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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 05 Mar 2013 13:59:39 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t136250999015vzuredzewy2rz.htm/, Retrieved Sat, 04 May 2024 11:27:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207467, Retrieved Sat, 04 May 2024 11:27:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-05 18:59:39] [72493e16725cf12b5fc5a9dfdf9b34f2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
106,1
106,17
105,75
106,49
106,61
106,61
106,61
106,61
106,92
106,94
107,28
107,36
107,36
107,39
107,46
107,51
108,21
108,33
108,33
108,36
108,89
109,3
109,55
109,45
109,45
109,4
109,45
109,5
109,91
109,9
109,9
109,92
109,74
110,28
110,97
111,02
111,02
111
111,43
111,52
112,29
112,27
112,27
112,39
112,31
112,91
112,9
113,08
113,08
113,54
114
115,28
116,4
116,56
116,56
116,59
116,96
117,17
117,83
117,84
117,84
117,84
117,69
117,9
118,05
118,08
118,08
118,08
118,16
118,53
118,5
118,62

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207467&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207467&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.8555555555560.493389275191088226.708526471789
Geometric Mean111.778856326189
Harmonic Mean111.702758685583
Quadratic Mean111.932788091783
Winsorized Mean ( 1 / 24 )111.8591666666670.492325203524093227.205850657192
Winsorized Mean ( 2 / 24 )111.8602777777780.491847860788332227.428615016213
Winsorized Mean ( 3 / 24 )111.8594444444440.48708869286195229.64902713549
Winsorized Mean ( 4 / 24 )111.8616666666670.485257099143506230.52041250732
Winsorized Mean ( 5 / 24 )111.8616666666670.485257099143506230.52041250732
Winsorized Mean ( 6 / 24 )111.8616666666670.485257099143506230.52041250732
Winsorized Mean ( 7 / 24 )111.858750.484731543141434230.764330447879
Winsorized Mean ( 8 / 24 )111.8765277777780.476598831302094234.739408554832
Winsorized Mean ( 9 / 24 )111.8715277777780.474901590156761235.567810461215
Winsorized Mean ( 10 / 24 )111.918750.468152018161584239.064973893525
Winsorized Mean ( 11 / 24 )111.9309722222220.466455693412724239.960566036408
Winsorized Mean ( 12 / 24 )111.9293055555560.46615843915004240.110005859037
Winsorized Mean ( 13 / 24 )111.9094444444440.460924595081338242.793388850721
Winsorized Mean ( 14 / 24 )111.8219444444440.441475494053875253.291396579304
Winsorized Mean ( 15 / 24 )111.7886111111110.432609376544611258.405428019157
Winsorized Mean ( 16 / 24 )111.8619444444440.397883762196248281.142270865708
Winsorized Mean ( 17 / 24 )111.8831944444440.39306223381963284.644987022045
Winsorized Mean ( 18 / 24 )111.8831944444440.39306223381963284.644987022045
Winsorized Mean ( 19 / 24 )111.8488888888890.38500007903763290.516534875716
Winsorized Mean ( 20 / 24 )111.6850.315436329941973354.065113617526
Winsorized Mean ( 21 / 24 )111.431250.242471860611857459.563636451721
Winsorized Mean ( 22 / 24 )111.321250.218107697756897510.395786782725
Winsorized Mean ( 23 / 24 )111.1902777777780.195561265632775568.570045903522
Winsorized Mean ( 24 / 24 )111.1902777777780.195561265632775568.570045903522
Trimmed Mean ( 1 / 24 )111.8461428571430.490360001816266228.089857335164
Trimmed Mean ( 2 / 24 )111.8323529411760.487707233711149229.302223159992
Trimmed Mean ( 3 / 24 )111.8171212121210.484526912954991230.7758727584
Trimmed Mean ( 4 / 24 )111.801250.482460495751017231.731408031585
Trimmed Mean ( 5 / 24 )111.7837096774190.48020857632694232.781576981486
Trimmed Mean ( 6 / 24 )111.7650.477072848551308234.272397474282
Trimmed Mean ( 7 / 24 )111.7450.472863824596702236.315391847337
Trimmed Mean ( 8 / 24 )111.7241071428570.467473367307625238.995662547202
Trimmed Mean ( 9 / 24 )111.6987037037040.462356786242515241.585517996735
Trimmed Mean ( 10 / 24 )111.6721153846150.45599040572804244.900142594707
Trimmed Mean ( 11 / 24 )111.63660.449047300812895248.607662929736
Trimmed Mean ( 12 / 24 )111.5964583333330.440209541657037253.507586212834
Trimmed Mean ( 13 / 24 )111.5530434782610.42861780657432260.262270412506
Trimmed Mean ( 14 / 24 )111.5081818181820.414589033724349268.960760530683
Trimmed Mean ( 15 / 24 )111.4697619047620.40085470359078278.080214367543
Trimmed Mean ( 16 / 24 )111.43150.384655781852841289.691472888429
Trimmed Mean ( 17 / 24 )111.3805263157890.371198885656242300.056197956737
Trimmed Mean ( 18 / 24 )111.3213888888890.353522221024899314.892197062341
Trimmed Mean ( 19 / 24 )111.2552941176470.328302834878601338.880089654988
Trimmed Mean ( 20 / 24 )111.1850.294306524978909377.786391273411
Trimmed Mean ( 21 / 24 )111.1250.270757451792466410.422683713159
Trimmed Mean ( 22 / 24 )111.08750.262627457088803422.985095432872
Trimmed Mean ( 23 / 24 )111.0580769230770.257976754606224430.496449544829
Trimmed Mean ( 24 / 24 )111.0408333333330.257417439041541431.36484360492
Median111.01
Midrange112.185
Midmean - Weighted Average at Xnp111.380526315789
Midmean - Weighted Average at X(n+1)p111.380526315789
Midmean - Empirical Distribution Function111.380526315789
Midmean - Empirical Distribution Function - Averaging111.380526315789
Midmean - Empirical Distribution Function - Interpolation111.380526315789
Midmean - Closest Observation111.380526315789
Midmean - True Basic - Statistics Graphics Toolkit111.380526315789
Midmean - MS Excel (old versions)111.380526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.855555555556 & 0.493389275191088 & 226.708526471789 \tabularnewline
Geometric Mean & 111.778856326189 &  &  \tabularnewline
Harmonic Mean & 111.702758685583 &  &  \tabularnewline
Quadratic Mean & 111.932788091783 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 111.859166666667 & 0.492325203524093 & 227.205850657192 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 111.860277777778 & 0.491847860788332 & 227.428615016213 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 111.859444444444 & 0.48708869286195 & 229.64902713549 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 111.861666666667 & 0.485257099143506 & 230.52041250732 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 111.861666666667 & 0.485257099143506 & 230.52041250732 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 111.861666666667 & 0.485257099143506 & 230.52041250732 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 111.85875 & 0.484731543141434 & 230.764330447879 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 111.876527777778 & 0.476598831302094 & 234.739408554832 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 111.871527777778 & 0.474901590156761 & 235.567810461215 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 111.91875 & 0.468152018161584 & 239.064973893525 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 111.930972222222 & 0.466455693412724 & 239.960566036408 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 111.929305555556 & 0.46615843915004 & 240.110005859037 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 111.909444444444 & 0.460924595081338 & 242.793388850721 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 111.821944444444 & 0.441475494053875 & 253.291396579304 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 111.788611111111 & 0.432609376544611 & 258.405428019157 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 111.861944444444 & 0.397883762196248 & 281.142270865708 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 111.883194444444 & 0.39306223381963 & 284.644987022045 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 111.883194444444 & 0.39306223381963 & 284.644987022045 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 111.848888888889 & 0.38500007903763 & 290.516534875716 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 111.685 & 0.315436329941973 & 354.065113617526 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 111.43125 & 0.242471860611857 & 459.563636451721 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 111.32125 & 0.218107697756897 & 510.395786782725 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 111.190277777778 & 0.195561265632775 & 568.570045903522 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 111.190277777778 & 0.195561265632775 & 568.570045903522 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 111.846142857143 & 0.490360001816266 & 228.089857335164 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 111.832352941176 & 0.487707233711149 & 229.302223159992 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 111.817121212121 & 0.484526912954991 & 230.7758727584 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 111.80125 & 0.482460495751017 & 231.731408031585 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 111.783709677419 & 0.48020857632694 & 232.781576981486 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 111.765 & 0.477072848551308 & 234.272397474282 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 111.745 & 0.472863824596702 & 236.315391847337 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 111.724107142857 & 0.467473367307625 & 238.995662547202 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 111.698703703704 & 0.462356786242515 & 241.585517996735 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 111.672115384615 & 0.45599040572804 & 244.900142594707 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 111.6366 & 0.449047300812895 & 248.607662929736 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 111.596458333333 & 0.440209541657037 & 253.507586212834 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 111.553043478261 & 0.42861780657432 & 260.262270412506 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 111.508181818182 & 0.414589033724349 & 268.960760530683 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 111.469761904762 & 0.40085470359078 & 278.080214367543 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 111.4315 & 0.384655781852841 & 289.691472888429 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 111.380526315789 & 0.371198885656242 & 300.056197956737 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 111.321388888889 & 0.353522221024899 & 314.892197062341 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 111.255294117647 & 0.328302834878601 & 338.880089654988 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 111.185 & 0.294306524978909 & 377.786391273411 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 111.125 & 0.270757451792466 & 410.422683713159 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 111.0875 & 0.262627457088803 & 422.985095432872 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 111.058076923077 & 0.257976754606224 & 430.496449544829 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 111.040833333333 & 0.257417439041541 & 431.36484360492 \tabularnewline
Median & 111.01 &  &  \tabularnewline
Midrange & 112.185 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.380526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.380526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.380526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.380526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.380526315789 &  &  \tabularnewline
Midmean - Closest Observation & 111.380526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.380526315789 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.380526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207467&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]111.855555555556[/C][C]0.493389275191088[/C][C]226.708526471789[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.778856326189[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.702758685583[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.932788091783[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]111.859166666667[/C][C]0.492325203524093[/C][C]227.205850657192[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]111.860277777778[/C][C]0.491847860788332[/C][C]227.428615016213[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]111.859444444444[/C][C]0.48708869286195[/C][C]229.64902713549[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]111.861666666667[/C][C]0.485257099143506[/C][C]230.52041250732[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]111.861666666667[/C][C]0.485257099143506[/C][C]230.52041250732[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]111.861666666667[/C][C]0.485257099143506[/C][C]230.52041250732[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]111.85875[/C][C]0.484731543141434[/C][C]230.764330447879[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]111.876527777778[/C][C]0.476598831302094[/C][C]234.739408554832[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]111.871527777778[/C][C]0.474901590156761[/C][C]235.567810461215[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]111.91875[/C][C]0.468152018161584[/C][C]239.064973893525[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]111.930972222222[/C][C]0.466455693412724[/C][C]239.960566036408[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]111.929305555556[/C][C]0.46615843915004[/C][C]240.110005859037[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]111.909444444444[/C][C]0.460924595081338[/C][C]242.793388850721[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]111.821944444444[/C][C]0.441475494053875[/C][C]253.291396579304[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]111.788611111111[/C][C]0.432609376544611[/C][C]258.405428019157[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]111.861944444444[/C][C]0.397883762196248[/C][C]281.142270865708[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]111.883194444444[/C][C]0.39306223381963[/C][C]284.644987022045[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]111.883194444444[/C][C]0.39306223381963[/C][C]284.644987022045[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]111.848888888889[/C][C]0.38500007903763[/C][C]290.516534875716[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]111.685[/C][C]0.315436329941973[/C][C]354.065113617526[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]111.43125[/C][C]0.242471860611857[/C][C]459.563636451721[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]111.32125[/C][C]0.218107697756897[/C][C]510.395786782725[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]111.190277777778[/C][C]0.195561265632775[/C][C]568.570045903522[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]111.190277777778[/C][C]0.195561265632775[/C][C]568.570045903522[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]111.846142857143[/C][C]0.490360001816266[/C][C]228.089857335164[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]111.832352941176[/C][C]0.487707233711149[/C][C]229.302223159992[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]111.817121212121[/C][C]0.484526912954991[/C][C]230.7758727584[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]111.80125[/C][C]0.482460495751017[/C][C]231.731408031585[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]111.783709677419[/C][C]0.48020857632694[/C][C]232.781576981486[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]111.765[/C][C]0.477072848551308[/C][C]234.272397474282[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]111.745[/C][C]0.472863824596702[/C][C]236.315391847337[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]111.724107142857[/C][C]0.467473367307625[/C][C]238.995662547202[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]111.698703703704[/C][C]0.462356786242515[/C][C]241.585517996735[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]111.672115384615[/C][C]0.45599040572804[/C][C]244.900142594707[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]111.6366[/C][C]0.449047300812895[/C][C]248.607662929736[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]111.596458333333[/C][C]0.440209541657037[/C][C]253.507586212834[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]111.553043478261[/C][C]0.42861780657432[/C][C]260.262270412506[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]111.508181818182[/C][C]0.414589033724349[/C][C]268.960760530683[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]111.469761904762[/C][C]0.40085470359078[/C][C]278.080214367543[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]111.4315[/C][C]0.384655781852841[/C][C]289.691472888429[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]111.380526315789[/C][C]0.371198885656242[/C][C]300.056197956737[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]111.321388888889[/C][C]0.353522221024899[/C][C]314.892197062341[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]111.255294117647[/C][C]0.328302834878601[/C][C]338.880089654988[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]111.185[/C][C]0.294306524978909[/C][C]377.786391273411[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]111.125[/C][C]0.270757451792466[/C][C]410.422683713159[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]111.0875[/C][C]0.262627457088803[/C][C]422.985095432872[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]111.058076923077[/C][C]0.257976754606224[/C][C]430.496449544829[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]111.040833333333[/C][C]0.257417439041541[/C][C]431.36484360492[/C][/ROW]
[ROW][C]Median[/C][C]111.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]112.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.380526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.380526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.380526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.380526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.380526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.380526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.380526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.380526315789[/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=207467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207467&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.8555555555560.493389275191088226.708526471789
Geometric Mean111.778856326189
Harmonic Mean111.702758685583
Quadratic Mean111.932788091783
Winsorized Mean ( 1 / 24 )111.8591666666670.492325203524093227.205850657192
Winsorized Mean ( 2 / 24 )111.8602777777780.491847860788332227.428615016213
Winsorized Mean ( 3 / 24 )111.8594444444440.48708869286195229.64902713549
Winsorized Mean ( 4 / 24 )111.8616666666670.485257099143506230.52041250732
Winsorized Mean ( 5 / 24 )111.8616666666670.485257099143506230.52041250732
Winsorized Mean ( 6 / 24 )111.8616666666670.485257099143506230.52041250732
Winsorized Mean ( 7 / 24 )111.858750.484731543141434230.764330447879
Winsorized Mean ( 8 / 24 )111.8765277777780.476598831302094234.739408554832
Winsorized Mean ( 9 / 24 )111.8715277777780.474901590156761235.567810461215
Winsorized Mean ( 10 / 24 )111.918750.468152018161584239.064973893525
Winsorized Mean ( 11 / 24 )111.9309722222220.466455693412724239.960566036408
Winsorized Mean ( 12 / 24 )111.9293055555560.46615843915004240.110005859037
Winsorized Mean ( 13 / 24 )111.9094444444440.460924595081338242.793388850721
Winsorized Mean ( 14 / 24 )111.8219444444440.441475494053875253.291396579304
Winsorized Mean ( 15 / 24 )111.7886111111110.432609376544611258.405428019157
Winsorized Mean ( 16 / 24 )111.8619444444440.397883762196248281.142270865708
Winsorized Mean ( 17 / 24 )111.8831944444440.39306223381963284.644987022045
Winsorized Mean ( 18 / 24 )111.8831944444440.39306223381963284.644987022045
Winsorized Mean ( 19 / 24 )111.8488888888890.38500007903763290.516534875716
Winsorized Mean ( 20 / 24 )111.6850.315436329941973354.065113617526
Winsorized Mean ( 21 / 24 )111.431250.242471860611857459.563636451721
Winsorized Mean ( 22 / 24 )111.321250.218107697756897510.395786782725
Winsorized Mean ( 23 / 24 )111.1902777777780.195561265632775568.570045903522
Winsorized Mean ( 24 / 24 )111.1902777777780.195561265632775568.570045903522
Trimmed Mean ( 1 / 24 )111.8461428571430.490360001816266228.089857335164
Trimmed Mean ( 2 / 24 )111.8323529411760.487707233711149229.302223159992
Trimmed Mean ( 3 / 24 )111.8171212121210.484526912954991230.7758727584
Trimmed Mean ( 4 / 24 )111.801250.482460495751017231.731408031585
Trimmed Mean ( 5 / 24 )111.7837096774190.48020857632694232.781576981486
Trimmed Mean ( 6 / 24 )111.7650.477072848551308234.272397474282
Trimmed Mean ( 7 / 24 )111.7450.472863824596702236.315391847337
Trimmed Mean ( 8 / 24 )111.7241071428570.467473367307625238.995662547202
Trimmed Mean ( 9 / 24 )111.6987037037040.462356786242515241.585517996735
Trimmed Mean ( 10 / 24 )111.6721153846150.45599040572804244.900142594707
Trimmed Mean ( 11 / 24 )111.63660.449047300812895248.607662929736
Trimmed Mean ( 12 / 24 )111.5964583333330.440209541657037253.507586212834
Trimmed Mean ( 13 / 24 )111.5530434782610.42861780657432260.262270412506
Trimmed Mean ( 14 / 24 )111.5081818181820.414589033724349268.960760530683
Trimmed Mean ( 15 / 24 )111.4697619047620.40085470359078278.080214367543
Trimmed Mean ( 16 / 24 )111.43150.384655781852841289.691472888429
Trimmed Mean ( 17 / 24 )111.3805263157890.371198885656242300.056197956737
Trimmed Mean ( 18 / 24 )111.3213888888890.353522221024899314.892197062341
Trimmed Mean ( 19 / 24 )111.2552941176470.328302834878601338.880089654988
Trimmed Mean ( 20 / 24 )111.1850.294306524978909377.786391273411
Trimmed Mean ( 21 / 24 )111.1250.270757451792466410.422683713159
Trimmed Mean ( 22 / 24 )111.08750.262627457088803422.985095432872
Trimmed Mean ( 23 / 24 )111.0580769230770.257976754606224430.496449544829
Trimmed Mean ( 24 / 24 )111.0408333333330.257417439041541431.36484360492
Median111.01
Midrange112.185
Midmean - Weighted Average at Xnp111.380526315789
Midmean - Weighted Average at X(n+1)p111.380526315789
Midmean - Empirical Distribution Function111.380526315789
Midmean - Empirical Distribution Function - Averaging111.380526315789
Midmean - Empirical Distribution Function - Interpolation111.380526315789
Midmean - Closest Observation111.380526315789
Midmean - True Basic - Statistics Graphics Toolkit111.380526315789
Midmean - MS Excel (old versions)111.380526315789
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

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')