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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Dec 2007 03:16:56 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/13/t11975400932u33d3xsclg3byq.htm/, Retrieved Sun, 05 May 2024 11:41:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3390, Retrieved Sun, 05 May 2024 11:41:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [ct] [2007-12-13 10:16:56] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]
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Dataseries X:
0.9383
0.9217
0.9095
0.892
0.8742
0.8532
0.8607
0.9005
0.9111
0.9059
0.8883
0.8924
0.8833
0.87
0.8758
0.8858
0.917
0.9554
0.9922
0.9778
0.9808
0.9811
1.0014
1.0183
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.249
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.202
1.2271
1.277
1.265
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3390&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3390&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3390&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.14115750.017999960599025163.3977776630137
Geometric Mean1.12925659335285
Harmonic Mean1.11675298915913
Quadratic Mean1.15231780674864
Winsorized Mean ( 1 / 26 )1.141133750.017962530968917963.528561313247
Winsorized Mean ( 2 / 26 )1.141101250.017876847474125163.8312348780526
Winsorized Mean ( 3 / 26 )1.141240.017844019456942663.9564422552776
Winsorized Mean ( 4 / 26 )1.140860.017761689465200964.231502427469
Winsorized Mean ( 5 / 26 )1.141260.017664247629146264.608469262903
Winsorized Mean ( 6 / 26 )1.14020250.017457526665099465.3129462078645
Winsorized Mean ( 7 / 26 )1.14016750.017383629518525265.5885756645329
Winsorized Mean ( 8 / 26 )1.14041750.017300271525545365.9190520978862
Winsorized Mean ( 9 / 26 )1.139540.017172834339168066.3571299585023
Winsorized Mean ( 10 / 26 )1.139990.016918927832086267.3795651423044
Winsorized Mean ( 11 / 26 )1.13990750.016684277046183368.3222591452213
Winsorized Mean ( 12 / 26 )1.14022250.016561211925074168.848977065119
Winsorized Mean ( 13 / 26 )1.14035250.016499572968678169.1140614466072
Winsorized Mean ( 14 / 26 )1.14045750.016206636472250270.3697835113872
Winsorized Mean ( 15 / 26 )1.140270.015926387366787371.5962743928925
Winsorized Mean ( 16 / 26 )1.142190.015192574864474475.180804451446
Winsorized Mean ( 17 / 26 )1.14495250.014482022353244579.0602632748657
Winsorized Mean ( 18 / 26 )1.1490250.013549187758830884.803976478303
Winsorized Mean ( 19 / 26 )1.148953750.013345326416531286.0940912300774
Winsorized Mean ( 20 / 26 )1.148778750.013304856314988986.3428151949162
Winsorized Mean ( 21 / 26 )1.15080.012741408994477790.3196813240022
Winsorized Mean ( 22 / 26 )1.153220.012332400646111193.5113959635793
Winsorized Mean ( 23 / 26 )1.157130.0114727313468486100.859155942656
Winsorized Mean ( 24 / 26 )1.170240.00950368476174547123.135397410327
Winsorized Mean ( 25 / 26 )1.17117750.00837767753816918139.797395479123
Winsorized Mean ( 26 / 26 )1.16584750.00749545790204924155.540530710106
Trimmed Mean ( 1 / 26 )1.141894871794870.017840476741978464.0058496367426
Trimmed Mean ( 2 / 26 )1.142696052631580.017691070543786464.5916848165487
Trimmed Mean ( 3 / 26 )1.143558108108110.017560877768911565.1196439697668
Trimmed Mean ( 4 / 26 )1.144416666666670.017414064544929265.7179525040814
Trimmed Mean ( 5 / 26 )1.145432857142860.017260549415771266.361320810348
Trimmed Mean ( 6 / 26 )1.146414705882350.017098830916798767.0463794548701
Trimmed Mean ( 7 / 26 )1.147669696969700.016949164493121967.7124643775467
Trimmed Mean ( 8 / 26 )1.1490093750.016776950853898268.4873780108272
Trimmed Mean ( 9 / 26 )1.150395161290320.016578151286923369.3922465406467
Trimmed Mean ( 10 / 26 )1.152003333333330.016352627765589470.4475971597347
Trimmed Mean ( 11 / 26 )1.153660344827590.016119867827494571.5676057132347
Trimmed Mean ( 12 / 26 )1.155446428571430.015869534229182872.8090952062507
Trimmed Mean ( 13 / 26 )1.157325925925930.015573437801457774.3140943368072
Trimmed Mean ( 14 / 26 )1.159334615384620.015205847213382776.2426847459236
Trimmed Mean ( 15 / 26 )1.1614920.014793129359432378.5156386981377
Trimmed Mean ( 16 / 26 )1.163850.014315857831823981.2979573890979
Trimmed Mean ( 17 / 26 )1.166204347826090.013857066059348884.1595430685917
Trimmed Mean ( 18 / 26 )1.168477272727270.013415942546640687.0961744704151
Trimmed Mean ( 19 / 26 )1.170535714285710.013047269916783489.7149918528162
Trimmed Mean ( 20 / 26 )1.17280750.012587080977416993.1754949463015
Trimmed Mean ( 21 / 26 )1.175336842105260.01195728494152798.2946252307982
Trimmed Mean ( 22 / 26 )1.177933333333330.0112406539661757104.792242237672
Trimmed Mean ( 23 / 26 )1.180576470588240.0103542959634547114.018034133374
Trimmed Mean ( 24 / 26 )1.1831250.00937747064219139126.166750624294
Trimmed Mean ( 25 / 26 )1.184556666666670.0087407760029702135.520766836279
Trimmed Mean ( 26 / 26 )1.186085714285710.0081929940297537144.768287390217
Median1.2011
Midrange1.1124
Midmean - Weighted Average at Xnp1.16812439024390
Midmean - Weighted Average at X(n+1)p1.1728075
Midmean - Empirical Distribution Function1.16812439024390
Midmean - Empirical Distribution Function - Averaging1.1728075
Midmean - Empirical Distribution Function - Interpolation1.1728075
Midmean - Closest Observation1.16812439024390
Midmean - True Basic - Statistics Graphics Toolkit1.1728075
Midmean - MS Excel (old versions)1.17053571428571
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.1411575 & 0.0179999605990251 & 63.3977776630137 \tabularnewline
Geometric Mean & 1.12925659335285 &  &  \tabularnewline
Harmonic Mean & 1.11675298915913 &  &  \tabularnewline
Quadratic Mean & 1.15231780674864 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 1.14113375 & 0.0179625309689179 & 63.528561313247 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 1.14110125 & 0.0178768474741251 & 63.8312348780526 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 1.14124 & 0.0178440194569426 & 63.9564422552776 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 1.14086 & 0.0177616894652009 & 64.231502427469 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 1.14126 & 0.0176642476291462 & 64.608469262903 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 1.1402025 & 0.0174575266650994 & 65.3129462078645 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 1.1401675 & 0.0173836295185252 & 65.5885756645329 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 1.1404175 & 0.0173002715255453 & 65.9190520978862 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 1.13954 & 0.0171728343391680 & 66.3571299585023 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 1.13999 & 0.0169189278320862 & 67.3795651423044 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 1.1399075 & 0.0166842770461833 & 68.3222591452213 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 1.1402225 & 0.0165612119250741 & 68.848977065119 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 1.1403525 & 0.0164995729686781 & 69.1140614466072 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 1.1404575 & 0.0162066364722502 & 70.3697835113872 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 1.14027 & 0.0159263873667873 & 71.5962743928925 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 1.14219 & 0.0151925748644744 & 75.180804451446 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 1.1449525 & 0.0144820223532445 & 79.0602632748657 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 1.149025 & 0.0135491877588308 & 84.803976478303 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 1.14895375 & 0.0133453264165312 & 86.0940912300774 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 1.14877875 & 0.0133048563149889 & 86.3428151949162 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 1.1508 & 0.0127414089944777 & 90.3196813240022 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 1.15322 & 0.0123324006461111 & 93.5113959635793 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 1.15713 & 0.0114727313468486 & 100.859155942656 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 1.17024 & 0.00950368476174547 & 123.135397410327 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 1.1711775 & 0.00837767753816918 & 139.797395479123 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 1.1658475 & 0.00749545790204924 & 155.540530710106 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 1.14189487179487 & 0.0178404767419784 & 64.0058496367426 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 1.14269605263158 & 0.0176910705437864 & 64.5916848165487 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 1.14355810810811 & 0.0175608777689115 & 65.1196439697668 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 1.14441666666667 & 0.0174140645449292 & 65.7179525040814 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 1.14543285714286 & 0.0172605494157712 & 66.361320810348 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 1.14641470588235 & 0.0170988309167987 & 67.0463794548701 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 1.14766969696970 & 0.0169491644931219 & 67.7124643775467 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 1.149009375 & 0.0167769508538982 & 68.4873780108272 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 1.15039516129032 & 0.0165781512869233 & 69.3922465406467 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 1.15200333333333 & 0.0163526277655894 & 70.4475971597347 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 1.15366034482759 & 0.0161198678274945 & 71.5676057132347 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 1.15544642857143 & 0.0158695342291828 & 72.8090952062507 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 1.15732592592593 & 0.0155734378014577 & 74.3140943368072 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 1.15933461538462 & 0.0152058472133827 & 76.2426847459236 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 1.161492 & 0.0147931293594323 & 78.5156386981377 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 1.16385 & 0.0143158578318239 & 81.2979573890979 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 1.16620434782609 & 0.0138570660593488 & 84.1595430685917 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 1.16847727272727 & 0.0134159425466406 & 87.0961744704151 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 1.17053571428571 & 0.0130472699167834 & 89.7149918528162 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 1.1728075 & 0.0125870809774169 & 93.1754949463015 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 1.17533684210526 & 0.011957284941527 & 98.2946252307982 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 1.17793333333333 & 0.0112406539661757 & 104.792242237672 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 1.18057647058824 & 0.0103542959634547 & 114.018034133374 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 1.183125 & 0.00937747064219139 & 126.166750624294 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 1.18455666666667 & 0.0087407760029702 & 135.520766836279 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 1.18608571428571 & 0.0081929940297537 & 144.768287390217 \tabularnewline
Median & 1.2011 &  &  \tabularnewline
Midrange & 1.1124 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.16812439024390 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.1728075 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.16812439024390 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.1728075 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.1728075 &  &  \tabularnewline
Midmean - Closest Observation & 1.16812439024390 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.1728075 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.17053571428571 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3390&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]1.1411575[/C][C]0.0179999605990251[/C][C]63.3977776630137[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.12925659335285[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.11675298915913[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.15231780674864[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]1.14113375[/C][C]0.0179625309689179[/C][C]63.528561313247[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]1.14110125[/C][C]0.0178768474741251[/C][C]63.8312348780526[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]1.14124[/C][C]0.0178440194569426[/C][C]63.9564422552776[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]1.14086[/C][C]0.0177616894652009[/C][C]64.231502427469[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]1.14126[/C][C]0.0176642476291462[/C][C]64.608469262903[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]1.1402025[/C][C]0.0174575266650994[/C][C]65.3129462078645[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]1.1401675[/C][C]0.0173836295185252[/C][C]65.5885756645329[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]1.1404175[/C][C]0.0173002715255453[/C][C]65.9190520978862[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]1.13954[/C][C]0.0171728343391680[/C][C]66.3571299585023[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]1.13999[/C][C]0.0169189278320862[/C][C]67.3795651423044[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]1.1399075[/C][C]0.0166842770461833[/C][C]68.3222591452213[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]1.1402225[/C][C]0.0165612119250741[/C][C]68.848977065119[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]1.1403525[/C][C]0.0164995729686781[/C][C]69.1140614466072[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]1.1404575[/C][C]0.0162066364722502[/C][C]70.3697835113872[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]1.14027[/C][C]0.0159263873667873[/C][C]71.5962743928925[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]1.14219[/C][C]0.0151925748644744[/C][C]75.180804451446[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]1.1449525[/C][C]0.0144820223532445[/C][C]79.0602632748657[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]1.149025[/C][C]0.0135491877588308[/C][C]84.803976478303[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]1.14895375[/C][C]0.0133453264165312[/C][C]86.0940912300774[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]1.14877875[/C][C]0.0133048563149889[/C][C]86.3428151949162[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]1.1508[/C][C]0.0127414089944777[/C][C]90.3196813240022[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]1.15322[/C][C]0.0123324006461111[/C][C]93.5113959635793[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]1.15713[/C][C]0.0114727313468486[/C][C]100.859155942656[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]1.17024[/C][C]0.00950368476174547[/C][C]123.135397410327[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]1.1711775[/C][C]0.00837767753816918[/C][C]139.797395479123[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]1.1658475[/C][C]0.00749545790204924[/C][C]155.540530710106[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]1.14189487179487[/C][C]0.0178404767419784[/C][C]64.0058496367426[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]1.14269605263158[/C][C]0.0176910705437864[/C][C]64.5916848165487[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]1.14355810810811[/C][C]0.0175608777689115[/C][C]65.1196439697668[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]1.14441666666667[/C][C]0.0174140645449292[/C][C]65.7179525040814[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]1.14543285714286[/C][C]0.0172605494157712[/C][C]66.361320810348[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]1.14641470588235[/C][C]0.0170988309167987[/C][C]67.0463794548701[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]1.14766969696970[/C][C]0.0169491644931219[/C][C]67.7124643775467[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]1.149009375[/C][C]0.0167769508538982[/C][C]68.4873780108272[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]1.15039516129032[/C][C]0.0165781512869233[/C][C]69.3922465406467[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]1.15200333333333[/C][C]0.0163526277655894[/C][C]70.4475971597347[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]1.15366034482759[/C][C]0.0161198678274945[/C][C]71.5676057132347[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]1.15544642857143[/C][C]0.0158695342291828[/C][C]72.8090952062507[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]1.15732592592593[/C][C]0.0155734378014577[/C][C]74.3140943368072[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]1.15933461538462[/C][C]0.0152058472133827[/C][C]76.2426847459236[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]1.161492[/C][C]0.0147931293594323[/C][C]78.5156386981377[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]1.16385[/C][C]0.0143158578318239[/C][C]81.2979573890979[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]1.16620434782609[/C][C]0.0138570660593488[/C][C]84.1595430685917[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]1.16847727272727[/C][C]0.0134159425466406[/C][C]87.0961744704151[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]1.17053571428571[/C][C]0.0130472699167834[/C][C]89.7149918528162[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]1.1728075[/C][C]0.0125870809774169[/C][C]93.1754949463015[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]1.17533684210526[/C][C]0.011957284941527[/C][C]98.2946252307982[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]1.17793333333333[/C][C]0.0112406539661757[/C][C]104.792242237672[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]1.18057647058824[/C][C]0.0103542959634547[/C][C]114.018034133374[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]1.183125[/C][C]0.00937747064219139[/C][C]126.166750624294[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]1.18455666666667[/C][C]0.0087407760029702[/C][C]135.520766836279[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]1.18608571428571[/C][C]0.0081929940297537[/C][C]144.768287390217[/C][/ROW]
[ROW][C]Median[/C][C]1.2011[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.1124[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.16812439024390[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.1728075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.16812439024390[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.1728075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.1728075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.16812439024390[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.1728075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.17053571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3390&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3390&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 Mean1.14115750.017999960599025163.3977776630137
Geometric Mean1.12925659335285
Harmonic Mean1.11675298915913
Quadratic Mean1.15231780674864
Winsorized Mean ( 1 / 26 )1.141133750.017962530968917963.528561313247
Winsorized Mean ( 2 / 26 )1.141101250.017876847474125163.8312348780526
Winsorized Mean ( 3 / 26 )1.141240.017844019456942663.9564422552776
Winsorized Mean ( 4 / 26 )1.140860.017761689465200964.231502427469
Winsorized Mean ( 5 / 26 )1.141260.017664247629146264.608469262903
Winsorized Mean ( 6 / 26 )1.14020250.017457526665099465.3129462078645
Winsorized Mean ( 7 / 26 )1.14016750.017383629518525265.5885756645329
Winsorized Mean ( 8 / 26 )1.14041750.017300271525545365.9190520978862
Winsorized Mean ( 9 / 26 )1.139540.017172834339168066.3571299585023
Winsorized Mean ( 10 / 26 )1.139990.016918927832086267.3795651423044
Winsorized Mean ( 11 / 26 )1.13990750.016684277046183368.3222591452213
Winsorized Mean ( 12 / 26 )1.14022250.016561211925074168.848977065119
Winsorized Mean ( 13 / 26 )1.14035250.016499572968678169.1140614466072
Winsorized Mean ( 14 / 26 )1.14045750.016206636472250270.3697835113872
Winsorized Mean ( 15 / 26 )1.140270.015926387366787371.5962743928925
Winsorized Mean ( 16 / 26 )1.142190.015192574864474475.180804451446
Winsorized Mean ( 17 / 26 )1.14495250.014482022353244579.0602632748657
Winsorized Mean ( 18 / 26 )1.1490250.013549187758830884.803976478303
Winsorized Mean ( 19 / 26 )1.148953750.013345326416531286.0940912300774
Winsorized Mean ( 20 / 26 )1.148778750.013304856314988986.3428151949162
Winsorized Mean ( 21 / 26 )1.15080.012741408994477790.3196813240022
Winsorized Mean ( 22 / 26 )1.153220.012332400646111193.5113959635793
Winsorized Mean ( 23 / 26 )1.157130.0114727313468486100.859155942656
Winsorized Mean ( 24 / 26 )1.170240.00950368476174547123.135397410327
Winsorized Mean ( 25 / 26 )1.17117750.00837767753816918139.797395479123
Winsorized Mean ( 26 / 26 )1.16584750.00749545790204924155.540530710106
Trimmed Mean ( 1 / 26 )1.141894871794870.017840476741978464.0058496367426
Trimmed Mean ( 2 / 26 )1.142696052631580.017691070543786464.5916848165487
Trimmed Mean ( 3 / 26 )1.143558108108110.017560877768911565.1196439697668
Trimmed Mean ( 4 / 26 )1.144416666666670.017414064544929265.7179525040814
Trimmed Mean ( 5 / 26 )1.145432857142860.017260549415771266.361320810348
Trimmed Mean ( 6 / 26 )1.146414705882350.017098830916798767.0463794548701
Trimmed Mean ( 7 / 26 )1.147669696969700.016949164493121967.7124643775467
Trimmed Mean ( 8 / 26 )1.1490093750.016776950853898268.4873780108272
Trimmed Mean ( 9 / 26 )1.150395161290320.016578151286923369.3922465406467
Trimmed Mean ( 10 / 26 )1.152003333333330.016352627765589470.4475971597347
Trimmed Mean ( 11 / 26 )1.153660344827590.016119867827494571.5676057132347
Trimmed Mean ( 12 / 26 )1.155446428571430.015869534229182872.8090952062507
Trimmed Mean ( 13 / 26 )1.157325925925930.015573437801457774.3140943368072
Trimmed Mean ( 14 / 26 )1.159334615384620.015205847213382776.2426847459236
Trimmed Mean ( 15 / 26 )1.1614920.014793129359432378.5156386981377
Trimmed Mean ( 16 / 26 )1.163850.014315857831823981.2979573890979
Trimmed Mean ( 17 / 26 )1.166204347826090.013857066059348884.1595430685917
Trimmed Mean ( 18 / 26 )1.168477272727270.013415942546640687.0961744704151
Trimmed Mean ( 19 / 26 )1.170535714285710.013047269916783489.7149918528162
Trimmed Mean ( 20 / 26 )1.17280750.012587080977416993.1754949463015
Trimmed Mean ( 21 / 26 )1.175336842105260.01195728494152798.2946252307982
Trimmed Mean ( 22 / 26 )1.177933333333330.0112406539661757104.792242237672
Trimmed Mean ( 23 / 26 )1.180576470588240.0103542959634547114.018034133374
Trimmed Mean ( 24 / 26 )1.1831250.00937747064219139126.166750624294
Trimmed Mean ( 25 / 26 )1.184556666666670.0087407760029702135.520766836279
Trimmed Mean ( 26 / 26 )1.186085714285710.0081929940297537144.768287390217
Median1.2011
Midrange1.1124
Midmean - Weighted Average at Xnp1.16812439024390
Midmean - Weighted Average at X(n+1)p1.1728075
Midmean - Empirical Distribution Function1.16812439024390
Midmean - Empirical Distribution Function - Averaging1.1728075
Midmean - Empirical Distribution Function - Interpolation1.1728075
Midmean - Closest Observation1.16812439024390
Midmean - True Basic - Statistics Graphics Toolkit1.1728075
Midmean - MS Excel (old versions)1.17053571428571
Number of observations80



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')