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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 computationWed, 17 Dec 2008 01:27:54 -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/2008/Dec/17/t1229502909c29wc7uid5bygoc.htm/, Retrieved Sun, 19 May 2024 07:58:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34275, Retrieved Sun, 19 May 2024 07:58:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact192
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper gemiddelde] [2008-12-17 08:27:54] [c66d07e79164cd7acb2569833ec5bcd8] [Current]
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Dataseries X:
15023.6
12083
15761.3
16943
15070.3
13659.6
14768.9
14725.1
15998.1
15370.6
14956.9
15469.7
15101.8
11703.7
16283.6
16726.5
14968.9
14861
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17420.4
16704.4
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18840.1
20304.8
21132.4
19753.9




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=34275&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=34275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34275&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 Mean17039.6065573771274.23205446981762.135721479826
Geometric Mean16903.8342980599
Harmonic Mean16764.1294910677
Quadratic Mean17171.4992010637
Winsorized Mean ( 1 / 20 )17042.2475409836271.35850407819462.803440042818
Winsorized Mean ( 2 / 20 )17091.9721311475257.17930707929866.4593599121778
Winsorized Mean ( 3 / 20 )17064.3967213115245.91373019673969.3918013754638
Winsorized Mean ( 4 / 20 )17088.868852459231.75436920965573.7369867534178
Winsorized Mean ( 5 / 20 )17098.1065573771229.21208626747174.5951351685051
Winsorized Mean ( 6 / 20 )17088.968852459225.74233590874275.701213880268
Winsorized Mean ( 7 / 20 )17094.7754098361223.00578712449476.6561963716792
Winsorized Mean ( 8 / 20 )17069.4114754098213.59875898999979.9134393669819
Winsorized Mean ( 9 / 20 )17067.4786885246212.61686133027880.2734015625039
Winsorized Mean ( 10 / 20 )17037.5278688525204.08016269102583.4844878806132
Winsorized Mean ( 11 / 20 )17031.7754098361200.21309006974985.0682410620738
Winsorized Mean ( 12 / 20 )17031.4016393443198.06289598941785.9898647561644
Winsorized Mean ( 13 / 20 )17004.5278688525190.65275203531789.1910957870804
Winsorized Mean ( 14 / 20 )17022.9114754098181.37742012332293.8535318444579
Winsorized Mean ( 15 / 20 )16976.4852459016168.680833821029100.642644818283
Winsorized Mean ( 16 / 20 )16986.268852459166.10458859611102.262490133622
Winsorized Mean ( 17 / 20 )16851.2721311475141.525507927579119.068798112144
Winsorized Mean ( 18 / 20 )16897.068852459122.255181448208138.211474166575
Winsorized Mean ( 19 / 20 )16934.3213114754113.69987146483148.938790284504
Winsorized Mean ( 20 / 20 )16959.5344262295109.818137415383154.432909038338
Trimmed Mean ( 1 / 20 )17056.9779661017258.21930830399366.0561678293286
Trimmed Mean ( 2 / 20 )17072.7421052632241.91547783152970.5731698455138
Trimmed Mean ( 3 / 20 )17062.0781818182231.48813938958873.7060577998046
Trimmed Mean ( 4 / 20 )17061.1886792453224.11385459933176.1273269327644
Trimmed Mean ( 5 / 20 )17052.9117647059220.40263938576677.371631357184
Trimmed Mean ( 6 / 20 )17041.6591836735216.41554443582778.7450791859674
Trimmed Mean ( 7 / 20 )17031.4255319149212.25638251704980.2398746739543
Trimmed Mean ( 8 / 20 )17019.1577777778207.52839196019682.0088163215858
Trimmed Mean ( 9 / 20 )17010.2465116279203.83667273371183.4503736913418
Trimmed Mean ( 10 / 20 )17000.7853658537199.03143315790685.4175900565702
Trimmed Mean ( 11 / 20 )16995.0384615385194.75203538078387.2650107523107
Trimmed Mean ( 12 / 20 )16989.5324324324189.77965364534989.5224124720011
Trimmed Mean ( 13 / 20 )16983.4514285714183.33172869347692.6378186122226
Trimmed Mean ( 14 / 20 )16980.4545454545176.34038618808896.2936223092016
Trimmed Mean ( 15 / 20 )16974.4870967742169.037283521289100.418598448646
Trimmed Mean ( 16 / 20 )16974.2068965517162.350383182435104.552921673598
Trimmed Mean ( 17 / 20 )16972.5037037037152.976388648062110.948518615841
Trimmed Mean ( 18 / 20 )16989.904147.319772544851115.326705346544
Trimmed Mean ( 19 / 20 )17003.5826086957145.2319213341117.078824355560
Trimmed Mean ( 20 / 20 )17014.1714285714144.142780593684118.036930871562
Median17170
Midrange16527.15
Midmean - Weighted Average at Xnp16920.7533333333
Midmean - Weighted Average at X(n+1)p16974.4870967742
Midmean - Empirical Distribution Function16974.4870967742
Midmean - Empirical Distribution Function - Averaging16974.4870967742
Midmean - Empirical Distribution Function - Interpolation16974.4870967742
Midmean - Closest Observation16922.340625
Midmean - True Basic - Statistics Graphics Toolkit16974.4870967742
Midmean - MS Excel (old versions)16974.4870967742
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17039.6065573771 & 274.232054469817 & 62.135721479826 \tabularnewline
Geometric Mean & 16903.8342980599 &  &  \tabularnewline
Harmonic Mean & 16764.1294910677 &  &  \tabularnewline
Quadratic Mean & 17171.4992010637 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17042.2475409836 & 271.358504078194 & 62.803440042818 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17091.9721311475 & 257.179307079298 & 66.4593599121778 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17064.3967213115 & 245.913730196739 & 69.3918013754638 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17088.868852459 & 231.754369209655 & 73.7369867534178 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17098.1065573771 & 229.212086267471 & 74.5951351685051 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 17088.968852459 & 225.742335908742 & 75.701213880268 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 17094.7754098361 & 223.005787124494 & 76.6561963716792 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17069.4114754098 & 213.598758989999 & 79.9134393669819 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17067.4786885246 & 212.616861330278 & 80.2734015625039 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17037.5278688525 & 204.080162691025 & 83.4844878806132 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17031.7754098361 & 200.213090069749 & 85.0682410620738 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17031.4016393443 & 198.062895989417 & 85.9898647561644 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17004.5278688525 & 190.652752035317 & 89.1910957870804 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17022.9114754098 & 181.377420123322 & 93.8535318444579 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 16976.4852459016 & 168.680833821029 & 100.642644818283 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 16986.268852459 & 166.10458859611 & 102.262490133622 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 16851.2721311475 & 141.525507927579 & 119.068798112144 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 16897.068852459 & 122.255181448208 & 138.211474166575 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 16934.3213114754 & 113.69987146483 & 148.938790284504 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 16959.5344262295 & 109.818137415383 & 154.432909038338 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17056.9779661017 & 258.219308303993 & 66.0561678293286 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17072.7421052632 & 241.915477831529 & 70.5731698455138 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17062.0781818182 & 231.488139389588 & 73.7060577998046 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17061.1886792453 & 224.113854599331 & 76.1273269327644 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17052.9117647059 & 220.402639385766 & 77.371631357184 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17041.6591836735 & 216.415544435827 & 78.7450791859674 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17031.4255319149 & 212.256382517049 & 80.2398746739543 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17019.1577777778 & 207.528391960196 & 82.0088163215858 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17010.2465116279 & 203.836672733711 & 83.4503736913418 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17000.7853658537 & 199.031433157906 & 85.4175900565702 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 16995.0384615385 & 194.752035380783 & 87.2650107523107 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 16989.5324324324 & 189.779653645349 & 89.5224124720011 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 16983.4514285714 & 183.331728693476 & 92.6378186122226 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 16980.4545454545 & 176.340386188088 & 96.2936223092016 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 16974.4870967742 & 169.037283521289 & 100.418598448646 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 16974.2068965517 & 162.350383182435 & 104.552921673598 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 16972.5037037037 & 152.976388648062 & 110.948518615841 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 16989.904 & 147.319772544851 & 115.326705346544 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17003.5826086957 & 145.2319213341 & 117.078824355560 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17014.1714285714 & 144.142780593684 & 118.036930871562 \tabularnewline
Median & 17170 &  &  \tabularnewline
Midrange & 16527.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16920.7533333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16974.4870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16974.4870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16974.4870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16974.4870967742 &  &  \tabularnewline
Midmean - Closest Observation & 16922.340625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16974.4870967742 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16974.4870967742 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34275&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]17039.6065573771[/C][C]274.232054469817[/C][C]62.135721479826[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16903.8342980599[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16764.1294910677[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17171.4992010637[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17042.2475409836[/C][C]271.358504078194[/C][C]62.803440042818[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17091.9721311475[/C][C]257.179307079298[/C][C]66.4593599121778[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17064.3967213115[/C][C]245.913730196739[/C][C]69.3918013754638[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17088.868852459[/C][C]231.754369209655[/C][C]73.7369867534178[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17098.1065573771[/C][C]229.212086267471[/C][C]74.5951351685051[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]17088.968852459[/C][C]225.742335908742[/C][C]75.701213880268[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]17094.7754098361[/C][C]223.005787124494[/C][C]76.6561963716792[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17069.4114754098[/C][C]213.598758989999[/C][C]79.9134393669819[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17067.4786885246[/C][C]212.616861330278[/C][C]80.2734015625039[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17037.5278688525[/C][C]204.080162691025[/C][C]83.4844878806132[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17031.7754098361[/C][C]200.213090069749[/C][C]85.0682410620738[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17031.4016393443[/C][C]198.062895989417[/C][C]85.9898647561644[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17004.5278688525[/C][C]190.652752035317[/C][C]89.1910957870804[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17022.9114754098[/C][C]181.377420123322[/C][C]93.8535318444579[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]16976.4852459016[/C][C]168.680833821029[/C][C]100.642644818283[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]16986.268852459[/C][C]166.10458859611[/C][C]102.262490133622[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]16851.2721311475[/C][C]141.525507927579[/C][C]119.068798112144[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]16897.068852459[/C][C]122.255181448208[/C][C]138.211474166575[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]16934.3213114754[/C][C]113.69987146483[/C][C]148.938790284504[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]16959.5344262295[/C][C]109.818137415383[/C][C]154.432909038338[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17056.9779661017[/C][C]258.219308303993[/C][C]66.0561678293286[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17072.7421052632[/C][C]241.915477831529[/C][C]70.5731698455138[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17062.0781818182[/C][C]231.488139389588[/C][C]73.7060577998046[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17061.1886792453[/C][C]224.113854599331[/C][C]76.1273269327644[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17052.9117647059[/C][C]220.402639385766[/C][C]77.371631357184[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17041.6591836735[/C][C]216.415544435827[/C][C]78.7450791859674[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17031.4255319149[/C][C]212.256382517049[/C][C]80.2398746739543[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17019.1577777778[/C][C]207.528391960196[/C][C]82.0088163215858[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17010.2465116279[/C][C]203.836672733711[/C][C]83.4503736913418[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17000.7853658537[/C][C]199.031433157906[/C][C]85.4175900565702[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]16995.0384615385[/C][C]194.752035380783[/C][C]87.2650107523107[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]16989.5324324324[/C][C]189.779653645349[/C][C]89.5224124720011[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]16983.4514285714[/C][C]183.331728693476[/C][C]92.6378186122226[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]16980.4545454545[/C][C]176.340386188088[/C][C]96.2936223092016[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]16974.4870967742[/C][C]169.037283521289[/C][C]100.418598448646[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]16974.2068965517[/C][C]162.350383182435[/C][C]104.552921673598[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]16972.5037037037[/C][C]152.976388648062[/C][C]110.948518615841[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]16989.904[/C][C]147.319772544851[/C][C]115.326705346544[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17003.5826086957[/C][C]145.2319213341[/C][C]117.078824355560[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17014.1714285714[/C][C]144.142780593684[/C][C]118.036930871562[/C][/ROW]
[ROW][C]Median[/C][C]17170[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16527.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16920.7533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16974.4870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16974.4870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16974.4870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16974.4870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16922.340625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16974.4870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16974.4870967742[/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=34275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34275&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 Mean17039.6065573771274.23205446981762.135721479826
Geometric Mean16903.8342980599
Harmonic Mean16764.1294910677
Quadratic Mean17171.4992010637
Winsorized Mean ( 1 / 20 )17042.2475409836271.35850407819462.803440042818
Winsorized Mean ( 2 / 20 )17091.9721311475257.17930707929866.4593599121778
Winsorized Mean ( 3 / 20 )17064.3967213115245.91373019673969.3918013754638
Winsorized Mean ( 4 / 20 )17088.868852459231.75436920965573.7369867534178
Winsorized Mean ( 5 / 20 )17098.1065573771229.21208626747174.5951351685051
Winsorized Mean ( 6 / 20 )17088.968852459225.74233590874275.701213880268
Winsorized Mean ( 7 / 20 )17094.7754098361223.00578712449476.6561963716792
Winsorized Mean ( 8 / 20 )17069.4114754098213.59875898999979.9134393669819
Winsorized Mean ( 9 / 20 )17067.4786885246212.61686133027880.2734015625039
Winsorized Mean ( 10 / 20 )17037.5278688525204.08016269102583.4844878806132
Winsorized Mean ( 11 / 20 )17031.7754098361200.21309006974985.0682410620738
Winsorized Mean ( 12 / 20 )17031.4016393443198.06289598941785.9898647561644
Winsorized Mean ( 13 / 20 )17004.5278688525190.65275203531789.1910957870804
Winsorized Mean ( 14 / 20 )17022.9114754098181.37742012332293.8535318444579
Winsorized Mean ( 15 / 20 )16976.4852459016168.680833821029100.642644818283
Winsorized Mean ( 16 / 20 )16986.268852459166.10458859611102.262490133622
Winsorized Mean ( 17 / 20 )16851.2721311475141.525507927579119.068798112144
Winsorized Mean ( 18 / 20 )16897.068852459122.255181448208138.211474166575
Winsorized Mean ( 19 / 20 )16934.3213114754113.69987146483148.938790284504
Winsorized Mean ( 20 / 20 )16959.5344262295109.818137415383154.432909038338
Trimmed Mean ( 1 / 20 )17056.9779661017258.21930830399366.0561678293286
Trimmed Mean ( 2 / 20 )17072.7421052632241.91547783152970.5731698455138
Trimmed Mean ( 3 / 20 )17062.0781818182231.48813938958873.7060577998046
Trimmed Mean ( 4 / 20 )17061.1886792453224.11385459933176.1273269327644
Trimmed Mean ( 5 / 20 )17052.9117647059220.40263938576677.371631357184
Trimmed Mean ( 6 / 20 )17041.6591836735216.41554443582778.7450791859674
Trimmed Mean ( 7 / 20 )17031.4255319149212.25638251704980.2398746739543
Trimmed Mean ( 8 / 20 )17019.1577777778207.52839196019682.0088163215858
Trimmed Mean ( 9 / 20 )17010.2465116279203.83667273371183.4503736913418
Trimmed Mean ( 10 / 20 )17000.7853658537199.03143315790685.4175900565702
Trimmed Mean ( 11 / 20 )16995.0384615385194.75203538078387.2650107523107
Trimmed Mean ( 12 / 20 )16989.5324324324189.77965364534989.5224124720011
Trimmed Mean ( 13 / 20 )16983.4514285714183.33172869347692.6378186122226
Trimmed Mean ( 14 / 20 )16980.4545454545176.34038618808896.2936223092016
Trimmed Mean ( 15 / 20 )16974.4870967742169.037283521289100.418598448646
Trimmed Mean ( 16 / 20 )16974.2068965517162.350383182435104.552921673598
Trimmed Mean ( 17 / 20 )16972.5037037037152.976388648062110.948518615841
Trimmed Mean ( 18 / 20 )16989.904147.319772544851115.326705346544
Trimmed Mean ( 19 / 20 )17003.5826086957145.2319213341117.078824355560
Trimmed Mean ( 20 / 20 )17014.1714285714144.142780593684118.036930871562
Median17170
Midrange16527.15
Midmean - Weighted Average at Xnp16920.7533333333
Midmean - Weighted Average at X(n+1)p16974.4870967742
Midmean - Empirical Distribution Function16974.4870967742
Midmean - Empirical Distribution Function - Averaging16974.4870967742
Midmean - Empirical Distribution Function - Interpolation16974.4870967742
Midmean - Closest Observation16922.340625
Midmean - True Basic - Statistics Graphics Toolkit16974.4870967742
Midmean - MS Excel (old versions)16974.4870967742
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')