Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 13:28:51 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/12/t1476275343ic7cjaamxvw8rwl.htm/, Retrieved Sun, 05 May 2024 16:46:06 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 16:46:06 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
95,97
96,22
95,8
96,02
96,04
96,15
96,15
95,99
96,08
96,29
96,3
96,44
96,44
96,83
96,7
97,06
97,64
97,61
97,61
97,61
97,55
97,58
97,79
97,79
97,79
97,79
98
98,37
98,68
98,89
98,89
98,89
98,88
98,97
99,05
99,05
99
99,03
99,2
100,3
100,79
100,75
100,75
100,17
99,98
99,93
100,04
100,04
100,49
100,71
100,7
101,27
101,07
101,17
100,71
100,59
100,52
100,65
100,62
100,62
100,59
100,42
100,55
100,41
100,4
99,93
100,26
100,34
100,24
99,98
100,08
100,24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.85347222222220.203853348715589484.924446152415
Geometric Mean98.8384768070465
Harmonic Mean98.8234113008388
Quadratic Mean98.8683946452162
Winsorized Mean ( 1 / 24 )98.85444444444450.203140723914231486.630364112428
Winsorized Mean ( 2 / 24 )98.85222222222220.202592761866487.935606937456
Winsorized Mean ( 3 / 24 )98.84180555555560.200646970629328492.61548901306
Winsorized Mean ( 4 / 24 )98.84069444444440.200126165838169493.891910787775
Winsorized Mean ( 5 / 24 )98.84347222222220.199581541860507495.253575560143
Winsorized Mean ( 6 / 24 )98.84597222222220.198008142657751499.201552499148
Winsorized Mean ( 7 / 24 )98.84597222222220.198008142657751499.201552499148
Winsorized Mean ( 8 / 24 )98.85263888888890.196380789383262503.372245316548
Winsorized Mean ( 9 / 24 )98.85513888888890.193918088584899509.777811911596
Winsorized Mean ( 10 / 24 )98.85236111111110.19311926519389511.872085945771
Winsorized Mean ( 11 / 24 )98.873750.189190313872215522.615286038281
Winsorized Mean ( 12 / 24 )98.868750.188543853578477524.380657992906
Winsorized Mean ( 13 / 24 )98.91569444444450.180216335219656548.871967260245
Winsorized Mean ( 14 / 24 )98.93319444444440.174870713072959565.750506222091
Winsorized Mean ( 15 / 24 )98.97486111111110.166101505753082595.869740387797
Winsorized Mean ( 16 / 24 )99.07708333333330.148435956152914667.473608828763
Winsorized Mean ( 17 / 24 )99.06763888888890.145219667003095682.19161311517
Winsorized Mean ( 18 / 24 )99.07263888888890.143813747932892688.895465926662
Winsorized Mean ( 19 / 24 )99.070.143468655413202690.53410805775
Winsorized Mean ( 20 / 24 )99.05333333333330.141311762017558700.956041585736
Winsorized Mean ( 21 / 24 )99.05041666666660.138566102808074714.824294393701
Winsorized Mean ( 22 / 24 )99.08402777777780.130526599817309759.109851298207
Winsorized Mean ( 23 / 24 )99.07763888888890.129718078360357763.792064616093
Winsorized Mean ( 24 / 24 )99.07763888888890.129718078360357763.792064616093
Trimmed Mean ( 1 / 24 )98.86257142857140.202093667244018489.19183256346
Trimmed Mean ( 2 / 24 )98.87117647058820.200728428682359492.561901269331
Trimmed Mean ( 3 / 24 )98.88151515151510.199315172800157496.106311237322
Trimmed Mean ( 4 / 24 )98.896406250.198320123508102498.670555970886
Trimmed Mean ( 5 / 24 )98.91258064516130.197131053682463501.760523253169
Trimmed Mean ( 6 / 24 )98.92916666666670.195684268306176505.555032721781
Trimmed Mean ( 7 / 24 )98.94637931034480.194169816452105509.586820023344
Trimmed Mean ( 8 / 24 )98.96482142857140.192128709407689515.096477427391
Trimmed Mean ( 9 / 24 )98.98351851851850.189826534041934521.441952349255
Trimmed Mean ( 10 / 24 )99.00326923076920.18734183296751528.463225017869
Trimmed Mean ( 11 / 24 )99.0250.184204910302608537.580674897992
Trimmed Mean ( 12 / 24 )99.0456250.180971302300132547.3001726856
Trimmed Mean ( 13 / 24 )99.06869565217390.176775358605796560.421409598688
Trimmed Mean ( 14 / 24 )99.08795454545460.173182369611747572.159595503845
Trimmed Mean ( 15 / 24 )99.10690476190480.169535297115639584.579768626615
Trimmed Mean ( 16 / 24 )99.122750.166597544961441594.983257544052
Trimmed Mean ( 17 / 24 )99.12815789473680.166448491497906595.548550801878
Trimmed Mean ( 18 / 24 )99.13527777777780.16639477160547595.783610393913
Trimmed Mean ( 19 / 24 )99.14264705882350.166039806248671597.101678800695
Trimmed Mean ( 20 / 24 )99.151250.164979073697437600.992888236468
Trimmed Mean ( 21 / 24 )99.1630.163326166861312607.147047565281
Trimmed Mean ( 22 / 24 )99.17678571428570.16097426062894616.10337781204
Trimmed Mean ( 23 / 24 )99.18846153846150.159276916389898622.742226473394
Trimmed Mean ( 24 / 24 )99.20291666666670.155942063710532636.152390870065
Median99.04
Midrange98.535
Midmean - Weighted Average at Xnp99.0932432432432
Midmean - Weighted Average at X(n+1)p99.1352777777778
Midmean - Empirical Distribution Function99.0932432432432
Midmean - Empirical Distribution Function - Averaging99.1352777777778
Midmean - Empirical Distribution Function - Interpolation99.1352777777778
Midmean - Closest Observation99.0932432432432
Midmean - True Basic - Statistics Graphics Toolkit99.1352777777778
Midmean - MS Excel (old versions)99.1281578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.8534722222222 & 0.203853348715589 & 484.924446152415 \tabularnewline
Geometric Mean & 98.8384768070465 &  &  \tabularnewline
Harmonic Mean & 98.8234113008388 &  &  \tabularnewline
Quadratic Mean & 98.8683946452162 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.8544444444445 & 0.203140723914231 & 486.630364112428 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.8522222222222 & 0.202592761866 & 487.935606937456 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.8418055555556 & 0.200646970629328 & 492.61548901306 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.8406944444444 & 0.200126165838169 & 493.891910787775 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.8434722222222 & 0.199581541860507 & 495.253575560143 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.8459722222222 & 0.198008142657751 & 499.201552499148 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.8459722222222 & 0.198008142657751 & 499.201552499148 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.8526388888889 & 0.196380789383262 & 503.372245316548 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.8551388888889 & 0.193918088584899 & 509.777811911596 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.8523611111111 & 0.19311926519389 & 511.872085945771 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.87375 & 0.189190313872215 & 522.615286038281 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.86875 & 0.188543853578477 & 524.380657992906 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.9156944444445 & 0.180216335219656 & 548.871967260245 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.9331944444444 & 0.174870713072959 & 565.750506222091 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.9748611111111 & 0.166101505753082 & 595.869740387797 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.0770833333333 & 0.148435956152914 & 667.473608828763 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.0676388888889 & 0.145219667003095 & 682.19161311517 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.0726388888889 & 0.143813747932892 & 688.895465926662 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.07 & 0.143468655413202 & 690.53410805775 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.0533333333333 & 0.141311762017558 & 700.956041585736 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.0504166666666 & 0.138566102808074 & 714.824294393701 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 99.0840277777778 & 0.130526599817309 & 759.109851298207 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 99.0776388888889 & 0.129718078360357 & 763.792064616093 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 99.0776388888889 & 0.129718078360357 & 763.792064616093 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.8625714285714 & 0.202093667244018 & 489.19183256346 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 98.8711764705882 & 0.200728428682359 & 492.561901269331 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.8815151515151 & 0.199315172800157 & 496.106311237322 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.89640625 & 0.198320123508102 & 498.670555970886 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.9125806451613 & 0.197131053682463 & 501.760523253169 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.9291666666667 & 0.195684268306176 & 505.555032721781 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.9463793103448 & 0.194169816452105 & 509.586820023344 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.9648214285714 & 0.192128709407689 & 515.096477427391 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.9835185185185 & 0.189826534041934 & 521.441952349255 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.0032692307692 & 0.18734183296751 & 528.463225017869 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.025 & 0.184204910302608 & 537.580674897992 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.045625 & 0.180971302300132 & 547.3001726856 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.0686956521739 & 0.176775358605796 & 560.421409598688 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.0879545454546 & 0.173182369611747 & 572.159595503845 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.1069047619048 & 0.169535297115639 & 584.579768626615 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.12275 & 0.166597544961441 & 594.983257544052 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.1281578947368 & 0.166448491497906 & 595.548550801878 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.1352777777778 & 0.16639477160547 & 595.783610393913 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.1426470588235 & 0.166039806248671 & 597.101678800695 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.15125 & 0.164979073697437 & 600.992888236468 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.163 & 0.163326166861312 & 607.147047565281 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.1767857142857 & 0.16097426062894 & 616.10337781204 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.1884615384615 & 0.159276916389898 & 622.742226473394 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.2029166666667 & 0.155942063710532 & 636.152390870065 \tabularnewline
Median & 99.04 &  &  \tabularnewline
Midrange & 98.535 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.0932432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.1352777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.0932432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.1352777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.1352777777778 &  &  \tabularnewline
Midmean - Closest Observation & 99.0932432432432 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.1352777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.1281578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]98.8534722222222[/C][C]0.203853348715589[/C][C]484.924446152415[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.8384768070465[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.8234113008388[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.8683946452162[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.8544444444445[/C][C]0.203140723914231[/C][C]486.630364112428[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.8522222222222[/C][C]0.202592761866[/C][C]487.935606937456[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.8418055555556[/C][C]0.200646970629328[/C][C]492.61548901306[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.8406944444444[/C][C]0.200126165838169[/C][C]493.891910787775[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.8434722222222[/C][C]0.199581541860507[/C][C]495.253575560143[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.8459722222222[/C][C]0.198008142657751[/C][C]499.201552499148[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.8459722222222[/C][C]0.198008142657751[/C][C]499.201552499148[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.8526388888889[/C][C]0.196380789383262[/C][C]503.372245316548[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.8551388888889[/C][C]0.193918088584899[/C][C]509.777811911596[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.8523611111111[/C][C]0.19311926519389[/C][C]511.872085945771[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.87375[/C][C]0.189190313872215[/C][C]522.615286038281[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.86875[/C][C]0.188543853578477[/C][C]524.380657992906[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.9156944444445[/C][C]0.180216335219656[/C][C]548.871967260245[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.9331944444444[/C][C]0.174870713072959[/C][C]565.750506222091[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.9748611111111[/C][C]0.166101505753082[/C][C]595.869740387797[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.0770833333333[/C][C]0.148435956152914[/C][C]667.473608828763[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.0676388888889[/C][C]0.145219667003095[/C][C]682.19161311517[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.0726388888889[/C][C]0.143813747932892[/C][C]688.895465926662[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.07[/C][C]0.143468655413202[/C][C]690.53410805775[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.0533333333333[/C][C]0.141311762017558[/C][C]700.956041585736[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.0504166666666[/C][C]0.138566102808074[/C][C]714.824294393701[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]99.0840277777778[/C][C]0.130526599817309[/C][C]759.109851298207[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]99.0776388888889[/C][C]0.129718078360357[/C][C]763.792064616093[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]99.0776388888889[/C][C]0.129718078360357[/C][C]763.792064616093[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.8625714285714[/C][C]0.202093667244018[/C][C]489.19183256346[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]98.8711764705882[/C][C]0.200728428682359[/C][C]492.561901269331[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.8815151515151[/C][C]0.199315172800157[/C][C]496.106311237322[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.89640625[/C][C]0.198320123508102[/C][C]498.670555970886[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.9125806451613[/C][C]0.197131053682463[/C][C]501.760523253169[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.9291666666667[/C][C]0.195684268306176[/C][C]505.555032721781[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.9463793103448[/C][C]0.194169816452105[/C][C]509.586820023344[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.9648214285714[/C][C]0.192128709407689[/C][C]515.096477427391[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.9835185185185[/C][C]0.189826534041934[/C][C]521.441952349255[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.0032692307692[/C][C]0.18734183296751[/C][C]528.463225017869[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.025[/C][C]0.184204910302608[/C][C]537.580674897992[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.045625[/C][C]0.180971302300132[/C][C]547.3001726856[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.0686956521739[/C][C]0.176775358605796[/C][C]560.421409598688[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.0879545454546[/C][C]0.173182369611747[/C][C]572.159595503845[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.1069047619048[/C][C]0.169535297115639[/C][C]584.579768626615[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.12275[/C][C]0.166597544961441[/C][C]594.983257544052[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.1281578947368[/C][C]0.166448491497906[/C][C]595.548550801878[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.1352777777778[/C][C]0.16639477160547[/C][C]595.783610393913[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.1426470588235[/C][C]0.166039806248671[/C][C]597.101678800695[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.15125[/C][C]0.164979073697437[/C][C]600.992888236468[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.163[/C][C]0.163326166861312[/C][C]607.147047565281[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.1767857142857[/C][C]0.16097426062894[/C][C]616.10337781204[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.1884615384615[/C][C]0.159276916389898[/C][C]622.742226473394[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.2029166666667[/C][C]0.155942063710532[/C][C]636.152390870065[/C][/ROW]
[ROW][C]Median[/C][C]99.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.535[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.0932432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.1352777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.0932432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.1352777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.1352777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.0932432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.1352777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.1281578947368[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean98.85347222222220.203853348715589484.924446152415
Geometric Mean98.8384768070465
Harmonic Mean98.8234113008388
Quadratic Mean98.8683946452162
Winsorized Mean ( 1 / 24 )98.85444444444450.203140723914231486.630364112428
Winsorized Mean ( 2 / 24 )98.85222222222220.202592761866487.935606937456
Winsorized Mean ( 3 / 24 )98.84180555555560.200646970629328492.61548901306
Winsorized Mean ( 4 / 24 )98.84069444444440.200126165838169493.891910787775
Winsorized Mean ( 5 / 24 )98.84347222222220.199581541860507495.253575560143
Winsorized Mean ( 6 / 24 )98.84597222222220.198008142657751499.201552499148
Winsorized Mean ( 7 / 24 )98.84597222222220.198008142657751499.201552499148
Winsorized Mean ( 8 / 24 )98.85263888888890.196380789383262503.372245316548
Winsorized Mean ( 9 / 24 )98.85513888888890.193918088584899509.777811911596
Winsorized Mean ( 10 / 24 )98.85236111111110.19311926519389511.872085945771
Winsorized Mean ( 11 / 24 )98.873750.189190313872215522.615286038281
Winsorized Mean ( 12 / 24 )98.868750.188543853578477524.380657992906
Winsorized Mean ( 13 / 24 )98.91569444444450.180216335219656548.871967260245
Winsorized Mean ( 14 / 24 )98.93319444444440.174870713072959565.750506222091
Winsorized Mean ( 15 / 24 )98.97486111111110.166101505753082595.869740387797
Winsorized Mean ( 16 / 24 )99.07708333333330.148435956152914667.473608828763
Winsorized Mean ( 17 / 24 )99.06763888888890.145219667003095682.19161311517
Winsorized Mean ( 18 / 24 )99.07263888888890.143813747932892688.895465926662
Winsorized Mean ( 19 / 24 )99.070.143468655413202690.53410805775
Winsorized Mean ( 20 / 24 )99.05333333333330.141311762017558700.956041585736
Winsorized Mean ( 21 / 24 )99.05041666666660.138566102808074714.824294393701
Winsorized Mean ( 22 / 24 )99.08402777777780.130526599817309759.109851298207
Winsorized Mean ( 23 / 24 )99.07763888888890.129718078360357763.792064616093
Winsorized Mean ( 24 / 24 )99.07763888888890.129718078360357763.792064616093
Trimmed Mean ( 1 / 24 )98.86257142857140.202093667244018489.19183256346
Trimmed Mean ( 2 / 24 )98.87117647058820.200728428682359492.561901269331
Trimmed Mean ( 3 / 24 )98.88151515151510.199315172800157496.106311237322
Trimmed Mean ( 4 / 24 )98.896406250.198320123508102498.670555970886
Trimmed Mean ( 5 / 24 )98.91258064516130.197131053682463501.760523253169
Trimmed Mean ( 6 / 24 )98.92916666666670.195684268306176505.555032721781
Trimmed Mean ( 7 / 24 )98.94637931034480.194169816452105509.586820023344
Trimmed Mean ( 8 / 24 )98.96482142857140.192128709407689515.096477427391
Trimmed Mean ( 9 / 24 )98.98351851851850.189826534041934521.441952349255
Trimmed Mean ( 10 / 24 )99.00326923076920.18734183296751528.463225017869
Trimmed Mean ( 11 / 24 )99.0250.184204910302608537.580674897992
Trimmed Mean ( 12 / 24 )99.0456250.180971302300132547.3001726856
Trimmed Mean ( 13 / 24 )99.06869565217390.176775358605796560.421409598688
Trimmed Mean ( 14 / 24 )99.08795454545460.173182369611747572.159595503845
Trimmed Mean ( 15 / 24 )99.10690476190480.169535297115639584.579768626615
Trimmed Mean ( 16 / 24 )99.122750.166597544961441594.983257544052
Trimmed Mean ( 17 / 24 )99.12815789473680.166448491497906595.548550801878
Trimmed Mean ( 18 / 24 )99.13527777777780.16639477160547595.783610393913
Trimmed Mean ( 19 / 24 )99.14264705882350.166039806248671597.101678800695
Trimmed Mean ( 20 / 24 )99.151250.164979073697437600.992888236468
Trimmed Mean ( 21 / 24 )99.1630.163326166861312607.147047565281
Trimmed Mean ( 22 / 24 )99.17678571428570.16097426062894616.10337781204
Trimmed Mean ( 23 / 24 )99.18846153846150.159276916389898622.742226473394
Trimmed Mean ( 24 / 24 )99.20291666666670.155942063710532636.152390870065
Median99.04
Midrange98.535
Midmean - Weighted Average at Xnp99.0932432432432
Midmean - Weighted Average at X(n+1)p99.1352777777778
Midmean - Empirical Distribution Function99.0932432432432
Midmean - Empirical Distribution Function - Averaging99.1352777777778
Midmean - Empirical Distribution Function - Interpolation99.1352777777778
Midmean - Closest Observation99.0932432432432
Midmean - True Basic - Statistics Graphics Toolkit99.1352777777778
Midmean - MS Excel (old versions)99.1281578947368
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')