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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 24 Dec 2010 10:58:09 +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/Dec/24/t12931881573kmdplp2sjobi2r.htm/, Retrieved Tue, 30 Apr 2024 07:17:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114747, Retrieved Tue, 30 Apr 2024 07:17:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2009-12-13 10:05:40] [ebd107afac1bd6180acb277edd05815b]
-    D    [Central Tendency] [CT uitvoer] [2010-12-24 10:58:09] [817f44ab92560f82acbc5e6c80d9a294] [Current]
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Post a new message
Dataseries X:
19685.6
19601.7
16006.9
17681.2
19790.4
17014.2
17424.5
18908.9
15692.1
15160.0
15794.3
16032.1
16065.0
16236.8
12521.0
14762.1
15446.9
13635.0
14212.6
15021.7
14134.3
13721.4
14384.5
15638.6
19711.6
20359.8
16141.4
20056.9
20605.5
19325.8
20547.7
19211.2
19009.5
18746.8
16471.5
18957.2
20515.2
18374.4
16192.9
18147.5
19301.4
18344.7
17183.6
19630.0
17167.2
17428.5
16016.5
18466.5
18406.6
18174.1
14851.9
16260.7
18329.6
18003.8
15903.8
19554.2
16554.2
16198.9
16571.8
17535.2
16198.1




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=114747&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=114747&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114747&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 Mean17262.7540983607256.23149682442267.3717100056189
Geometric Mean17145.9222433747
Harmonic Mean17026.4637780688
Quadratic Mean17376.4770266691
Winsorized Mean ( 1 / 20 )17280.068852459250.99297995474468.84682135562
Winsorized Mean ( 2 / 20 )17281.8360655738250.08363965944669.1042248469651
Winsorized Mean ( 3 / 20 )17294.5243.85440718108770.9214165941116
Winsorized Mean ( 4 / 20 )17279.7721311475238.74254979513872.3782674934783
Winsorized Mean ( 5 / 20 )17272.0180327869231.67150733050474.5539157223443
Winsorized Mean ( 6 / 20 )17301.4081967213222.88050191248277.6263874509534
Winsorized Mean ( 7 / 20 )17308.7295081967220.40778827670578.53048044957
Winsorized Mean ( 8 / 20 )17323.7065573771215.04468758954680.5586352844142
Winsorized Mean ( 9 / 20 )17339.9360655738210.71805317676482.2897507079184
Winsorized Mean ( 10 / 20 )17379.1819672131201.50136846825786.2484562726475
Winsorized Mean ( 11 / 20 )17372.5639344262188.82974025152492.001206543449
Winsorized Mean ( 12 / 20 )17378.2885245902186.40449194701393.2289149422973
Winsorized Mean ( 13 / 20 )17380.8459016393179.87792916876396.6257838410653
Winsorized Mean ( 14 / 20 )17359.6852459016168.513159039868103.016793138360
Winsorized Mean ( 15 / 20 )17372.1770491803162.822784575788106.693771970803
Winsorized Mean ( 16 / 20 )17362.0262295082160.425066703383108.225145772322
Winsorized Mean ( 17 / 20 )17321.1983606557152.66713182378113.457285492526
Winsorized Mean ( 18 / 20 )17248.1950819672138.789544818632124.275896318465
Winsorized Mean ( 19 / 20 )17253.3344262295132.720786045567129.997229072362
Winsorized Mean ( 20 / 20 )17259.6622950820128.851104462144133.950441225382
Trimmed Mean ( 1 / 20 )17286.4661016949245.71393568896470.3519971434463
Trimmed Mean ( 2 / 20 )17293.3122807018239.19827744786172.2969766555751
Trimmed Mean ( 3 / 20 )17299.6763636364231.73444910524674.6530195680117
Trimmed Mean ( 4 / 20 )17301.6622641509225.47109675819076.7356105191006
Trimmed Mean ( 5 / 20 )17308.2078431373219.59993938788378.8169973606663
Trimmed Mean ( 6 / 20 )17317.2183673469214.54172838870480.717250193733
Trimmed Mean ( 7 / 20 )17320.6382978723210.71655797172782.1987529817013
Trimmed Mean ( 8 / 20 )17322.9444444444206.34875527512083.9498373583506
Trimmed Mean ( 9 / 20 )17322.8093023256201.99693718865885.7577819912522
Trimmed Mean ( 10 / 20 )17319.9780487805197.26541142032987.8003798236856
Trimmed Mean ( 11 / 20 )17310.7179487179193.19541203594489.6021171843217
Trimmed Mean ( 12 / 20 )17301.4486486486190.72948961168090.711974765276
Trimmed Mean ( 13 / 20 )17290.2885714286187.55610847981392.1872857758167
Trimmed Mean ( 14 / 20 )17277.4121212121184.45154583402293.6691099176755
Trimmed Mean ( 15 / 20 )17265.8483870968182.68175994493894.5132584243816
Trimmed Mean ( 16 / 20 )17250.9379310345180.94059454427195.3403407039964
Trimmed Mean ( 17 / 20 )17235.2518518519178.25185584760796.6904482979792
Trimmed Mean ( 18 / 20 )17222.916175.92137360006497.9012137499234
Trimmed Mean ( 19 / 20 )17219.1913043478176.04239573289597.812752619398
Trimmed Mean ( 20 / 20 )17213.9714285714176.67068101587397.4353601264766
Median17183.6
Midrange16563.25
Midmean - Weighted Average at Xnp17209.47
Midmean - Weighted Average at X(n+1)p17265.8483870968
Midmean - Empirical Distribution Function17265.8483870968
Midmean - Empirical Distribution Function - Averaging17265.8483870968
Midmean - Empirical Distribution Function - Interpolation17265.8483870968
Midmean - Closest Observation17223.284375
Midmean - True Basic - Statistics Graphics Toolkit17265.8483870968
Midmean - MS Excel (old versions)17265.8483870968
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17262.7540983607 & 256.231496824422 & 67.3717100056189 \tabularnewline
Geometric Mean & 17145.9222433747 &  &  \tabularnewline
Harmonic Mean & 17026.4637780688 &  &  \tabularnewline
Quadratic Mean & 17376.4770266691 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17280.068852459 & 250.992979954744 & 68.84682135562 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17281.8360655738 & 250.083639659446 & 69.1042248469651 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17294.5 & 243.854407181087 & 70.9214165941116 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17279.7721311475 & 238.742549795138 & 72.3782674934783 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17272.0180327869 & 231.671507330504 & 74.5539157223443 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 17301.4081967213 & 222.880501912482 & 77.6263874509534 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 17308.7295081967 & 220.407788276705 & 78.53048044957 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17323.7065573771 & 215.044687589546 & 80.5586352844142 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17339.9360655738 & 210.718053176764 & 82.2897507079184 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17379.1819672131 & 201.501368468257 & 86.2484562726475 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17372.5639344262 & 188.829740251524 & 92.001206543449 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17378.2885245902 & 186.404491947013 & 93.2289149422973 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17380.8459016393 & 179.877929168763 & 96.6257838410653 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17359.6852459016 & 168.513159039868 & 103.016793138360 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17372.1770491803 & 162.822784575788 & 106.693771970803 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 17362.0262295082 & 160.425066703383 & 108.225145772322 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17321.1983606557 & 152.66713182378 & 113.457285492526 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17248.1950819672 & 138.789544818632 & 124.275896318465 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17253.3344262295 & 132.720786045567 & 129.997229072362 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 17259.6622950820 & 128.851104462144 & 133.950441225382 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17286.4661016949 & 245.713935688964 & 70.3519971434463 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17293.3122807018 & 239.198277447861 & 72.2969766555751 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17299.6763636364 & 231.734449105246 & 74.6530195680117 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17301.6622641509 & 225.471096758190 & 76.7356105191006 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17308.2078431373 & 219.599939387883 & 78.8169973606663 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17317.2183673469 & 214.541728388704 & 80.717250193733 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17320.6382978723 & 210.716557971727 & 82.1987529817013 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17322.9444444444 & 206.348755275120 & 83.9498373583506 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17322.8093023256 & 201.996937188658 & 85.7577819912522 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17319.9780487805 & 197.265411420329 & 87.8003798236856 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17310.7179487179 & 193.195412035944 & 89.6021171843217 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17301.4486486486 & 190.729489611680 & 90.711974765276 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17290.2885714286 & 187.556108479813 & 92.1872857758167 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17277.4121212121 & 184.451545834022 & 93.6691099176755 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 17265.8483870968 & 182.681759944938 & 94.5132584243816 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 17250.9379310345 & 180.940594544271 & 95.3403407039964 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 17235.2518518519 & 178.251855847607 & 96.6904482979792 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 17222.916 & 175.921373600064 & 97.9012137499234 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17219.1913043478 & 176.042395732895 & 97.812752619398 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17213.9714285714 & 176.670681015873 & 97.4353601264766 \tabularnewline
Median & 17183.6 &  &  \tabularnewline
Midrange & 16563.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17209.47 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17265.8483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17265.8483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17265.8483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17265.8483870968 &  &  \tabularnewline
Midmean - Closest Observation & 17223.284375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17265.8483870968 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17265.8483870968 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114747&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]17262.7540983607[/C][C]256.231496824422[/C][C]67.3717100056189[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17145.9222433747[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17026.4637780688[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17376.4770266691[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17280.068852459[/C][C]250.992979954744[/C][C]68.84682135562[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17281.8360655738[/C][C]250.083639659446[/C][C]69.1042248469651[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17294.5[/C][C]243.854407181087[/C][C]70.9214165941116[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17279.7721311475[/C][C]238.742549795138[/C][C]72.3782674934783[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17272.0180327869[/C][C]231.671507330504[/C][C]74.5539157223443[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]17301.4081967213[/C][C]222.880501912482[/C][C]77.6263874509534[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]17308.7295081967[/C][C]220.407788276705[/C][C]78.53048044957[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17323.7065573771[/C][C]215.044687589546[/C][C]80.5586352844142[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17339.9360655738[/C][C]210.718053176764[/C][C]82.2897507079184[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17379.1819672131[/C][C]201.501368468257[/C][C]86.2484562726475[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17372.5639344262[/C][C]188.829740251524[/C][C]92.001206543449[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17378.2885245902[/C][C]186.404491947013[/C][C]93.2289149422973[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17380.8459016393[/C][C]179.877929168763[/C][C]96.6257838410653[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17359.6852459016[/C][C]168.513159039868[/C][C]103.016793138360[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17372.1770491803[/C][C]162.822784575788[/C][C]106.693771970803[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]17362.0262295082[/C][C]160.425066703383[/C][C]108.225145772322[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17321.1983606557[/C][C]152.66713182378[/C][C]113.457285492526[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17248.1950819672[/C][C]138.789544818632[/C][C]124.275896318465[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17253.3344262295[/C][C]132.720786045567[/C][C]129.997229072362[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]17259.6622950820[/C][C]128.851104462144[/C][C]133.950441225382[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17286.4661016949[/C][C]245.713935688964[/C][C]70.3519971434463[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17293.3122807018[/C][C]239.198277447861[/C][C]72.2969766555751[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17299.6763636364[/C][C]231.734449105246[/C][C]74.6530195680117[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17301.6622641509[/C][C]225.471096758190[/C][C]76.7356105191006[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17308.2078431373[/C][C]219.599939387883[/C][C]78.8169973606663[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17317.2183673469[/C][C]214.541728388704[/C][C]80.717250193733[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17320.6382978723[/C][C]210.716557971727[/C][C]82.1987529817013[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17322.9444444444[/C][C]206.348755275120[/C][C]83.9498373583506[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17322.8093023256[/C][C]201.996937188658[/C][C]85.7577819912522[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17319.9780487805[/C][C]197.265411420329[/C][C]87.8003798236856[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17310.7179487179[/C][C]193.195412035944[/C][C]89.6021171843217[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17301.4486486486[/C][C]190.729489611680[/C][C]90.711974765276[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17290.2885714286[/C][C]187.556108479813[/C][C]92.1872857758167[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17277.4121212121[/C][C]184.451545834022[/C][C]93.6691099176755[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]17265.8483870968[/C][C]182.681759944938[/C][C]94.5132584243816[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]17250.9379310345[/C][C]180.940594544271[/C][C]95.3403407039964[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]17235.2518518519[/C][C]178.251855847607[/C][C]96.6904482979792[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]17222.916[/C][C]175.921373600064[/C][C]97.9012137499234[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17219.1913043478[/C][C]176.042395732895[/C][C]97.812752619398[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17213.9714285714[/C][C]176.670681015873[/C][C]97.4353601264766[/C][/ROW]
[ROW][C]Median[/C][C]17183.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16563.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17209.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17265.8483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17265.8483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17265.8483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17265.8483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17223.284375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17265.8483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17265.8483870968[/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=114747&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114747&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 Mean17262.7540983607256.23149682442267.3717100056189
Geometric Mean17145.9222433747
Harmonic Mean17026.4637780688
Quadratic Mean17376.4770266691
Winsorized Mean ( 1 / 20 )17280.068852459250.99297995474468.84682135562
Winsorized Mean ( 2 / 20 )17281.8360655738250.08363965944669.1042248469651
Winsorized Mean ( 3 / 20 )17294.5243.85440718108770.9214165941116
Winsorized Mean ( 4 / 20 )17279.7721311475238.74254979513872.3782674934783
Winsorized Mean ( 5 / 20 )17272.0180327869231.67150733050474.5539157223443
Winsorized Mean ( 6 / 20 )17301.4081967213222.88050191248277.6263874509534
Winsorized Mean ( 7 / 20 )17308.7295081967220.40778827670578.53048044957
Winsorized Mean ( 8 / 20 )17323.7065573771215.04468758954680.5586352844142
Winsorized Mean ( 9 / 20 )17339.9360655738210.71805317676482.2897507079184
Winsorized Mean ( 10 / 20 )17379.1819672131201.50136846825786.2484562726475
Winsorized Mean ( 11 / 20 )17372.5639344262188.82974025152492.001206543449
Winsorized Mean ( 12 / 20 )17378.2885245902186.40449194701393.2289149422973
Winsorized Mean ( 13 / 20 )17380.8459016393179.87792916876396.6257838410653
Winsorized Mean ( 14 / 20 )17359.6852459016168.513159039868103.016793138360
Winsorized Mean ( 15 / 20 )17372.1770491803162.822784575788106.693771970803
Winsorized Mean ( 16 / 20 )17362.0262295082160.425066703383108.225145772322
Winsorized Mean ( 17 / 20 )17321.1983606557152.66713182378113.457285492526
Winsorized Mean ( 18 / 20 )17248.1950819672138.789544818632124.275896318465
Winsorized Mean ( 19 / 20 )17253.3344262295132.720786045567129.997229072362
Winsorized Mean ( 20 / 20 )17259.6622950820128.851104462144133.950441225382
Trimmed Mean ( 1 / 20 )17286.4661016949245.71393568896470.3519971434463
Trimmed Mean ( 2 / 20 )17293.3122807018239.19827744786172.2969766555751
Trimmed Mean ( 3 / 20 )17299.6763636364231.73444910524674.6530195680117
Trimmed Mean ( 4 / 20 )17301.6622641509225.47109675819076.7356105191006
Trimmed Mean ( 5 / 20 )17308.2078431373219.59993938788378.8169973606663
Trimmed Mean ( 6 / 20 )17317.2183673469214.54172838870480.717250193733
Trimmed Mean ( 7 / 20 )17320.6382978723210.71655797172782.1987529817013
Trimmed Mean ( 8 / 20 )17322.9444444444206.34875527512083.9498373583506
Trimmed Mean ( 9 / 20 )17322.8093023256201.99693718865885.7577819912522
Trimmed Mean ( 10 / 20 )17319.9780487805197.26541142032987.8003798236856
Trimmed Mean ( 11 / 20 )17310.7179487179193.19541203594489.6021171843217
Trimmed Mean ( 12 / 20 )17301.4486486486190.72948961168090.711974765276
Trimmed Mean ( 13 / 20 )17290.2885714286187.55610847981392.1872857758167
Trimmed Mean ( 14 / 20 )17277.4121212121184.45154583402293.6691099176755
Trimmed Mean ( 15 / 20 )17265.8483870968182.68175994493894.5132584243816
Trimmed Mean ( 16 / 20 )17250.9379310345180.94059454427195.3403407039964
Trimmed Mean ( 17 / 20 )17235.2518518519178.25185584760796.6904482979792
Trimmed Mean ( 18 / 20 )17222.916175.92137360006497.9012137499234
Trimmed Mean ( 19 / 20 )17219.1913043478176.04239573289597.812752619398
Trimmed Mean ( 20 / 20 )17213.9714285714176.67068101587397.4353601264766
Median17183.6
Midrange16563.25
Midmean - Weighted Average at Xnp17209.47
Midmean - Weighted Average at X(n+1)p17265.8483870968
Midmean - Empirical Distribution Function17265.8483870968
Midmean - Empirical Distribution Function - Averaging17265.8483870968
Midmean - Empirical Distribution Function - Interpolation17265.8483870968
Midmean - Closest Observation17223.284375
Midmean - True Basic - Statistics Graphics Toolkit17265.8483870968
Midmean - MS Excel (old versions)17265.8483870968
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')