( 17 / 24 )112.1926315789470.279069956154796402.023324634471
Trimmed Mean ( 18 / 24 )112.1783333333330.273794181764796409.717739837513
Trimmed Mean ( 19 / 24 )112.170.268506133397385417.755820251562
Trimmed Mean ( 20 / 24 )112.1668750.262559301097375427.205871325811
Trimmed Mean ( 21 / 24 )112.1640.25411582118143441.38928256623
Trimmed Mean ( 22 / 24 )112.1617857142860.242652915607373462.231353921872
Trimmed Mean ( 23 / 24 )112.1423076923080.235376822394878476.437342263772
Trimmed Mean ( 24 / 24 )112.1450.232947403406055481.417686397293
Median112.295
Midrange112.065
Midmean - Weighted Average at Xnp112.111891891892
Midmean - Weighted Average at X(n+1)p112.111891891892
Midmean - Empirical Distribution Function112.111891891892
Midmean - Empirical Distribution Function - Averaging112.111891891892
Midmean - Empirical Distribution Function - Interpolation112.111891891892
Midmean - Closest Observation112.111891891892
Midmean - True Basic - Statistics Graphics Toolkit112.111891891892
Midmean - MS Excel (old versions)112.192631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.024027777778 & 0.403137473286532 & 277.880463119726 \tabularnewline
Geometric Mean & 111.972366856062 &  &  \tabularnewline
Harmonic Mean & 111.920559039095 &  &  \tabularnewline
Quadratic Mean & 112.075517874978 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 112.024027777778 & 0.402480409019923 & 278.334113331297 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 112.016805555556 & 0.400147802622015 & 279.938574750511 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 111.981388888889 & 0.392700030543507 & 285.157576213844 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 112.0075 & 0.38526045241782 & 290.731891366121 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 112.016527777778 & 0.381720589898981 & 293.451625984918 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 112.016527777778 & 0.381720589898981 & 293.451625984918 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 112.0175 & 0.378350124237025 & 296.068357915549 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 112.006388888889 & 0.363066583043428 & 308.500958556936 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 111.973888888889 & 0.342763015739939 & 326.680195198906 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 111.973888888889 & 0.334664861415386 & 334.585138144834 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 111.978472222222 & 0.333378791484972 & 335.889609904204 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 111.991805555556 & 0.329486804349684 & 339.897695680398 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 111.962916666667 & 0.325332767974332 & 344.148907482632 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 112.100972222222 & 0.302430824726913 & 370.666489844236 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 112.140555555556 & 0.294330616968155 & 381.002006215645 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 112.309444444444 & 0.269568998203076 & 416.625966609995 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 112.314166666667 & 0.266874387260936 & 420.850302718828 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 112.249166666667 & 0.257202564592923 & 436.423201472833 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 112.196388888889 & 0.249583401369688 & 449.534657646168 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 112.190833333333 & 0.247228356643486 & 453.794357801429 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 112.182083333333 & 0.242714817610696 & 462.197093847268 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 112.316527777778 & 0.21193821623499 & 529.949387010246 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 112.121666666667 & 0.185179775612172 & 605.474686941443 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 112.091666666667 & 0.177758606165012 & 630.5836273413 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 112.022857142857 & 0.3950505978473 & 283.565846383449 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 112.021617647059 & 0.386189405366234 & 290.069111400986 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 112.024242424242 & 0.377074560625188 & 297.087775527754 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 112.0403125 & 0.369489738830044 & 303.229834892751 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 112.049838709677 & 0.363003984484667 & 308.673853453006 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 112.057833333333 & 0.356156197218756 & 314.631148379276 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 112.066379310345 & 0.347712662236341 & 322.295939956806 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 112.075357142857 & 0.338177695191517 & 331.40966638674 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 112.086851851852 & 0.330168711936797 & 339.483566429844 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 112.104230769231 & 0.324819284500238 & 345.128002303536 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 112.123 & 0.319688655936825 & 350.725613554949 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 112.142708333333 & 0.313234348460159 & 358.015360973725 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 112.162391304348 & 0.305657789889377 & 366.954139611299 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 112.1875 & 0.296563674804469 & 378.291441370788 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 112.198095238095 & 0.290026279015837 & 386.854927832138 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 112.205 & 0.283025549268015 & 396.448307547478 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 112.192631578947 & 0.279069956154796 & 402.023324634471 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 112.178333333333 & 0.273794181764796 & 409.717739837513 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 112.17 & 0.268506133397385 & 417.755820251562 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 112.166875 & 0.262559301097375 & 427.205871325811 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 112.164 & 0.25411582118143 & 441.38928256623 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 112.161785714286 & 0.242652915607373 & 462.231353921872 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 112.142307692308 & 0.235376822394878 & 476.437342263772 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 112.145 & 0.232947403406055 & 481.417686397293 \tabularnewline
Median & 112.295 &  &  \tabularnewline
Midrange & 112.065 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.111891891892 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.111891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.111891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.111891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.111891891892 &  &  \tabularnewline
Midmean - Closest Observation & 112.111891891892 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.111891891892 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.192631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240345&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]112.024027777778[/C][C]0.403137473286532[/C][C]277.880463119726[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.972366856062[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.920559039095[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112.075517874978[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]112.024027777778[/C][C]0.402480409019923[/C][C]278.334113331297[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]112.016805555556[/C][C]0.400147802622015[/C][C]279.938574750511[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]111.981388888889[/C][C]0.392700030543507[/C][C]285.157576213844[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]112.0075[/C][C]0.38526045241782[/C][C]290.731891366121[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]112.016527777778[/C][C]0.381720589898981[/C][C]293.451625984918[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]112.016527777778[/C][C]0.381720589898981[/C][C]293.451625984918[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]112.0175[/C][C]0.378350124237025[/C][C]296.068357915549[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]112.006388888889[/C][C]0.363066583043428[/C][C]308.500958556936[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]111.973888888889[/C][C]0.342763015739939[/C][C]326.680195198906[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]111.973888888889[/C][C]0.334664861415386[/C][C]334.585138144834[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]111.978472222222[/C][C]0.333378791484972[/C][C]335.889609904204[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]111.991805555556[/C][C]0.329486804349684[/C][C]339.897695680398[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]111.962916666667[/C][C]0.325332767974332[/C][C]344.148907482632[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]112.100972222222[/C][C]0.302430824726913[/C][C]370.666489844236[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]112.140555555556[/C][C]0.294330616968155[/C][C]381.002006215645[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]112.309444444444[/C][C]0.269568998203076[/C][C]416.625966609995[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]112.314166666667[/C][C]0.266874387260936[/C][C]420.850302718828[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]112.249166666667[/C][C]0.257202564592923[/C][C]436.423201472833[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]112.196388888889[/C][C]0.249583401369688[/C][C]449.534657646168[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]112.190833333333[/C][C]0.247228356643486[/C][C]453.794357801429[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]112.182083333333[/C][C]0.242714817610696[/C][C]462.197093847268[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]112.316527777778[/C][C]0.21193821623499[/C][C]529.949387010246[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]112.121666666667[/C][C]0.185179775612172[/C][C]605.474686941443[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]112.091666666667[/C][C]0.177758606165012[/C][C]630.5836273413[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]112.022857142857[/C][C]0.3950505978473[/C][C]283.565846383449[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]112.021617647059[/C][C]0.386189405366234[/C][C]290.069111400986[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]112.024242424242[/C][C]0.377074560625188[/C][C]297.087775527754[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]112.0403125[/C][C]0.369489738830044[/C][C]303.229834892751[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]112.049838709677[/C][C]0.363003984484667[/C][C]308.673853453006[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]112.057833333333[/C][C]0.356156197218756[/C][C]314.631148379276[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]112.066379310345[/C][C]0.347712662236341[/C][C]322.295939956806[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]112.075357142857[/C][C]0.338177695191517[/C][C]331.40966638674[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]112.086851851852[/C][C]0.330168711936797[/C][C]339.483566429844[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]112.104230769231[/C][C]0.324819284500238[/C][C]345.128002303536[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]112.123[/C][C]0.319688655936825[/C][C]350.725613554949[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]112.142708333333[/C][C]0.313234348460159[/C][C]358.015360973725[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]112.162391304348[/C][C]0.305657789889377[/C][C]366.954139611299[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]112.1875[/C][C]0.296563674804469[/C][C]378.291441370788[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]112.198095238095[/C][C]0.290026279015837[/C][C]386.854927832138[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]112.205[/C][C]0.283025549268015[/C][C]396.448307547478[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]112.192631578947[/C][C]0.279069956154796[/C][C]402.023324634471[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]112.178333333333[/C][C]0.273794181764796[/C][C]409.717739837513[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]112.17[/C][C]0.268506133397385[/C][C]417.755820251562[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]112.166875[/C][C]0.262559301097375[/C][C]427.205871325811[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]112.164[/C][C]0.25411582118143[/C][C]441.38928256623[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]112.161785714286[/C][C]0.242652915607373[/C][C]462.231353921872[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]112.142307692308[/C][C]0.235376822394878[/C][C]476.437342263772[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]112.145[/C][C]0.232947403406055[/C][C]481.417686397293[/C][/ROW]
[ROW][C]Median[/C][C]112.295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]112.065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.111891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.111891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.111891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.111891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.111891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.111891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.111891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.192631578947[/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=240345&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240345&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 Mean112.0240277777780.403137473286532277.880463119726
Geometric Mean111.972366856062
Harmonic Mean111.920559039095
Quadratic Mean112.075517874978
Winsorized Mean ( 1 / 24 )112.0240277777780.402480409019923278.334113331297
Winsorized Mean ( 2 / 24 )112.0168055555560.400147802622015279.938574750511
Winsorized Mean ( 3 / 24 )111.9813888888890.392700030543507285.157576213844
Winsorized Mean ( 4 / 24 )112.00750.38526045241782290.731891366121
Winsorized Mean ( 5 / 24 )112.0165277777780.381720589898981293.451625984918
Winsorized Mean ( 6 / 24 )112.0165277777780.381720589898981293.451625984918
Winsorized Mean ( 7 / 24 )112.01750.378350124237025296.068357915549
Winsorized Mean ( 8 / 24 )112.0063888888890.363066583043428308.500958556936
Winsorized Mean ( 9 / 24 )111.9738888888890.342763015739939326.680195198906
Winsorized Mean ( 10 / 24 )111.9738888888890.334664861415386334.585138144834
Winsorized Mean ( 11 / 24 )111.9784722222220.333378791484972335.889609904204
Winsorized Mean ( 12 / 24 )111.9918055555560.329486804349684339.897695680398
Winsorized Mean ( 13 / 24 )111.9629166666670.325332767974332344.148907482632
Winsorized Mean ( 14 / 24 )112.1009722222220.302430824726913370.666489844236
Winsorized Mean ( 15 / 24 )112.1405555555560.294330616968155381.002006215645
Winsorized Mean ( 16 / 24 )112.3094444444440.269568998203076416.625966609995
Winsorized Mean ( 17 / 24 )112.3141666666670.266874387260936420.850302718828
Winsorized Mean ( 18 / 24 )112.2491666666670.257202564592923436.423201472833
Winsorized Mean ( 19 / 24 )112.1963888888890.249583401369688449.534657646168
Winsorized Mean ( 20 / 24 )112.1908333333330.247228356643486453.794357801429
Winsorized Mean ( 21 / 24 )112.1820833333330.242714817610696462.197093847268
Winsorized Mean ( 22 / 24 )112.3165277777780.21193821623499529.949387010246
Winsorized Mean ( 23 / 24 )112.1216666666670.185179775612172605.474686941443
Winsorized Mean ( 24 / 24 )112.0916666666670.177758606165012630.5836273413
Trimmed Mean ( 1 / 24 )112.0228571428570.3950505978473283.565846383449
Trimmed Mean ( 2 / 24 )112.0216176470590.386189405366234290.069111400986
Trimmed Mean ( 3 / 24 )112.0242424242420.377074560625188297.087775527754
Trimmed Mean ( 4 / 24 )112.04031250.369489738830044303.229834892751
Trimmed Mean ( 5 / 24 )112.0498387096770.363003984484667308.673853453006
Trimmed Mean ( 6 / 24 )112.0578333333330.356156197218756314.631148379276
Trimmed Mean ( 7 / 24 )112.0663793103450.347712662236341322.295939956806
Trimmed Mean ( 8 / 24 )112.0753571428570.338177695191517331.40966638674
Trimmed Mean ( 9 / 24 )112.0868518518520.330168711936797339.483566429844
Trimmed Mean ( 10 / 24 )112.1042307692310.324819284500238345.128002303536
Trimmed Mean ( 11 / 24 )112.1230.319688655936825350.725613554949
Trimmed Mean ( 12 / 24 )112.1427083333330.313234348460159358.015360973725
Trimmed Mean ( 13 / 24 )112.1623913043480.305657789889377366.954139611299
Trimmed Mean ( 14 / 24 )112.18750.296563674804469378.291441370788
Trimmed Mean ( 15 / 24 )112.1980952380950.290026279015837386.854927832138
Trimmed Mean ( 16 / 24 )112.2050.283025549268015396.448307547478
Trimmed Mean ( 17 / 24 )112.1926315789470.279069956154796402.023324634471
Trimmed Mean ( 18 / 24 )112.1783333333330.273794181764796409.717739837513
Trimmed Mean ( 19 / 24 )112.170.268506133397385417.755820251562
Trimmed Mean ( 20 / 24 )112.1668750.262559301097375427.205871325811
Trimmed Mean ( 21 / 24 )112.1640.25411582118143441.38928256623
Trimmed Mean ( 22 / 24 )112.1617857142860.242652915607373462.231353921872
Trimmed Mean ( 23 / 24 )112.1423076923080.235376822394878476.437342263772
Trimmed Mean ( 24 / 24 )112.1450.232947403406055481.417686397293
Median112.295
Midrange112.065
Midmean - Weighted Average at Xnp112.111891891892
Midmean - Weighted Average at X(n+1)p112.111891891892
Midmean - Empirical Distribution Function112.111891891892
Midmean - Empirical Distribution Function - Averaging112.111891891892
Midmean - Empirical Distribution Function - Interpolation112.111891891892
Midmean - Closest Observation112.111891891892
Midmean - True Basic - Statistics Graphics Toolkit112.111891891892
Midmean - MS Excel (old versions)112.192631578947
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')