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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 computationThu, 17 Dec 2009 10:52:23 -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/2009/Dec/17/t12610725790x7c7fxv8cvpn9g.htm/, Retrieved Tue, 30 Apr 2024 00:32:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69018, Retrieved Tue, 30 Apr 2024 00:32:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper central ten...] [2009-12-17 17:52:23] [f47dffd5f5a8c03c3681db4cc9472742] [Current]
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Dataseries X:
286.445
288.576
293.299
295.881
292.710
271.993
267.430
273.963
273.046
268.347
264.319
255.765
246.263
245.098
246.969
248.333
247.934
226.839
225.554
237.085
237.080
245.039
248.541
247.105
243.422
250.643
254.663
260.993
258.556
235.372
246.057
253.353
255.198
264.176
269.034
265.861
269.826
278.506
292.300
290.726
289.802
271.311
274.352
275.216
276.836
280.408
280.190
282.656
281.477
288.186
292.300
291.186
287.259
264.993
267.140
270.150
275.037
277.103
277.128
277.915
276.687




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=69018&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=69018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69018&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 Mean266.8792131147542.33689383094566114.202540817508
Geometric Mean266.252970318369
Harmonic Mean265.614659636326
Quadratic Mean267.492390096199
Winsorized Mean ( 1 / 20 )266.8579508196722.32236958028778114.907615516822
Winsorized Mean ( 2 / 20 )267.1184098360662.24544491050386118.960126158752
Winsorized Mean ( 3 / 20 )267.1822459016392.22224955016305120.230532111948
Winsorized Mean ( 4 / 20 )267.1825737704922.22217553366889120.234684309283
Winsorized Mean ( 5 / 20 )267.610688524592.09618674377463127.665480816227
Winsorized Mean ( 6 / 20 )267.7244918032792.05781932202248130.101068124947
Winsorized Mean ( 7 / 20 )267.6252295081972.03707605229602131.377141862991
Winsorized Mean ( 8 / 20 )267.5902131147541.98535997522118134.781710346983
Winsorized Mean ( 9 / 20 )267.5630655737711.96978508270813135.833633792127
Winsorized Mean ( 10 / 20 )267.5268360655741.92278446973092139.135113829483
Winsorized Mean ( 11 / 20 )267.4045737704921.89355348506380141.218389593828
Winsorized Mean ( 12 / 20 )266.8222786885251.74521950286674152.887518303707
Winsorized Mean ( 13 / 20 )266.6560491803281.69253715175442157.548121708242
Winsorized Mean ( 14 / 20 )266.4584426229511.64869748382862161.617546721899
Winsorized Mean ( 15 / 20 )266.9217213114751.54896554995102172.322568000248
Winsorized Mean ( 16 / 20 )267.1908360655741.36437768199093195.833484813152
Winsorized Mean ( 17 / 20 )267.3912131147541.28059764333159208.801893793207
Winsorized Mean ( 18 / 20 )267.3168524590161.22304858104836218.566013322121
Winsorized Mean ( 19 / 20 )267.4856721311481.19296106544717224.219951412147
Winsorized Mean ( 20 / 20 )268.3132131147541.03398369788619259.494626137023
Trimmed Mean ( 1 / 20 )267.0880847457632.25727445834506118.323265369148
Trimmed Mean ( 2 / 20 )267.3343684210532.17683299272481122.808855486163
Trimmed Mean ( 3 / 20 )267.4541272727272.12879193876603125.636574623520
Trimmed Mean ( 4 / 20 )267.5584339622642.07958763051637128.659369788533
Trimmed Mean ( 5 / 20 )267.6708235294122.01731831306810132.686458946738
Trimmed Mean ( 6 / 20 )267.6857959183671.98167965930205135.080256115989
Trimmed Mean ( 7 / 20 )267.6774255319151.94664016933921137.507398515658
Trimmed Mean ( 8 / 20 )267.6875333333331.90604674908486140.441221319391
Trimmed Mean ( 9 / 20 )267.7047906976741.86610901491475143.456137105636
Trimmed Mean ( 10 / 20 )267.7282195121951.81623681050796147.408211287887
Trimmed Mean ( 11 / 20 )267.7597179487181.76130610617828152.023385946074
Trimmed Mean ( 12 / 20 )267.8129459459461.69383204640258158.110685480734
Trimmed Mean ( 13 / 20 )267.9568285714291.64121903939423163.266951052634
Trimmed Mean ( 14 / 20 )268.1417878787881.58005001824212169.704619969631
Trimmed Mean ( 15 / 20 )268.3783870967741.50267829398719178.600029141741
Trimmed Mean ( 16 / 20 )268.5826551724141.42320274638918188.717072008073
Trimmed Mean ( 17 / 20 )268.7791851851851.36774655067602196.512420413226
Trimmed Mean ( 18 / 20 )268.97841.30991789819057205.339892195952
Trimmed Mean ( 19 / 20 )269.2232173913041.23505854137311217.984175140386
Trimmed Mean ( 20 / 20 )269.4888571428571.12031094171326240.548268439417
Median269.826
Midrange260.7175
Midmean - Weighted Average at Xnp267.984666666667
Midmean - Weighted Average at X(n+1)p268.378387096774
Midmean - Empirical Distribution Function268.378387096774
Midmean - Empirical Distribution Function - Averaging268.378387096774
Midmean - Empirical Distribution Function - Interpolation268.378387096774
Midmean - Closest Observation267.75846875
Midmean - True Basic - Statistics Graphics Toolkit268.378387096774
Midmean - MS Excel (old versions)268.378387096774
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 266.879213114754 & 2.33689383094566 & 114.202540817508 \tabularnewline
Geometric Mean & 266.252970318369 &  &  \tabularnewline
Harmonic Mean & 265.614659636326 &  &  \tabularnewline
Quadratic Mean & 267.492390096199 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 266.857950819672 & 2.32236958028778 & 114.907615516822 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 267.118409836066 & 2.24544491050386 & 118.960126158752 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 267.182245901639 & 2.22224955016305 & 120.230532111948 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 267.182573770492 & 2.22217553366889 & 120.234684309283 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 267.61068852459 & 2.09618674377463 & 127.665480816227 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 267.724491803279 & 2.05781932202248 & 130.101068124947 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 267.625229508197 & 2.03707605229602 & 131.377141862991 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 267.590213114754 & 1.98535997522118 & 134.781710346983 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 267.563065573771 & 1.96978508270813 & 135.833633792127 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 267.526836065574 & 1.92278446973092 & 139.135113829483 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 267.404573770492 & 1.89355348506380 & 141.218389593828 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 266.822278688525 & 1.74521950286674 & 152.887518303707 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 266.656049180328 & 1.69253715175442 & 157.548121708242 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 266.458442622951 & 1.64869748382862 & 161.617546721899 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 266.921721311475 & 1.54896554995102 & 172.322568000248 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 267.190836065574 & 1.36437768199093 & 195.833484813152 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 267.391213114754 & 1.28059764333159 & 208.801893793207 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 267.316852459016 & 1.22304858104836 & 218.566013322121 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 267.485672131148 & 1.19296106544717 & 224.219951412147 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 268.313213114754 & 1.03398369788619 & 259.494626137023 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 267.088084745763 & 2.25727445834506 & 118.323265369148 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 267.334368421053 & 2.17683299272481 & 122.808855486163 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 267.454127272727 & 2.12879193876603 & 125.636574623520 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 267.558433962264 & 2.07958763051637 & 128.659369788533 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 267.670823529412 & 2.01731831306810 & 132.686458946738 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 267.685795918367 & 1.98167965930205 & 135.080256115989 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 267.677425531915 & 1.94664016933921 & 137.507398515658 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 267.687533333333 & 1.90604674908486 & 140.441221319391 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 267.704790697674 & 1.86610901491475 & 143.456137105636 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 267.728219512195 & 1.81623681050796 & 147.408211287887 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 267.759717948718 & 1.76130610617828 & 152.023385946074 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 267.812945945946 & 1.69383204640258 & 158.110685480734 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 267.956828571429 & 1.64121903939423 & 163.266951052634 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 268.141787878788 & 1.58005001824212 & 169.704619969631 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 268.378387096774 & 1.50267829398719 & 178.600029141741 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 268.582655172414 & 1.42320274638918 & 188.717072008073 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 268.779185185185 & 1.36774655067602 & 196.512420413226 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 268.9784 & 1.30991789819057 & 205.339892195952 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 269.223217391304 & 1.23505854137311 & 217.984175140386 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 269.488857142857 & 1.12031094171326 & 240.548268439417 \tabularnewline
Median & 269.826 &  &  \tabularnewline
Midrange & 260.7175 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 267.984666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 268.378387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 268.378387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 268.378387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 268.378387096774 &  &  \tabularnewline
Midmean - Closest Observation & 267.75846875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 268.378387096774 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 268.378387096774 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69018&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]266.879213114754[/C][C]2.33689383094566[/C][C]114.202540817508[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]266.252970318369[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]265.614659636326[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]267.492390096199[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]266.857950819672[/C][C]2.32236958028778[/C][C]114.907615516822[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]267.118409836066[/C][C]2.24544491050386[/C][C]118.960126158752[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]267.182245901639[/C][C]2.22224955016305[/C][C]120.230532111948[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]267.182573770492[/C][C]2.22217553366889[/C][C]120.234684309283[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]267.61068852459[/C][C]2.09618674377463[/C][C]127.665480816227[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]267.724491803279[/C][C]2.05781932202248[/C][C]130.101068124947[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]267.625229508197[/C][C]2.03707605229602[/C][C]131.377141862991[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]267.590213114754[/C][C]1.98535997522118[/C][C]134.781710346983[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]267.563065573771[/C][C]1.96978508270813[/C][C]135.833633792127[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]267.526836065574[/C][C]1.92278446973092[/C][C]139.135113829483[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]267.404573770492[/C][C]1.89355348506380[/C][C]141.218389593828[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]266.822278688525[/C][C]1.74521950286674[/C][C]152.887518303707[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]266.656049180328[/C][C]1.69253715175442[/C][C]157.548121708242[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]266.458442622951[/C][C]1.64869748382862[/C][C]161.617546721899[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]266.921721311475[/C][C]1.54896554995102[/C][C]172.322568000248[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]267.190836065574[/C][C]1.36437768199093[/C][C]195.833484813152[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]267.391213114754[/C][C]1.28059764333159[/C][C]208.801893793207[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]267.316852459016[/C][C]1.22304858104836[/C][C]218.566013322121[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]267.485672131148[/C][C]1.19296106544717[/C][C]224.219951412147[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]268.313213114754[/C][C]1.03398369788619[/C][C]259.494626137023[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]267.088084745763[/C][C]2.25727445834506[/C][C]118.323265369148[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]267.334368421053[/C][C]2.17683299272481[/C][C]122.808855486163[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]267.454127272727[/C][C]2.12879193876603[/C][C]125.636574623520[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]267.558433962264[/C][C]2.07958763051637[/C][C]128.659369788533[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]267.670823529412[/C][C]2.01731831306810[/C][C]132.686458946738[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]267.685795918367[/C][C]1.98167965930205[/C][C]135.080256115989[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]267.677425531915[/C][C]1.94664016933921[/C][C]137.507398515658[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]267.687533333333[/C][C]1.90604674908486[/C][C]140.441221319391[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]267.704790697674[/C][C]1.86610901491475[/C][C]143.456137105636[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]267.728219512195[/C][C]1.81623681050796[/C][C]147.408211287887[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]267.759717948718[/C][C]1.76130610617828[/C][C]152.023385946074[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]267.812945945946[/C][C]1.69383204640258[/C][C]158.110685480734[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]267.956828571429[/C][C]1.64121903939423[/C][C]163.266951052634[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]268.141787878788[/C][C]1.58005001824212[/C][C]169.704619969631[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]268.378387096774[/C][C]1.50267829398719[/C][C]178.600029141741[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]268.582655172414[/C][C]1.42320274638918[/C][C]188.717072008073[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]268.779185185185[/C][C]1.36774655067602[/C][C]196.512420413226[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]268.9784[/C][C]1.30991789819057[/C][C]205.339892195952[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]269.223217391304[/C][C]1.23505854137311[/C][C]217.984175140386[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]269.488857142857[/C][C]1.12031094171326[/C][C]240.548268439417[/C][/ROW]
[ROW][C]Median[/C][C]269.826[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]260.7175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]267.984666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]268.378387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]268.378387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]268.378387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]268.378387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]267.75846875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]268.378387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]268.378387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69018&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 Mean266.8792131147542.33689383094566114.202540817508
Geometric Mean266.252970318369
Harmonic Mean265.614659636326
Quadratic Mean267.492390096199
Winsorized Mean ( 1 / 20 )266.8579508196722.32236958028778114.907615516822
Winsorized Mean ( 2 / 20 )267.1184098360662.24544491050386118.960126158752
Winsorized Mean ( 3 / 20 )267.1822459016392.22224955016305120.230532111948
Winsorized Mean ( 4 / 20 )267.1825737704922.22217553366889120.234684309283
Winsorized Mean ( 5 / 20 )267.610688524592.09618674377463127.665480816227
Winsorized Mean ( 6 / 20 )267.7244918032792.05781932202248130.101068124947
Winsorized Mean ( 7 / 20 )267.6252295081972.03707605229602131.377141862991
Winsorized Mean ( 8 / 20 )267.5902131147541.98535997522118134.781710346983
Winsorized Mean ( 9 / 20 )267.5630655737711.96978508270813135.833633792127
Winsorized Mean ( 10 / 20 )267.5268360655741.92278446973092139.135113829483
Winsorized Mean ( 11 / 20 )267.4045737704921.89355348506380141.218389593828
Winsorized Mean ( 12 / 20 )266.8222786885251.74521950286674152.887518303707
Winsorized Mean ( 13 / 20 )266.6560491803281.69253715175442157.548121708242
Winsorized Mean ( 14 / 20 )266.4584426229511.64869748382862161.617546721899
Winsorized Mean ( 15 / 20 )266.9217213114751.54896554995102172.322568000248
Winsorized Mean ( 16 / 20 )267.1908360655741.36437768199093195.833484813152
Winsorized Mean ( 17 / 20 )267.3912131147541.28059764333159208.801893793207
Winsorized Mean ( 18 / 20 )267.3168524590161.22304858104836218.566013322121
Winsorized Mean ( 19 / 20 )267.4856721311481.19296106544717224.219951412147
Winsorized Mean ( 20 / 20 )268.3132131147541.03398369788619259.494626137023
Trimmed Mean ( 1 / 20 )267.0880847457632.25727445834506118.323265369148
Trimmed Mean ( 2 / 20 )267.3343684210532.17683299272481122.808855486163
Trimmed Mean ( 3 / 20 )267.4541272727272.12879193876603125.636574623520
Trimmed Mean ( 4 / 20 )267.5584339622642.07958763051637128.659369788533
Trimmed Mean ( 5 / 20 )267.6708235294122.01731831306810132.686458946738
Trimmed Mean ( 6 / 20 )267.6857959183671.98167965930205135.080256115989
Trimmed Mean ( 7 / 20 )267.6774255319151.94664016933921137.507398515658
Trimmed Mean ( 8 / 20 )267.6875333333331.90604674908486140.441221319391
Trimmed Mean ( 9 / 20 )267.7047906976741.86610901491475143.456137105636
Trimmed Mean ( 10 / 20 )267.7282195121951.81623681050796147.408211287887
Trimmed Mean ( 11 / 20 )267.7597179487181.76130610617828152.023385946074
Trimmed Mean ( 12 / 20 )267.8129459459461.69383204640258158.110685480734
Trimmed Mean ( 13 / 20 )267.9568285714291.64121903939423163.266951052634
Trimmed Mean ( 14 / 20 )268.1417878787881.58005001824212169.704619969631
Trimmed Mean ( 15 / 20 )268.3783870967741.50267829398719178.600029141741
Trimmed Mean ( 16 / 20 )268.5826551724141.42320274638918188.717072008073
Trimmed Mean ( 17 / 20 )268.7791851851851.36774655067602196.512420413226
Trimmed Mean ( 18 / 20 )268.97841.30991789819057205.339892195952
Trimmed Mean ( 19 / 20 )269.2232173913041.23505854137311217.984175140386
Trimmed Mean ( 20 / 20 )269.4888571428571.12031094171326240.548268439417
Median269.826
Midrange260.7175
Midmean - Weighted Average at Xnp267.984666666667
Midmean - Weighted Average at X(n+1)p268.378387096774
Midmean - Empirical Distribution Function268.378387096774
Midmean - Empirical Distribution Function - Averaging268.378387096774
Midmean - Empirical Distribution Function - Interpolation268.378387096774
Midmean - Closest Observation267.75846875
Midmean - True Basic - Statistics Graphics Toolkit268.378387096774
Midmean - MS Excel (old versions)268.378387096774
Number of observations61



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')