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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Nov 2010 19:47:03 +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/Nov/15/t12898506533mmyxvl6emx81cz.htm/, Retrieved Sat, 27 Apr 2024 19:44:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95032, Retrieved Sat, 27 Apr 2024 19:44:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
167.16
179.84
174.44
180.35
193.17
195.16
202.43
189.91
195.98
212.09
205.81
204.31
196.07
199.98
199.10
198.31
195.72
223.04
238.41
259.73
326.54
335.15
321.81
368.62
369.59
425.00
439.72
362.23
328.76
348.55
328.18
329.34
295.55
237.38
226.85
220.14
239.36
224.69
230.98
233.47
256.70
253.41
224.95
210.37
191.09
198.85
211.04
206.25
201.51
194.54
191.07
192.82
181.88
157.67
195.82
246.25
271.69
270.29




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95032&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 Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95032&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95032&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean242.3986206896558.7694143703998127.6413692467133
Geometric Mean234.662564079130
Harmonic Mean228.127380258404
Quadratic Mean251.277816631382
Winsorized Mean ( 1 / 19 )242.3084482758628.6459055935786528.0258031565630
Winsorized Mean ( 2 / 19 )240.6487931034487.980158433222630.1558916551821
Winsorized Mean ( 3 / 19 )240.8779310344837.9267559185669430.3879586439985
Winsorized Mean ( 4 / 19 )240.4724137931037.7993406902947730.8324028071166
Winsorized Mean ( 5 / 19 )239.4257.4686380755509432.0573841680417
Winsorized Mean ( 6 / 19 )238.8694827586217.0166279968804834.0433443051020
Winsorized Mean ( 7 / 19 )238.3082758620696.8331911578525234.8751074508155
Winsorized Mean ( 8 / 19 )238.2310344827596.8141845966676434.9610479585865
Winsorized Mean ( 9 / 19 )238.4094827586216.7610430356096435.2622341705185
Winsorized Mean ( 10 / 19 )238.1870689655176.6882110078630135.6129716430137
Winsorized Mean ( 11 / 19 )237.5498275862076.4509156367458836.8242030996451
Winsorized Mean ( 12 / 19 )232.2455.2314915778252644.3936488370578
Winsorized Mean ( 13 / 19 )227.0225862068974.1337122596272954.9197844330282
Winsorized Mean ( 14 / 19 )226.7087931034484.0666999696968255.7476073457048
Winsorized Mean ( 15 / 19 )224.0191379310343.5631668375122362.8707967229068
Winsorized Mean ( 16 / 19 )223.2081034482763.4142814667915865.374839660781
Winsorized Mean ( 17 / 19 )222.9003448275863.1589120988477470.5623764931263
Winsorized Mean ( 18 / 19 )220.8458620689662.7680376602341379.7842692827688
Winsorized Mean ( 19 / 19 )218.6706896551722.4035631553228490.9777174653859
Trimmed Mean ( 1 / 19 )240.3880357142868.2158195179741429.2591670482022
Trimmed Mean ( 2 / 19 )238.3253703703707.6667435950609631.0856059571241
Trimmed Mean ( 3 / 19 )237.0296153846157.4407241643951431.8557186300271
Trimmed Mean ( 4 / 19 )235.54167.175039912340132.8279149492813
Trimmed Mean ( 5 / 19 )234.0520833333336.8845074618857133.9969249258719
Trimmed Mean ( 6 / 19 )232.6971739130436.6307084724538235.0938628775108
Trimmed Mean ( 7 / 19 )231.3411363636366.4454942570237835.8919156760615
Trimmed Mean ( 8 / 19 )229.9666666666676.2514625899969136.786058199347
Trimmed Mean ( 9 / 19 )228.468755.9880138202260338.1543458080021
Trimmed Mean ( 10 / 19 )226.7828947368425.6330837902804840.2591019732639
Trimmed Mean ( 11 / 19 )224.9455555555565.1494983488831143.683003724886
Trimmed Mean ( 12 / 19 )222.9908823529414.5251048651471949.2786109931814
Trimmed Mean ( 13 / 19 )221.5931254.1241828720849953.7301889544905
Trimmed Mean ( 14 / 19 )220.7856666666673.9645176449459955.6904235117042
Trimmed Mean ( 15 / 19 )219.9092857142863.7407150282937258.7880349213863
Trimmed Mean ( 16 / 19 )219.2980769230773.5971476742736860.9644353751356
Trimmed Mean ( 17 / 19 )218.70753.4219660872331763.9128192462117
Trimmed Mean ( 18 / 19 )218.0572727272733.2347595494531667.4106589357269
Trimmed Mean ( 19 / 19 )217.6083.1062030977079670.0559471338404
Median216.115
Midrange298.695
Midmean - Weighted Average at Xnp219.078620689655
Midmean - Weighted Average at X(n+1)p220.785666666667
Midmean - Empirical Distribution Function220.785666666667
Midmean - Empirical Distribution Function - Averaging220.785666666667
Midmean - Empirical Distribution Function - Interpolation219.909285714286
Midmean - Closest Observation220.785666666667
Midmean - True Basic - Statistics Graphics Toolkit220.785666666667
Midmean - MS Excel (old versions)220.785666666667
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 242.398620689655 & 8.76941437039981 & 27.6413692467133 \tabularnewline
Geometric Mean & 234.662564079130 &  &  \tabularnewline
Harmonic Mean & 228.127380258404 &  &  \tabularnewline
Quadratic Mean & 251.277816631382 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 242.308448275862 & 8.64590559357865 & 28.0258031565630 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 240.648793103448 & 7.9801584332226 & 30.1558916551821 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 240.877931034483 & 7.92675591856694 & 30.3879586439985 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 240.472413793103 & 7.79934069029477 & 30.8324028071166 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 239.425 & 7.46863807555094 & 32.0573841680417 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 238.869482758621 & 7.01662799688048 & 34.0433443051020 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 238.308275862069 & 6.83319115785252 & 34.8751074508155 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 238.231034482759 & 6.81418459666764 & 34.9610479585865 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 238.409482758621 & 6.76104303560964 & 35.2622341705185 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 238.187068965517 & 6.68821100786301 & 35.6129716430137 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 237.549827586207 & 6.45091563674588 & 36.8242030996451 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 232.245 & 5.23149157782526 & 44.3936488370578 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 227.022586206897 & 4.13371225962729 & 54.9197844330282 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 226.708793103448 & 4.06669996969682 & 55.7476073457048 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 224.019137931034 & 3.56316683751223 & 62.8707967229068 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 223.208103448276 & 3.41428146679158 & 65.374839660781 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 222.900344827586 & 3.15891209884774 & 70.5623764931263 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 220.845862068966 & 2.76803766023413 & 79.7842692827688 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 218.670689655172 & 2.40356315532284 & 90.9777174653859 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 240.388035714286 & 8.21581951797414 & 29.2591670482022 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 238.325370370370 & 7.66674359506096 & 31.0856059571241 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 237.029615384615 & 7.44072416439514 & 31.8557186300271 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 235.5416 & 7.1750399123401 & 32.8279149492813 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 234.052083333333 & 6.88450746188571 & 33.9969249258719 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 232.697173913043 & 6.63070847245382 & 35.0938628775108 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 231.341136363636 & 6.44549425702378 & 35.8919156760615 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 229.966666666667 & 6.25146258999691 & 36.786058199347 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 228.46875 & 5.98801382022603 & 38.1543458080021 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 226.782894736842 & 5.63308379028048 & 40.2591019732639 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 224.945555555556 & 5.14949834888311 & 43.683003724886 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 222.990882352941 & 4.52510486514719 & 49.2786109931814 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 221.593125 & 4.12418287208499 & 53.7301889544905 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 220.785666666667 & 3.96451764494599 & 55.6904235117042 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 219.909285714286 & 3.74071502829372 & 58.7880349213863 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 219.298076923077 & 3.59714767427368 & 60.9644353751356 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 218.7075 & 3.42196608723317 & 63.9128192462117 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 218.057272727273 & 3.23475954945316 & 67.4106589357269 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 217.608 & 3.10620309770796 & 70.0559471338404 \tabularnewline
Median & 216.115 &  &  \tabularnewline
Midrange & 298.695 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 219.078620689655 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 220.785666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 220.785666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 220.785666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 219.909285714286 &  &  \tabularnewline
Midmean - Closest Observation & 220.785666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 220.785666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 220.785666666667 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95032&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]242.398620689655[/C][C]8.76941437039981[/C][C]27.6413692467133[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]234.662564079130[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]228.127380258404[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]251.277816631382[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]242.308448275862[/C][C]8.64590559357865[/C][C]28.0258031565630[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]240.648793103448[/C][C]7.9801584332226[/C][C]30.1558916551821[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]240.877931034483[/C][C]7.92675591856694[/C][C]30.3879586439985[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]240.472413793103[/C][C]7.79934069029477[/C][C]30.8324028071166[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]239.425[/C][C]7.46863807555094[/C][C]32.0573841680417[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]238.869482758621[/C][C]7.01662799688048[/C][C]34.0433443051020[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]238.308275862069[/C][C]6.83319115785252[/C][C]34.8751074508155[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]238.231034482759[/C][C]6.81418459666764[/C][C]34.9610479585865[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]238.409482758621[/C][C]6.76104303560964[/C][C]35.2622341705185[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]238.187068965517[/C][C]6.68821100786301[/C][C]35.6129716430137[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]237.549827586207[/C][C]6.45091563674588[/C][C]36.8242030996451[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]232.245[/C][C]5.23149157782526[/C][C]44.3936488370578[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]227.022586206897[/C][C]4.13371225962729[/C][C]54.9197844330282[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]226.708793103448[/C][C]4.06669996969682[/C][C]55.7476073457048[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]224.019137931034[/C][C]3.56316683751223[/C][C]62.8707967229068[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]223.208103448276[/C][C]3.41428146679158[/C][C]65.374839660781[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]222.900344827586[/C][C]3.15891209884774[/C][C]70.5623764931263[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]220.845862068966[/C][C]2.76803766023413[/C][C]79.7842692827688[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]218.670689655172[/C][C]2.40356315532284[/C][C]90.9777174653859[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]240.388035714286[/C][C]8.21581951797414[/C][C]29.2591670482022[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]238.325370370370[/C][C]7.66674359506096[/C][C]31.0856059571241[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]237.029615384615[/C][C]7.44072416439514[/C][C]31.8557186300271[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]235.5416[/C][C]7.1750399123401[/C][C]32.8279149492813[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]234.052083333333[/C][C]6.88450746188571[/C][C]33.9969249258719[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]232.697173913043[/C][C]6.63070847245382[/C][C]35.0938628775108[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]231.341136363636[/C][C]6.44549425702378[/C][C]35.8919156760615[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]229.966666666667[/C][C]6.25146258999691[/C][C]36.786058199347[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]228.46875[/C][C]5.98801382022603[/C][C]38.1543458080021[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]226.782894736842[/C][C]5.63308379028048[/C][C]40.2591019732639[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]224.945555555556[/C][C]5.14949834888311[/C][C]43.683003724886[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]222.990882352941[/C][C]4.52510486514719[/C][C]49.2786109931814[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]221.593125[/C][C]4.12418287208499[/C][C]53.7301889544905[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]220.785666666667[/C][C]3.96451764494599[/C][C]55.6904235117042[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]219.909285714286[/C][C]3.74071502829372[/C][C]58.7880349213863[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]219.298076923077[/C][C]3.59714767427368[/C][C]60.9644353751356[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]218.7075[/C][C]3.42196608723317[/C][C]63.9128192462117[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]218.057272727273[/C][C]3.23475954945316[/C][C]67.4106589357269[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]217.608[/C][C]3.10620309770796[/C][C]70.0559471338404[/C][/ROW]
[ROW][C]Median[/C][C]216.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]298.695[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]219.078620689655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]220.785666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]220.785666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]220.785666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]219.909285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]220.785666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]220.785666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]220.785666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95032&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95032&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 Mean242.3986206896558.7694143703998127.6413692467133
Geometric Mean234.662564079130
Harmonic Mean228.127380258404
Quadratic Mean251.277816631382
Winsorized Mean ( 1 / 19 )242.3084482758628.6459055935786528.0258031565630
Winsorized Mean ( 2 / 19 )240.6487931034487.980158433222630.1558916551821
Winsorized Mean ( 3 / 19 )240.8779310344837.9267559185669430.3879586439985
Winsorized Mean ( 4 / 19 )240.4724137931037.7993406902947730.8324028071166
Winsorized Mean ( 5 / 19 )239.4257.4686380755509432.0573841680417
Winsorized Mean ( 6 / 19 )238.8694827586217.0166279968804834.0433443051020
Winsorized Mean ( 7 / 19 )238.3082758620696.8331911578525234.8751074508155
Winsorized Mean ( 8 / 19 )238.2310344827596.8141845966676434.9610479585865
Winsorized Mean ( 9 / 19 )238.4094827586216.7610430356096435.2622341705185
Winsorized Mean ( 10 / 19 )238.1870689655176.6882110078630135.6129716430137
Winsorized Mean ( 11 / 19 )237.5498275862076.4509156367458836.8242030996451
Winsorized Mean ( 12 / 19 )232.2455.2314915778252644.3936488370578
Winsorized Mean ( 13 / 19 )227.0225862068974.1337122596272954.9197844330282
Winsorized Mean ( 14 / 19 )226.7087931034484.0666999696968255.7476073457048
Winsorized Mean ( 15 / 19 )224.0191379310343.5631668375122362.8707967229068
Winsorized Mean ( 16 / 19 )223.2081034482763.4142814667915865.374839660781
Winsorized Mean ( 17 / 19 )222.9003448275863.1589120988477470.5623764931263
Winsorized Mean ( 18 / 19 )220.8458620689662.7680376602341379.7842692827688
Winsorized Mean ( 19 / 19 )218.6706896551722.4035631553228490.9777174653859
Trimmed Mean ( 1 / 19 )240.3880357142868.2158195179741429.2591670482022
Trimmed Mean ( 2 / 19 )238.3253703703707.6667435950609631.0856059571241
Trimmed Mean ( 3 / 19 )237.0296153846157.4407241643951431.8557186300271
Trimmed Mean ( 4 / 19 )235.54167.175039912340132.8279149492813
Trimmed Mean ( 5 / 19 )234.0520833333336.8845074618857133.9969249258719
Trimmed Mean ( 6 / 19 )232.6971739130436.6307084724538235.0938628775108
Trimmed Mean ( 7 / 19 )231.3411363636366.4454942570237835.8919156760615
Trimmed Mean ( 8 / 19 )229.9666666666676.2514625899969136.786058199347
Trimmed Mean ( 9 / 19 )228.468755.9880138202260338.1543458080021
Trimmed Mean ( 10 / 19 )226.7828947368425.6330837902804840.2591019732639
Trimmed Mean ( 11 / 19 )224.9455555555565.1494983488831143.683003724886
Trimmed Mean ( 12 / 19 )222.9908823529414.5251048651471949.2786109931814
Trimmed Mean ( 13 / 19 )221.5931254.1241828720849953.7301889544905
Trimmed Mean ( 14 / 19 )220.7856666666673.9645176449459955.6904235117042
Trimmed Mean ( 15 / 19 )219.9092857142863.7407150282937258.7880349213863
Trimmed Mean ( 16 / 19 )219.2980769230773.5971476742736860.9644353751356
Trimmed Mean ( 17 / 19 )218.70753.4219660872331763.9128192462117
Trimmed Mean ( 18 / 19 )218.0572727272733.2347595494531667.4106589357269
Trimmed Mean ( 19 / 19 )217.6083.1062030977079670.0559471338404
Median216.115
Midrange298.695
Midmean - Weighted Average at Xnp219.078620689655
Midmean - Weighted Average at X(n+1)p220.785666666667
Midmean - Empirical Distribution Function220.785666666667
Midmean - Empirical Distribution Function - Averaging220.785666666667
Midmean - Empirical Distribution Function - Interpolation219.909285714286
Midmean - Closest Observation220.785666666667
Midmean - True Basic - Statistics Graphics Toolkit220.785666666667
Midmean - MS Excel (old versions)220.785666666667
Number of observations58



Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')