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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, 22 Oct 2007 11:09:20 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/ttg6sdv6xnnotqe1193079284.htm/, Retrieved Mon, 06 May 2024 04:23:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1603, Retrieved Mon, 06 May 2024 04:23:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsTaak2.8G19
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Time serie Centra...] [2007-10-22 18:09:20] [40a229849a2b804e343854d9b3fa1a24] [Current]
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Dataseries X:
106,48
106,83
107,14
107,94
108,46
108,81
108,92
108,99
109,16
109,22
109,43
109,23
109,93
110,09
110,33
110,11
110,35
110,09
110,44
110,39
110,62
110,43
110,46
110,55
110,94
111,56
111,82
111,73
111,57
111,85
112,06
112,2
112,47
112,15
112,36
112,32
112,67
113,02
113,05
113,5
113,67
113,65
114
114,03
114,08
114,49
114,48
114,25
114,68
115,28
115,9
115,87
116,09
116,29
116,76
116,78
116,65
116,46
116,82
116,91




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1603&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1603&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1603&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean112.11350.361405044143276310.215648112408
Geometric Mean112.079166095633
Harmonic Mean112.044869918057
Quadratic Mean112.147862596663
Winsorized Mean ( 1 / 20 )112.1178333333330.359572414908442311.808772544140
Winsorized Mean ( 2 / 20 )112.1268333333330.356765166054621314.287503383014
Winsorized Mean ( 3 / 20 )112.1658333333330.34767624816845322.615749347907
Winsorized Mean ( 4 / 20 )112.1931666666670.339230476097551330.728441492986
Winsorized Mean ( 5 / 20 )112.20650.330477297783497339.528617404482
Winsorized Mean ( 6 / 20 )112.20050.324909933195748345.328007969527
Winsorized Mean ( 7 / 20 )112.1853333333330.318604076305993352.115185198034
Winsorized Mean ( 8 / 20 )112.1826666666670.309591663513023362.356871608552
Winsorized Mean ( 9 / 20 )112.1871666666670.307195174498892365.198336366026
Winsorized Mean ( 10 / 20 )112.09050.287663628208973389.658229293319
Winsorized Mean ( 11 / 20 )112.0171666666670.261636537003707428.140381116112
Winsorized Mean ( 12 / 20 )112.0791666666670.239077829521556468.797825758082
Winsorized Mean ( 13 / 20 )112.1116666666670.233520969753256480.092502121444
Winsorized Mean ( 14 / 20 )112.0580.224463679696348499.225532396113
Winsorized Mean ( 15 / 20 )112.02050.216778079786002516.751971004559
Winsorized Mean ( 16 / 20 )112.0658333333330.206052663399826543.869860667028
Winsorized Mean ( 17 / 20 )112.0630.203873548379415549.669149778309
Winsorized Mean ( 18 / 20 )111.9760.186549579904946600.247934393934
Winsorized Mean ( 19 / 20 )111.9823333333330.183755605113276609.409074973806
Winsorized Mean ( 20 / 20 )111.9356666666670.175655731389181637.244602162528
Trimmed Mean ( 1 / 20 )112.1279310344830.351135635675589319.329397652127
Trimmed Mean ( 2 / 20 )112.138750.340705538256573329.136856928789
Trimmed Mean ( 3 / 20 )112.1453703703700.329642110843407340.203410551644
Trimmed Mean ( 4 / 20 )112.13750.320263945985244350.140880376109
Trimmed Mean ( 5 / 20 )112.12080.311751057147611359.648499754443
Trimmed Mean ( 6 / 20 )112.0993750.303861292288507368.916271486021
Trimmed Mean ( 7 / 20 )112.0773913043480.295381753282482379.43234495316
Trimmed Mean ( 8 / 20 )112.0563636363640.286182700649544391.555336440781
Trimmed Mean ( 9 / 20 )112.0338095238100.27662726285194404.999161574952
Trimmed Mean ( 10 / 20 )112.008250.264468476988303423.522119821311
Trimmed Mean ( 11 / 20 )111.9952631578950.253962267120944440.991744275772
Trimmed Mean ( 12 / 20 )111.9919444444440.247036023156975453.342565239083
Trimmed Mean ( 13 / 20 )111.9791176470590.243262644842133460.321878518292
Trimmed Mean ( 14 / 20 )111.960.238783459064025468.876698741433
Trimmed Mean ( 15 / 20 )111.9460.234433825184858477.516416036496
Trimmed Mean ( 16 / 20 )111.9353571428570.229695267497632487.321129261015
Trimmed Mean ( 17 / 20 )111.9165384615380.225021668910552497.358938823027
Trimmed Mean ( 18 / 20 )111.8950.217473136771858514.523318424309
Trimmed Mean ( 19 / 20 )111.8827272727270.211609153127942528.723477311407
Trimmed Mean ( 20 / 20 )111.8670.201631633900719554.808775963606
Median111.955
Midrange111.695
Midmean - Weighted Average at Xnp111.83
Midmean - Weighted Average at X(n+1)p111.946
Midmean - Empirical Distribution Function111.83
Midmean - Empirical Distribution Function - Averaging111.946
Midmean - Empirical Distribution Function - Interpolation111.946
Midmean - Closest Observation111.83
Midmean - True Basic - Statistics Graphics Toolkit111.946
Midmean - MS Excel (old versions)111.903333333333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 112.1135 & 0.361405044143276 & 310.215648112408 \tabularnewline
Geometric Mean & 112.079166095633 &  &  \tabularnewline
Harmonic Mean & 112.044869918057 &  &  \tabularnewline
Quadratic Mean & 112.147862596663 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 112.117833333333 & 0.359572414908442 & 311.808772544140 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 112.126833333333 & 0.356765166054621 & 314.287503383014 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 112.165833333333 & 0.34767624816845 & 322.615749347907 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 112.193166666667 & 0.339230476097551 & 330.728441492986 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 112.2065 & 0.330477297783497 & 339.528617404482 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 112.2005 & 0.324909933195748 & 345.328007969527 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 112.185333333333 & 0.318604076305993 & 352.115185198034 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 112.182666666667 & 0.309591663513023 & 362.356871608552 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 112.187166666667 & 0.307195174498892 & 365.198336366026 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 112.0905 & 0.287663628208973 & 389.658229293319 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 112.017166666667 & 0.261636537003707 & 428.140381116112 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 112.079166666667 & 0.239077829521556 & 468.797825758082 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 112.111666666667 & 0.233520969753256 & 480.092502121444 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 112.058 & 0.224463679696348 & 499.225532396113 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 112.0205 & 0.216778079786002 & 516.751971004559 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 112.065833333333 & 0.206052663399826 & 543.869860667028 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 112.063 & 0.203873548379415 & 549.669149778309 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 111.976 & 0.186549579904946 & 600.247934393934 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 111.982333333333 & 0.183755605113276 & 609.409074973806 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 111.935666666667 & 0.175655731389181 & 637.244602162528 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 112.127931034483 & 0.351135635675589 & 319.329397652127 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 112.13875 & 0.340705538256573 & 329.136856928789 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 112.145370370370 & 0.329642110843407 & 340.203410551644 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 112.1375 & 0.320263945985244 & 350.140880376109 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 112.1208 & 0.311751057147611 & 359.648499754443 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 112.099375 & 0.303861292288507 & 368.916271486021 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 112.077391304348 & 0.295381753282482 & 379.43234495316 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 112.056363636364 & 0.286182700649544 & 391.555336440781 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 112.033809523810 & 0.27662726285194 & 404.999161574952 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 112.00825 & 0.264468476988303 & 423.522119821311 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 111.995263157895 & 0.253962267120944 & 440.991744275772 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 111.991944444444 & 0.247036023156975 & 453.342565239083 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 111.979117647059 & 0.243262644842133 & 460.321878518292 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 111.96 & 0.238783459064025 & 468.876698741433 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 111.946 & 0.234433825184858 & 477.516416036496 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 111.935357142857 & 0.229695267497632 & 487.321129261015 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 111.916538461538 & 0.225021668910552 & 497.358938823027 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 111.895 & 0.217473136771858 & 514.523318424309 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 111.882727272727 & 0.211609153127942 & 528.723477311407 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 111.867 & 0.201631633900719 & 554.808775963606 \tabularnewline
Median & 111.955 &  &  \tabularnewline
Midrange & 111.695 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 111.83 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 111.946 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 111.83 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 111.946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 111.946 &  &  \tabularnewline
Midmean - Closest Observation & 111.83 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 111.946 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 111.903333333333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1603&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]112.1135[/C][C]0.361405044143276[/C][C]310.215648112408[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.079166095633[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112.044869918057[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112.147862596663[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]112.117833333333[/C][C]0.359572414908442[/C][C]311.808772544140[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]112.126833333333[/C][C]0.356765166054621[/C][C]314.287503383014[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]112.165833333333[/C][C]0.34767624816845[/C][C]322.615749347907[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]112.193166666667[/C][C]0.339230476097551[/C][C]330.728441492986[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]112.2065[/C][C]0.330477297783497[/C][C]339.528617404482[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]112.2005[/C][C]0.324909933195748[/C][C]345.328007969527[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]112.185333333333[/C][C]0.318604076305993[/C][C]352.115185198034[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]112.182666666667[/C][C]0.309591663513023[/C][C]362.356871608552[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]112.187166666667[/C][C]0.307195174498892[/C][C]365.198336366026[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]112.0905[/C][C]0.287663628208973[/C][C]389.658229293319[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]112.017166666667[/C][C]0.261636537003707[/C][C]428.140381116112[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]112.079166666667[/C][C]0.239077829521556[/C][C]468.797825758082[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]112.111666666667[/C][C]0.233520969753256[/C][C]480.092502121444[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]112.058[/C][C]0.224463679696348[/C][C]499.225532396113[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]112.0205[/C][C]0.216778079786002[/C][C]516.751971004559[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]112.065833333333[/C][C]0.206052663399826[/C][C]543.869860667028[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]112.063[/C][C]0.203873548379415[/C][C]549.669149778309[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]111.976[/C][C]0.186549579904946[/C][C]600.247934393934[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]111.982333333333[/C][C]0.183755605113276[/C][C]609.409074973806[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]111.935666666667[/C][C]0.175655731389181[/C][C]637.244602162528[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]112.127931034483[/C][C]0.351135635675589[/C][C]319.329397652127[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]112.13875[/C][C]0.340705538256573[/C][C]329.136856928789[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]112.145370370370[/C][C]0.329642110843407[/C][C]340.203410551644[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]112.1375[/C][C]0.320263945985244[/C][C]350.140880376109[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]112.1208[/C][C]0.311751057147611[/C][C]359.648499754443[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]112.099375[/C][C]0.303861292288507[/C][C]368.916271486021[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]112.077391304348[/C][C]0.295381753282482[/C][C]379.43234495316[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]112.056363636364[/C][C]0.286182700649544[/C][C]391.555336440781[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]112.033809523810[/C][C]0.27662726285194[/C][C]404.999161574952[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]112.00825[/C][C]0.264468476988303[/C][C]423.522119821311[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]111.995263157895[/C][C]0.253962267120944[/C][C]440.991744275772[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]111.991944444444[/C][C]0.247036023156975[/C][C]453.342565239083[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]111.979117647059[/C][C]0.243262644842133[/C][C]460.321878518292[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]111.96[/C][C]0.238783459064025[/C][C]468.876698741433[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]111.946[/C][C]0.234433825184858[/C][C]477.516416036496[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]111.935357142857[/C][C]0.229695267497632[/C][C]487.321129261015[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]111.916538461538[/C][C]0.225021668910552[/C][C]497.358938823027[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]111.895[/C][C]0.217473136771858[/C][C]514.523318424309[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]111.882727272727[/C][C]0.211609153127942[/C][C]528.723477311407[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]111.867[/C][C]0.201631633900719[/C][C]554.808775963606[/C][/ROW]
[ROW][C]Median[/C][C]111.955[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.695[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]111.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]111.946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]111.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]111.946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]111.946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]111.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]111.946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]111.903333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1603&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1603&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 Mean112.11350.361405044143276310.215648112408
Geometric Mean112.079166095633
Harmonic Mean112.044869918057
Quadratic Mean112.147862596663
Winsorized Mean ( 1 / 20 )112.1178333333330.359572414908442311.808772544140
Winsorized Mean ( 2 / 20 )112.1268333333330.356765166054621314.287503383014
Winsorized Mean ( 3 / 20 )112.1658333333330.34767624816845322.615749347907
Winsorized Mean ( 4 / 20 )112.1931666666670.339230476097551330.728441492986
Winsorized Mean ( 5 / 20 )112.20650.330477297783497339.528617404482
Winsorized Mean ( 6 / 20 )112.20050.324909933195748345.328007969527
Winsorized Mean ( 7 / 20 )112.1853333333330.318604076305993352.115185198034
Winsorized Mean ( 8 / 20 )112.1826666666670.309591663513023362.356871608552
Winsorized Mean ( 9 / 20 )112.1871666666670.307195174498892365.198336366026
Winsorized Mean ( 10 / 20 )112.09050.287663628208973389.658229293319
Winsorized Mean ( 11 / 20 )112.0171666666670.261636537003707428.140381116112
Winsorized Mean ( 12 / 20 )112.0791666666670.239077829521556468.797825758082
Winsorized Mean ( 13 / 20 )112.1116666666670.233520969753256480.092502121444
Winsorized Mean ( 14 / 20 )112.0580.224463679696348499.225532396113
Winsorized Mean ( 15 / 20 )112.02050.216778079786002516.751971004559
Winsorized Mean ( 16 / 20 )112.0658333333330.206052663399826543.869860667028
Winsorized Mean ( 17 / 20 )112.0630.203873548379415549.669149778309
Winsorized Mean ( 18 / 20 )111.9760.186549579904946600.247934393934
Winsorized Mean ( 19 / 20 )111.9823333333330.183755605113276609.409074973806
Winsorized Mean ( 20 / 20 )111.9356666666670.175655731389181637.244602162528
Trimmed Mean ( 1 / 20 )112.1279310344830.351135635675589319.329397652127
Trimmed Mean ( 2 / 20 )112.138750.340705538256573329.136856928789
Trimmed Mean ( 3 / 20 )112.1453703703700.329642110843407340.203410551644
Trimmed Mean ( 4 / 20 )112.13750.320263945985244350.140880376109
Trimmed Mean ( 5 / 20 )112.12080.311751057147611359.648499754443
Trimmed Mean ( 6 / 20 )112.0993750.303861292288507368.916271486021
Trimmed Mean ( 7 / 20 )112.0773913043480.295381753282482379.43234495316
Trimmed Mean ( 8 / 20 )112.0563636363640.286182700649544391.555336440781
Trimmed Mean ( 9 / 20 )112.0338095238100.27662726285194404.999161574952
Trimmed Mean ( 10 / 20 )112.008250.264468476988303423.522119821311
Trimmed Mean ( 11 / 20 )111.9952631578950.253962267120944440.991744275772
Trimmed Mean ( 12 / 20 )111.9919444444440.247036023156975453.342565239083
Trimmed Mean ( 13 / 20 )111.9791176470590.243262644842133460.321878518292
Trimmed Mean ( 14 / 20 )111.960.238783459064025468.876698741433
Trimmed Mean ( 15 / 20 )111.9460.234433825184858477.516416036496
Trimmed Mean ( 16 / 20 )111.9353571428570.229695267497632487.321129261015
Trimmed Mean ( 17 / 20 )111.9165384615380.225021668910552497.358938823027
Trimmed Mean ( 18 / 20 )111.8950.217473136771858514.523318424309
Trimmed Mean ( 19 / 20 )111.8827272727270.211609153127942528.723477311407
Trimmed Mean ( 20 / 20 )111.8670.201631633900719554.808775963606
Median111.955
Midrange111.695
Midmean - Weighted Average at Xnp111.83
Midmean - Weighted Average at X(n+1)p111.946
Midmean - Empirical Distribution Function111.83
Midmean - Empirical Distribution Function - Averaging111.946
Midmean - Empirical Distribution Function - Interpolation111.946
Midmean - Closest Observation111.83
Midmean - True Basic - Statistics Graphics Toolkit111.946
Midmean - MS Excel (old versions)111.903333333333
Number of observations60



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')