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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 computationMon, 18 Oct 2010 14:16:36 +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/18/t128741141826mcouo3te0tm6x.htm/, Retrieved Sat, 04 May 2024 15:32:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=84908, Retrieved Sat, 04 May 2024 15:32:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Inde...] [2010-10-18 14:16:36] [97f4c042a3a976df335275c19da76a25] [Current]
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Dataseries X:
95,05
96,84
96,92
97,44
97,78
97,69
96,67
98,29
98,2
98,71
98,54
98,2
96,92
99,06
99,65
99,82
99,99
100,33
99,31
101,1
101,1
100,93
100,85
100,93
99,6
101,88
101,81
102,38
102,74
102,82
101,72
103,47
102,98
102,68
102,9
103,03
101,29
103,69
103,68
104,2
104,08
104,16
103,05
104,66
104,46
104,95
105,85
106,23
104,86
107,44
108,23
108,45
109,39
110,15
109,13
110,28
110,17
109,99
109,26
109,11
107,06
109,53
108,92
109,24
109,12
109
107,23
109,49
109,04
109,02
109,23
109,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84908&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=84908&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84908&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.6309722222220.519121502708587199.627585606671
Geometric Mean103.538595894003
Harmonic Mean103.446218992539
Quadratic Mean103.723247106315
Winsorized Mean ( 1 / 24 )103.6519444444440.514073822622004201.628520813944
Winsorized Mean ( 2 / 24 )103.6561111111110.513081250050312202.026698697227
Winsorized Mean ( 3 / 24 )103.6527777777780.511284140100128202.730281751902
Winsorized Mean ( 4 / 24 )103.6272222222220.506957432251575204.410105523017
Winsorized Mean ( 5 / 24 )103.6605555555560.499971669341697207.332858863870
Winsorized Mean ( 6 / 24 )103.6788888888890.495963974802465209.045201176522
Winsorized Mean ( 7 / 24 )103.6808333333330.493369643616798210.148384025553
Winsorized Mean ( 8 / 24 )103.7130555555560.483344124814322214.573944796365
Winsorized Mean ( 9 / 24 )103.7105555555560.482940502856462214.748100319058
Winsorized Mean ( 10 / 24 )103.7216666666670.480717341848933215.764353887740
Winsorized Mean ( 11 / 24 )103.7445833333330.4722534024388219.679906587391
Winsorized Mean ( 12 / 24 )103.771250.467626567164941221.910509980495
Winsorized Mean ( 13 / 24 )103.8326388888890.457877280280607226.769580760276
Winsorized Mean ( 14 / 24 )103.8676388888890.448620363512101231.526803811899
Winsorized Mean ( 15 / 24 )103.9238888888890.439431431069422236.496257529815
Winsorized Mean ( 16 / 24 )103.9305555555560.437169409588015237.735196644932
Winsorized Mean ( 17 / 24 )103.9518055555560.428591714618868242.542732418419
Winsorized Mean ( 18 / 24 )103.8768055555560.403857225154416257.211705240232
Winsorized Mean ( 19 / 24 )103.9084722222220.382614382936425271.574924666352
Winsorized Mean ( 20 / 24 )103.8334722222220.329454376534315315.1679856692
Winsorized Mean ( 21 / 24 )103.7955555555560.317086569199241327.341381306932
Winsorized Mean ( 22 / 24 )103.7436111111110.309200424333921335.522214546100
Winsorized Mean ( 23 / 24 )103.5327777777780.262935697154486393.757024619399
Winsorized Mean ( 24 / 24 )103.4061111111110.244873938022236422.28304059749
Trimmed Mean ( 1 / 24 )103.6585714285710.510697622395347202.974454712315
Trimmed Mean ( 2 / 24 )103.6655882352940.506429269513407204.699045801399
Trimmed Mean ( 3 / 24 )103.6707575757580.50170851736032206.635434696642
Trimmed Mean ( 4 / 24 )103.67750.496598948723229208.775109706853
Trimmed Mean ( 5 / 24 )103.6920967741940.491709379686568210.880859828809
Trimmed Mean ( 6 / 24 )103.6996666666670.487614101765991212.667489088395
Trimmed Mean ( 7 / 24 )103.7039655172410.483358382624057214.548809424289
Trimmed Mean ( 8 / 24 )103.7082142857140.478421722562496216.771541497401
Trimmed Mean ( 9 / 24 )103.7074074074070.474290170655893218.658141837498
Trimmed Mean ( 10 / 24 )103.7069230769230.468812042728593221.212156738392
Trimmed Mean ( 11 / 24 )103.70480.462036948783121224.451313413635
Trimmed Mean ( 12 / 24 )103.6993750.454933594079579227.943982043807
Trimmed Mean ( 13 / 24 )103.690.446473568470739232.242191525825
Trimmed Mean ( 14 / 24 )103.6720454545450.437296322815231237.075045102425
Trimmed Mean ( 15 / 24 )103.6480952380950.426977225929981242.748533044927
Trimmed Mean ( 16 / 24 )103.6150.414982854140709249.685014612355
Trimmed Mean ( 17 / 24 )103.5776315789470.399035364980416259.570054859751
Trimmed Mean ( 18 / 24 )103.5336111111110.379165573578284273.056464842094
Trimmed Mean ( 19 / 24 )103.4932352941180.358699304202967288.523657786514
Trimmed Mean ( 20 / 24 )103.44406250.335773619066610308.076801231603
Trimmed Mean ( 21 / 24 )103.3973333333330.319985248702144323.131562322674
Trimmed Mean ( 22 / 24 )103.3485714285710.300432102518579343.999760885008
Trimmed Mean ( 23 / 24 )103.2988461538460.273292363552902377.979262980213
Trimmed Mean ( 24 / 24 )103.2683333333330.252159992535986409.534963475999
Median103.04
Midrange102.665
Midmean - Weighted Average at Xnp103.433243243243
Midmean - Weighted Average at X(n+1)p103.533611111111
Midmean - Empirical Distribution Function103.433243243243
Midmean - Empirical Distribution Function - Averaging103.533611111111
Midmean - Empirical Distribution Function - Interpolation103.533611111111
Midmean - Closest Observation103.433243243243
Midmean - True Basic - Statistics Graphics Toolkit103.533611111111
Midmean - MS Excel (old versions)103.577631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.630972222222 & 0.519121502708587 & 199.627585606671 \tabularnewline
Geometric Mean & 103.538595894003 &  &  \tabularnewline
Harmonic Mean & 103.446218992539 &  &  \tabularnewline
Quadratic Mean & 103.723247106315 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 103.651944444444 & 0.514073822622004 & 201.628520813944 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 103.656111111111 & 0.513081250050312 & 202.026698697227 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 103.652777777778 & 0.511284140100128 & 202.730281751902 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 103.627222222222 & 0.506957432251575 & 204.410105523017 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 103.660555555556 & 0.499971669341697 & 207.332858863870 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 103.678888888889 & 0.495963974802465 & 209.045201176522 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 103.680833333333 & 0.493369643616798 & 210.148384025553 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 103.713055555556 & 0.483344124814322 & 214.573944796365 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 103.710555555556 & 0.482940502856462 & 214.748100319058 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 103.721666666667 & 0.480717341848933 & 215.764353887740 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 103.744583333333 & 0.4722534024388 & 219.679906587391 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 103.77125 & 0.467626567164941 & 221.910509980495 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 103.832638888889 & 0.457877280280607 & 226.769580760276 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 103.867638888889 & 0.448620363512101 & 231.526803811899 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 103.923888888889 & 0.439431431069422 & 236.496257529815 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 103.930555555556 & 0.437169409588015 & 237.735196644932 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 103.951805555556 & 0.428591714618868 & 242.542732418419 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 103.876805555556 & 0.403857225154416 & 257.211705240232 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 103.908472222222 & 0.382614382936425 & 271.574924666352 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 103.833472222222 & 0.329454376534315 & 315.1679856692 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 103.795555555556 & 0.317086569199241 & 327.341381306932 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 103.743611111111 & 0.309200424333921 & 335.522214546100 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 103.532777777778 & 0.262935697154486 & 393.757024619399 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 103.406111111111 & 0.244873938022236 & 422.28304059749 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 103.658571428571 & 0.510697622395347 & 202.974454712315 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 103.665588235294 & 0.506429269513407 & 204.699045801399 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 103.670757575758 & 0.50170851736032 & 206.635434696642 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 103.6775 & 0.496598948723229 & 208.775109706853 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 103.692096774194 & 0.491709379686568 & 210.880859828809 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 103.699666666667 & 0.487614101765991 & 212.667489088395 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 103.703965517241 & 0.483358382624057 & 214.548809424289 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 103.708214285714 & 0.478421722562496 & 216.771541497401 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 103.707407407407 & 0.474290170655893 & 218.658141837498 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 103.706923076923 & 0.468812042728593 & 221.212156738392 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 103.7048 & 0.462036948783121 & 224.451313413635 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 103.699375 & 0.454933594079579 & 227.943982043807 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 103.69 & 0.446473568470739 & 232.242191525825 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 103.672045454545 & 0.437296322815231 & 237.075045102425 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 103.648095238095 & 0.426977225929981 & 242.748533044927 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 103.615 & 0.414982854140709 & 249.685014612355 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 103.577631578947 & 0.399035364980416 & 259.570054859751 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 103.533611111111 & 0.379165573578284 & 273.056464842094 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 103.493235294118 & 0.358699304202967 & 288.523657786514 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 103.4440625 & 0.335773619066610 & 308.076801231603 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 103.397333333333 & 0.319985248702144 & 323.131562322674 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 103.348571428571 & 0.300432102518579 & 343.999760885008 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 103.298846153846 & 0.273292363552902 & 377.979262980213 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 103.268333333333 & 0.252159992535986 & 409.534963475999 \tabularnewline
Median & 103.04 &  &  \tabularnewline
Midrange & 102.665 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.433243243243 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.533611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.433243243243 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.533611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.533611111111 &  &  \tabularnewline
Midmean - Closest Observation & 103.433243243243 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.533611111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.577631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84908&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]103.630972222222[/C][C]0.519121502708587[/C][C]199.627585606671[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.538595894003[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.446218992539[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.723247106315[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]103.651944444444[/C][C]0.514073822622004[/C][C]201.628520813944[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]103.656111111111[/C][C]0.513081250050312[/C][C]202.026698697227[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]103.652777777778[/C][C]0.511284140100128[/C][C]202.730281751902[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]103.627222222222[/C][C]0.506957432251575[/C][C]204.410105523017[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]103.660555555556[/C][C]0.499971669341697[/C][C]207.332858863870[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]103.678888888889[/C][C]0.495963974802465[/C][C]209.045201176522[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]103.680833333333[/C][C]0.493369643616798[/C][C]210.148384025553[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]103.713055555556[/C][C]0.483344124814322[/C][C]214.573944796365[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]103.710555555556[/C][C]0.482940502856462[/C][C]214.748100319058[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]103.721666666667[/C][C]0.480717341848933[/C][C]215.764353887740[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]103.744583333333[/C][C]0.4722534024388[/C][C]219.679906587391[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]103.77125[/C][C]0.467626567164941[/C][C]221.910509980495[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]103.832638888889[/C][C]0.457877280280607[/C][C]226.769580760276[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]103.867638888889[/C][C]0.448620363512101[/C][C]231.526803811899[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]103.923888888889[/C][C]0.439431431069422[/C][C]236.496257529815[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]103.930555555556[/C][C]0.437169409588015[/C][C]237.735196644932[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]103.951805555556[/C][C]0.428591714618868[/C][C]242.542732418419[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]103.876805555556[/C][C]0.403857225154416[/C][C]257.211705240232[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]103.908472222222[/C][C]0.382614382936425[/C][C]271.574924666352[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]103.833472222222[/C][C]0.329454376534315[/C][C]315.1679856692[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]103.795555555556[/C][C]0.317086569199241[/C][C]327.341381306932[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]103.743611111111[/C][C]0.309200424333921[/C][C]335.522214546100[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]103.532777777778[/C][C]0.262935697154486[/C][C]393.757024619399[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]103.406111111111[/C][C]0.244873938022236[/C][C]422.28304059749[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]103.658571428571[/C][C]0.510697622395347[/C][C]202.974454712315[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]103.665588235294[/C][C]0.506429269513407[/C][C]204.699045801399[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]103.670757575758[/C][C]0.50170851736032[/C][C]206.635434696642[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]103.6775[/C][C]0.496598948723229[/C][C]208.775109706853[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]103.692096774194[/C][C]0.491709379686568[/C][C]210.880859828809[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]103.699666666667[/C][C]0.487614101765991[/C][C]212.667489088395[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]103.703965517241[/C][C]0.483358382624057[/C][C]214.548809424289[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]103.708214285714[/C][C]0.478421722562496[/C][C]216.771541497401[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]103.707407407407[/C][C]0.474290170655893[/C][C]218.658141837498[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]103.706923076923[/C][C]0.468812042728593[/C][C]221.212156738392[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]103.7048[/C][C]0.462036948783121[/C][C]224.451313413635[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]103.699375[/C][C]0.454933594079579[/C][C]227.943982043807[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]103.69[/C][C]0.446473568470739[/C][C]232.242191525825[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]103.672045454545[/C][C]0.437296322815231[/C][C]237.075045102425[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]103.648095238095[/C][C]0.426977225929981[/C][C]242.748533044927[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]103.615[/C][C]0.414982854140709[/C][C]249.685014612355[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]103.577631578947[/C][C]0.399035364980416[/C][C]259.570054859751[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]103.533611111111[/C][C]0.379165573578284[/C][C]273.056464842094[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]103.493235294118[/C][C]0.358699304202967[/C][C]288.523657786514[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]103.4440625[/C][C]0.335773619066610[/C][C]308.076801231603[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]103.397333333333[/C][C]0.319985248702144[/C][C]323.131562322674[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]103.348571428571[/C][C]0.300432102518579[/C][C]343.999760885008[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]103.298846153846[/C][C]0.273292363552902[/C][C]377.979262980213[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]103.268333333333[/C][C]0.252159992535986[/C][C]409.534963475999[/C][/ROW]
[ROW][C]Median[/C][C]103.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.665[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.433243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.533611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.433243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.533611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.533611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.433243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.533611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.577631578947[/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=84908&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84908&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 Mean103.6309722222220.519121502708587199.627585606671
Geometric Mean103.538595894003
Harmonic Mean103.446218992539
Quadratic Mean103.723247106315
Winsorized Mean ( 1 / 24 )103.6519444444440.514073822622004201.628520813944
Winsorized Mean ( 2 / 24 )103.6561111111110.513081250050312202.026698697227
Winsorized Mean ( 3 / 24 )103.6527777777780.511284140100128202.730281751902
Winsorized Mean ( 4 / 24 )103.6272222222220.506957432251575204.410105523017
Winsorized Mean ( 5 / 24 )103.6605555555560.499971669341697207.332858863870
Winsorized Mean ( 6 / 24 )103.6788888888890.495963974802465209.045201176522
Winsorized Mean ( 7 / 24 )103.6808333333330.493369643616798210.148384025553
Winsorized Mean ( 8 / 24 )103.7130555555560.483344124814322214.573944796365
Winsorized Mean ( 9 / 24 )103.7105555555560.482940502856462214.748100319058
Winsorized Mean ( 10 / 24 )103.7216666666670.480717341848933215.764353887740
Winsorized Mean ( 11 / 24 )103.7445833333330.4722534024388219.679906587391
Winsorized Mean ( 12 / 24 )103.771250.467626567164941221.910509980495
Winsorized Mean ( 13 / 24 )103.8326388888890.457877280280607226.769580760276
Winsorized Mean ( 14 / 24 )103.8676388888890.448620363512101231.526803811899
Winsorized Mean ( 15 / 24 )103.9238888888890.439431431069422236.496257529815
Winsorized Mean ( 16 / 24 )103.9305555555560.437169409588015237.735196644932
Winsorized Mean ( 17 / 24 )103.9518055555560.428591714618868242.542732418419
Winsorized Mean ( 18 / 24 )103.8768055555560.403857225154416257.211705240232
Winsorized Mean ( 19 / 24 )103.9084722222220.382614382936425271.574924666352
Winsorized Mean ( 20 / 24 )103.8334722222220.329454376534315315.1679856692
Winsorized Mean ( 21 / 24 )103.7955555555560.317086569199241327.341381306932
Winsorized Mean ( 22 / 24 )103.7436111111110.309200424333921335.522214546100
Winsorized Mean ( 23 / 24 )103.5327777777780.262935697154486393.757024619399
Winsorized Mean ( 24 / 24 )103.4061111111110.244873938022236422.28304059749
Trimmed Mean ( 1 / 24 )103.6585714285710.510697622395347202.974454712315
Trimmed Mean ( 2 / 24 )103.6655882352940.506429269513407204.699045801399
Trimmed Mean ( 3 / 24 )103.6707575757580.50170851736032206.635434696642
Trimmed Mean ( 4 / 24 )103.67750.496598948723229208.775109706853
Trimmed Mean ( 5 / 24 )103.6920967741940.491709379686568210.880859828809
Trimmed Mean ( 6 / 24 )103.6996666666670.487614101765991212.667489088395
Trimmed Mean ( 7 / 24 )103.7039655172410.483358382624057214.548809424289
Trimmed Mean ( 8 / 24 )103.7082142857140.478421722562496216.771541497401
Trimmed Mean ( 9 / 24 )103.7074074074070.474290170655893218.658141837498
Trimmed Mean ( 10 / 24 )103.7069230769230.468812042728593221.212156738392
Trimmed Mean ( 11 / 24 )103.70480.462036948783121224.451313413635
Trimmed Mean ( 12 / 24 )103.6993750.454933594079579227.943982043807
Trimmed Mean ( 13 / 24 )103.690.446473568470739232.242191525825
Trimmed Mean ( 14 / 24 )103.6720454545450.437296322815231237.075045102425
Trimmed Mean ( 15 / 24 )103.6480952380950.426977225929981242.748533044927
Trimmed Mean ( 16 / 24 )103.6150.414982854140709249.685014612355
Trimmed Mean ( 17 / 24 )103.5776315789470.399035364980416259.570054859751
Trimmed Mean ( 18 / 24 )103.5336111111110.379165573578284273.056464842094
Trimmed Mean ( 19 / 24 )103.4932352941180.358699304202967288.523657786514
Trimmed Mean ( 20 / 24 )103.44406250.335773619066610308.076801231603
Trimmed Mean ( 21 / 24 )103.3973333333330.319985248702144323.131562322674
Trimmed Mean ( 22 / 24 )103.3485714285710.300432102518579343.999760885008
Trimmed Mean ( 23 / 24 )103.2988461538460.273292363552902377.979262980213
Trimmed Mean ( 24 / 24 )103.2683333333330.252159992535986409.534963475999
Median103.04
Midrange102.665
Midmean - Weighted Average at Xnp103.433243243243
Midmean - Weighted Average at X(n+1)p103.533611111111
Midmean - Empirical Distribution Function103.433243243243
Midmean - Empirical Distribution Function - Averaging103.533611111111
Midmean - Empirical Distribution Function - Interpolation103.533611111111
Midmean - Closest Observation103.433243243243
Midmean - True Basic - Statistics Graphics Toolkit103.533611111111
Midmean - MS Excel (old versions)103.577631578947
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')