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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 30 Nov 2007 07:20:22 -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/Nov/30/t1196431757qkt3nlxadzydxp6.htm/, Retrieved Sun, 28 Apr 2024 08:07:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7695, Retrieved Sun, 28 Apr 2024 08:07:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-30 14:20:22] [2467046df5c61f7ccf2ce4e184abae94] [Current]
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Dataseries X:
0,96
1
1,05
1,03
1,07
1,12
1,1
1,06
1,11
1,08
1,07
1,02
1
1,04
1,02
1,07
1,12
1,08
1,02
1,01
1,04
0,98
0,95
0,94
0,94
0,96
0,97
1,03
1,01
0,99
1
1
1,02
1,01
0,99
0,98
1,01
1,03
1,03
1
0,96
0,97
0,98
1,02
1,04
1,01
1,01
1
1,01
1,02
1,03
1,06
1,12
1,12
1,13
1,13
1,13
1,17
1,14
1,08
1,07
1,12
1,14
1,21
1,2
1,23
1,29
1,31
1,37
1,35
1,26
1,26




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7695&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7695&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7695&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.067361111111110.011504563045793292.7771969141762
Geometric Mean1.06324476162025
Harmonic Mean1.05939351649448
Quadratic Mean1.07175414365630
Winsorized Mean ( 1 / 24 )1.067083333333330.011404563338647793.5663472285002
Winsorized Mean ( 2 / 24 )1.066250.010994089854876196.9839262799092
Winsorized Mean ( 3 / 24 )1.065833333333330.010680577050636699.7917367460783
Winsorized Mean ( 4 / 24 )1.064166666666670.0102086028037635104.242146268474
Winsorized Mean ( 5 / 24 )1.064166666666670.0102086028037635104.242146268474
Winsorized Mean ( 6 / 24 )1.06250.0094400132290828112.552808371777
Winsorized Mean ( 7 / 24 )1.060555555555560.00896849137778824118.253506736058
Winsorized Mean ( 8 / 24 )1.060555555555560.00855775026216841123.929248116061
Winsorized Mean ( 9 / 24 )1.056805555555560.00773895899092756136.556551959308
Winsorized Mean ( 10 / 24 )1.052638888888890.00693698738904864151.742943997661
Winsorized Mean ( 11 / 24 )1.054166666666670.00672145910644123156.835986051964
Winsorized Mean ( 12 / 24 )1.05250.0064299219834781163.687833647816
Winsorized Mean ( 13 / 24 )1.054305555555560.00619463391921984170.196587773234
Winsorized Mean ( 14 / 24 )1.054305555555560.00619463391921984170.196587773234
Winsorized Mean ( 15 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 16 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 17 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 18 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 19 / 24 )1.054861111111110.00552768340841586190.832403589738
Winsorized Mean ( 20 / 24 )1.052083333333330.00507354942381254207.366331821942
Winsorized Mean ( 21 / 24 )1.049166666666670.0046123176580114227.470600348679
Winsorized Mean ( 22 / 24 )1.043055555555560.00370381781253536281.616323574392
Winsorized Mean ( 23 / 24 )1.043055555555560.00370381781253536281.616323574392
Winsorized Mean ( 24 / 24 )1.043055555555560.00370381781253536281.616323574392
Trimmed Mean ( 1 / 24 )1.064857142857140.010847603960457598.1651935984054
Trimmed Mean ( 2 / 24 )1.06250.0101684128477342104.490249944636
Trimmed Mean ( 3 / 24 )1.060454545454550.0096184356252948110.252289121293
Trimmed Mean ( 4 / 24 )1.05843750.00909937080831103116.319855767749
Trimmed Mean ( 5 / 24 )1.056774193548390.0086557470096766122.089311571489
Trimmed Mean ( 6 / 24 )1.0550.00810419435241375130.179503862192
Trimmed Mean ( 7 / 24 )1.053448275862070.00767043382079983137.338812963283
Trimmed Mean ( 8 / 24 )1.052142857142860.00727348094425098144.654652319462
Trimmed Mean ( 9 / 24 )1.050740740740740.00688759634109906152.555505390299
Trimmed Mean ( 10 / 24 )1.049807692307690.00662784919588948158.393418631005
Trimmed Mean ( 11 / 24 )1.04940.00649904231563453161.46994419093
Trimmed Mean ( 12 / 24 )1.048750.00637638178600145164.474154026097
Trimmed Mean ( 13 / 24 )1.048260869565220.00628089925425763166.896622144454
Trimmed Mean ( 14 / 24 )1.04750.00619558766816444169.071935723305
Trimmed Mean ( 15 / 24 )1.046666666666670.00607413230318098172.315421269065
Trimmed Mean ( 16 / 24 )1.0460.00598930671044612174.644587523902
Trimmed Mean ( 17 / 24 )1.045263157894740.00586399727373345178.250962458113
Trimmed Mean ( 18 / 24 )1.044444444444440.00568267269508245183.794580558592
Trimmed Mean ( 19 / 24 )1.043529411764710.0054213276741639192.485950764015
Trimmed Mean ( 20 / 24 )1.04218750.00511430581720878203.778877769338
Trimmed Mean ( 21 / 24 )1.0410.00482688829109528215.666892875987
Trimmed Mean ( 22 / 24 )1.040.00457159391235387227.491772003108
Trimmed Mean ( 23 / 24 )1.039615384615380.00452278910648896229.861565537916
Trimmed Mean ( 24 / 24 )1.039166666666670.00441984435863859235.113859752915
Median1.03
Midrange1.155
Midmean - Weighted Average at Xnp1.04454545454545
Midmean - Weighted Average at X(n+1)p1.04454545454545
Midmean - Empirical Distribution Function1.04454545454545
Midmean - Empirical Distribution Function - Averaging1.04454545454545
Midmean - Empirical Distribution Function - Interpolation1.04454545454545
Midmean - Closest Observation1.04454545454545
Midmean - True Basic - Statistics Graphics Toolkit1.04454545454545
Midmean - MS Excel (old versions)1.04454545454545
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.06736111111111 & 0.0115045630457932 & 92.7771969141762 \tabularnewline
Geometric Mean & 1.06324476162025 &  &  \tabularnewline
Harmonic Mean & 1.05939351649448 &  &  \tabularnewline
Quadratic Mean & 1.07175414365630 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.06708333333333 & 0.0114045633386477 & 93.5663472285002 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.06625 & 0.0109940898548761 & 96.9839262799092 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.06583333333333 & 0.0106805770506366 & 99.7917367460783 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.06416666666667 & 0.0102086028037635 & 104.242146268474 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.06416666666667 & 0.0102086028037635 & 104.242146268474 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.0625 & 0.0094400132290828 & 112.552808371777 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.06055555555556 & 0.00896849137778824 & 118.253506736058 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.06055555555556 & 0.00855775026216841 & 123.929248116061 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.05680555555556 & 0.00773895899092756 & 136.556551959308 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.05263888888889 & 0.00693698738904864 & 151.742943997661 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.05416666666667 & 0.00672145910644123 & 156.835986051964 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.0525 & 0.0064299219834781 & 163.687833647816 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.05430555555556 & 0.00619463391921984 & 170.196587773234 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.05430555555556 & 0.00619463391921984 & 170.196587773234 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.05222222222222 & 0.00584496567292011 & 180.021967810213 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.05222222222222 & 0.00584496567292011 & 180.021967810213 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.05222222222222 & 0.00584496567292011 & 180.021967810213 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.05222222222222 & 0.00584496567292011 & 180.021967810213 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.05486111111111 & 0.00552768340841586 & 190.832403589738 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.05208333333333 & 0.00507354942381254 & 207.366331821942 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.04916666666667 & 0.0046123176580114 & 227.470600348679 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.04305555555556 & 0.00370381781253536 & 281.616323574392 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.04305555555556 & 0.00370381781253536 & 281.616323574392 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.04305555555556 & 0.00370381781253536 & 281.616323574392 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.06485714285714 & 0.0108476039604575 & 98.1651935984054 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.0625 & 0.0101684128477342 & 104.490249944636 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.06045454545455 & 0.0096184356252948 & 110.252289121293 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.0584375 & 0.00909937080831103 & 116.319855767749 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.05677419354839 & 0.0086557470096766 & 122.089311571489 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.055 & 0.00810419435241375 & 130.179503862192 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.05344827586207 & 0.00767043382079983 & 137.338812963283 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.05214285714286 & 0.00727348094425098 & 144.654652319462 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.05074074074074 & 0.00688759634109906 & 152.555505390299 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.04980769230769 & 0.00662784919588948 & 158.393418631005 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.0494 & 0.00649904231563453 & 161.46994419093 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.04875 & 0.00637638178600145 & 164.474154026097 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.04826086956522 & 0.00628089925425763 & 166.896622144454 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.0475 & 0.00619558766816444 & 169.071935723305 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.04666666666667 & 0.00607413230318098 & 172.315421269065 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.046 & 0.00598930671044612 & 174.644587523902 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.04526315789474 & 0.00586399727373345 & 178.250962458113 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.04444444444444 & 0.00568267269508245 & 183.794580558592 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.04352941176471 & 0.0054213276741639 & 192.485950764015 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.0421875 & 0.00511430581720878 & 203.778877769338 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.041 & 0.00482688829109528 & 215.666892875987 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.04 & 0.00457159391235387 & 227.491772003108 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.03961538461538 & 0.00452278910648896 & 229.861565537916 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.03916666666667 & 0.00441984435863859 & 235.113859752915 \tabularnewline
Median & 1.03 &  &  \tabularnewline
Midrange & 1.155 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.04454545454545 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.04454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.04454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.04454545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.04454545454545 &  &  \tabularnewline
Midmean - Closest Observation & 1.04454545454545 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.04454545454545 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.04454545454545 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7695&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]1.06736111111111[/C][C]0.0115045630457932[/C][C]92.7771969141762[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.06324476162025[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.05939351649448[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.07175414365630[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.06708333333333[/C][C]0.0114045633386477[/C][C]93.5663472285002[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.06625[/C][C]0.0109940898548761[/C][C]96.9839262799092[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.06583333333333[/C][C]0.0106805770506366[/C][C]99.7917367460783[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.06416666666667[/C][C]0.0102086028037635[/C][C]104.242146268474[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.06416666666667[/C][C]0.0102086028037635[/C][C]104.242146268474[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.0625[/C][C]0.0094400132290828[/C][C]112.552808371777[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.06055555555556[/C][C]0.00896849137778824[/C][C]118.253506736058[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.06055555555556[/C][C]0.00855775026216841[/C][C]123.929248116061[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.05680555555556[/C][C]0.00773895899092756[/C][C]136.556551959308[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.05263888888889[/C][C]0.00693698738904864[/C][C]151.742943997661[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.05416666666667[/C][C]0.00672145910644123[/C][C]156.835986051964[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.0525[/C][C]0.0064299219834781[/C][C]163.687833647816[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.05430555555556[/C][C]0.00619463391921984[/C][C]170.196587773234[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.05430555555556[/C][C]0.00619463391921984[/C][C]170.196587773234[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.05222222222222[/C][C]0.00584496567292011[/C][C]180.021967810213[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.05222222222222[/C][C]0.00584496567292011[/C][C]180.021967810213[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.05222222222222[/C][C]0.00584496567292011[/C][C]180.021967810213[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.05222222222222[/C][C]0.00584496567292011[/C][C]180.021967810213[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.05486111111111[/C][C]0.00552768340841586[/C][C]190.832403589738[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.05208333333333[/C][C]0.00507354942381254[/C][C]207.366331821942[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.04916666666667[/C][C]0.0046123176580114[/C][C]227.470600348679[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.04305555555556[/C][C]0.00370381781253536[/C][C]281.616323574392[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.04305555555556[/C][C]0.00370381781253536[/C][C]281.616323574392[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.04305555555556[/C][C]0.00370381781253536[/C][C]281.616323574392[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.06485714285714[/C][C]0.0108476039604575[/C][C]98.1651935984054[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.0625[/C][C]0.0101684128477342[/C][C]104.490249944636[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.06045454545455[/C][C]0.0096184356252948[/C][C]110.252289121293[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.0584375[/C][C]0.00909937080831103[/C][C]116.319855767749[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.05677419354839[/C][C]0.0086557470096766[/C][C]122.089311571489[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.055[/C][C]0.00810419435241375[/C][C]130.179503862192[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.05344827586207[/C][C]0.00767043382079983[/C][C]137.338812963283[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.05214285714286[/C][C]0.00727348094425098[/C][C]144.654652319462[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.05074074074074[/C][C]0.00688759634109906[/C][C]152.555505390299[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.04980769230769[/C][C]0.00662784919588948[/C][C]158.393418631005[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.0494[/C][C]0.00649904231563453[/C][C]161.46994419093[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.04875[/C][C]0.00637638178600145[/C][C]164.474154026097[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.04826086956522[/C][C]0.00628089925425763[/C][C]166.896622144454[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.0475[/C][C]0.00619558766816444[/C][C]169.071935723305[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.04666666666667[/C][C]0.00607413230318098[/C][C]172.315421269065[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.046[/C][C]0.00598930671044612[/C][C]174.644587523902[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.04526315789474[/C][C]0.00586399727373345[/C][C]178.250962458113[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.04444444444444[/C][C]0.00568267269508245[/C][C]183.794580558592[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.04352941176471[/C][C]0.0054213276741639[/C][C]192.485950764015[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.0421875[/C][C]0.00511430581720878[/C][C]203.778877769338[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.041[/C][C]0.00482688829109528[/C][C]215.666892875987[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.04[/C][C]0.00457159391235387[/C][C]227.491772003108[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.03961538461538[/C][C]0.00452278910648896[/C][C]229.861565537916[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.03916666666667[/C][C]0.00441984435863859[/C][C]235.113859752915[/C][/ROW]
[ROW][C]Median[/C][C]1.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.04454545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7695&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7695&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 Mean1.067361111111110.011504563045793292.7771969141762
Geometric Mean1.06324476162025
Harmonic Mean1.05939351649448
Quadratic Mean1.07175414365630
Winsorized Mean ( 1 / 24 )1.067083333333330.011404563338647793.5663472285002
Winsorized Mean ( 2 / 24 )1.066250.010994089854876196.9839262799092
Winsorized Mean ( 3 / 24 )1.065833333333330.010680577050636699.7917367460783
Winsorized Mean ( 4 / 24 )1.064166666666670.0102086028037635104.242146268474
Winsorized Mean ( 5 / 24 )1.064166666666670.0102086028037635104.242146268474
Winsorized Mean ( 6 / 24 )1.06250.0094400132290828112.552808371777
Winsorized Mean ( 7 / 24 )1.060555555555560.00896849137778824118.253506736058
Winsorized Mean ( 8 / 24 )1.060555555555560.00855775026216841123.929248116061
Winsorized Mean ( 9 / 24 )1.056805555555560.00773895899092756136.556551959308
Winsorized Mean ( 10 / 24 )1.052638888888890.00693698738904864151.742943997661
Winsorized Mean ( 11 / 24 )1.054166666666670.00672145910644123156.835986051964
Winsorized Mean ( 12 / 24 )1.05250.0064299219834781163.687833647816
Winsorized Mean ( 13 / 24 )1.054305555555560.00619463391921984170.196587773234
Winsorized Mean ( 14 / 24 )1.054305555555560.00619463391921984170.196587773234
Winsorized Mean ( 15 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 16 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 17 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 18 / 24 )1.052222222222220.00584496567292011180.021967810213
Winsorized Mean ( 19 / 24 )1.054861111111110.00552768340841586190.832403589738
Winsorized Mean ( 20 / 24 )1.052083333333330.00507354942381254207.366331821942
Winsorized Mean ( 21 / 24 )1.049166666666670.0046123176580114227.470600348679
Winsorized Mean ( 22 / 24 )1.043055555555560.00370381781253536281.616323574392
Winsorized Mean ( 23 / 24 )1.043055555555560.00370381781253536281.616323574392
Winsorized Mean ( 24 / 24 )1.043055555555560.00370381781253536281.616323574392
Trimmed Mean ( 1 / 24 )1.064857142857140.010847603960457598.1651935984054
Trimmed Mean ( 2 / 24 )1.06250.0101684128477342104.490249944636
Trimmed Mean ( 3 / 24 )1.060454545454550.0096184356252948110.252289121293
Trimmed Mean ( 4 / 24 )1.05843750.00909937080831103116.319855767749
Trimmed Mean ( 5 / 24 )1.056774193548390.0086557470096766122.089311571489
Trimmed Mean ( 6 / 24 )1.0550.00810419435241375130.179503862192
Trimmed Mean ( 7 / 24 )1.053448275862070.00767043382079983137.338812963283
Trimmed Mean ( 8 / 24 )1.052142857142860.00727348094425098144.654652319462
Trimmed Mean ( 9 / 24 )1.050740740740740.00688759634109906152.555505390299
Trimmed Mean ( 10 / 24 )1.049807692307690.00662784919588948158.393418631005
Trimmed Mean ( 11 / 24 )1.04940.00649904231563453161.46994419093
Trimmed Mean ( 12 / 24 )1.048750.00637638178600145164.474154026097
Trimmed Mean ( 13 / 24 )1.048260869565220.00628089925425763166.896622144454
Trimmed Mean ( 14 / 24 )1.04750.00619558766816444169.071935723305
Trimmed Mean ( 15 / 24 )1.046666666666670.00607413230318098172.315421269065
Trimmed Mean ( 16 / 24 )1.0460.00598930671044612174.644587523902
Trimmed Mean ( 17 / 24 )1.045263157894740.00586399727373345178.250962458113
Trimmed Mean ( 18 / 24 )1.044444444444440.00568267269508245183.794580558592
Trimmed Mean ( 19 / 24 )1.043529411764710.0054213276741639192.485950764015
Trimmed Mean ( 20 / 24 )1.04218750.00511430581720878203.778877769338
Trimmed Mean ( 21 / 24 )1.0410.00482688829109528215.666892875987
Trimmed Mean ( 22 / 24 )1.040.00457159391235387227.491772003108
Trimmed Mean ( 23 / 24 )1.039615384615380.00452278910648896229.861565537916
Trimmed Mean ( 24 / 24 )1.039166666666670.00441984435863859235.113859752915
Median1.03
Midrange1.155
Midmean - Weighted Average at Xnp1.04454545454545
Midmean - Weighted Average at X(n+1)p1.04454545454545
Midmean - Empirical Distribution Function1.04454545454545
Midmean - Empirical Distribution Function - Averaging1.04454545454545
Midmean - Empirical Distribution Function - Interpolation1.04454545454545
Midmean - Closest Observation1.04454545454545
Midmean - True Basic - Statistics Graphics Toolkit1.04454545454545
Midmean - MS Excel (old versions)1.04454545454545
Number of observations72



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')