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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 computationTue, 13 Nov 2007 13:05:49 -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/13/t1194984047noujmc3q6m56zz6.htm/, Retrieved Tue, 30 Apr 2024 06:00:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5379, Retrieved Tue, 30 Apr 2024 06:00:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact248
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-13 20:05:49] [bc15d8d2f79dc0888573b215bcd9118f] [Current]
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Dataseries X:
99,20
95,80
93,80
94,40
94,80
96,90
93,10
92,20
90,80
92,40
91,20
89,80
85,80
88,20
89,90
91,80
93,40
93,80
95,00
97,30
95,30
97,90
97,00
97,00
65,20
64,10
65,60
66,50
65,60
66,10
65,90
65,80
64,10
63,50
64,40
66,00
67,70
70,40
74,10
75,50
80,80
83,90
83,60
88,70
87,00
86,90
88,60
88,60
86,90
86,10
86,60
83,90
84,20
83,20
78,40
77,60
77,10
76,80
76,80
76,80
76,80
78,70
78,70
78,70
78,70
78,70
83,70
83,70
87,90
87,90
84,50
84,50
84,40
87,50
89,20
88,90
88,80
89,50
90,40
87,90




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=5379&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=5379&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5379&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 Mean83.361251.1304621181068873.7408610733464
Geometric Mean82.7190524039892
Harmonic Mean82.0408445607866
Quadratic Mean83.9646093601346
Winsorized Mean ( 1 / 26 )83.35251.1260465947483374.022247737119
Winsorized Mean ( 2 / 26 )83.33751.1236403527842374.1674146834448
Winsorized Mean ( 3 / 26 )83.33751.1194629914564074.4441760344214
Winsorized Mean ( 4 / 26 )83.37751.1110377960165175.0447017184655
Winsorized Mean ( 5 / 26 )83.396251.1049320440613975.4763611465746
Winsorized Mean ( 6 / 26 )83.313751.0925810570833976.254067796492
Winsorized Mean ( 7 / 26 )83.28751.0827595648695376.9215093565448
Winsorized Mean ( 8 / 26 )83.26751.0765403668197577.3473086252991
Winsorized Mean ( 9 / 26 )83.256251.0711579026331477.7254686683805
Winsorized Mean ( 10 / 26 )83.218751.0618649908074678.3703679096896
Winsorized Mean ( 11 / 26 )83.191251.0398380986291980.0040411191614
Winsorized Mean ( 12 / 26 )83.371251.0037559113592383.0592866816624
Winsorized Mean ( 13 / 26 )83.7450.91096155207949891.930334281212
Winsorized Mean ( 14 / 26 )84.340.79013017674465106.741904666244
Winsorized Mean ( 15 / 26 )84.471250.729893337426084115.730950905624
Winsorized Mean ( 16 / 26 )84.691250.685150343267627123.609731546057
Winsorized Mean ( 17 / 26 )84.606250.673507124914152125.620423111017
Winsorized Mean ( 18 / 26 )84.471250.655606767343105128.84438387103
Winsorized Mean ( 19 / 26 )84.376250.64343137623038131.134808026193
Winsorized Mean ( 20 / 26 )84.351250.619789658455067136.096575425702
Winsorized Mean ( 21 / 26 )84.351250.584472048226627144.320417470663
Winsorized Mean ( 22 / 26 )84.543750.549487228603845153.85935395589
Winsorized Mean ( 23 / 26 )84.543750.526971415379034160.433274998778
Winsorized Mean ( 24 / 26 )84.453750.516377179602201163.550507915668
Winsorized Mean ( 25 / 26 )84.360.505594023358362166.853238176445
Winsorized Mean ( 26 / 26 )84.32750.501913979089109168.011857635526
Trimmed Mean ( 1 / 26 )83.41282051282051.1123281542146474.9893996630109
Trimmed Mean ( 2 / 26 )83.47631578947371.0960773253889476.159148497897
Trimmed Mean ( 3 / 26 )83.55135135135141.0782890640280777.4851142783883
Trimmed Mean ( 4 / 26 )83.63055555555561.0589853983413578.9723405880222
Trimmed Mean ( 5 / 26 )83.70285714285711.0389973097376780.5611875587923
Trimmed Mean ( 6 / 26 )83.7751.0169575702735182.3780681208444
Trimmed Mean ( 7 / 26 )83.86818181818180.9937242681799384.3978400283931
Trimmed Mean ( 8 / 26 )83.9718750.96805234415388286.743114158145
Trimmed Mean ( 9 / 26 )84.08548387096770.93826873090379789.617698108698
Trimmed Mean ( 10 / 26 )84.20833333333330.90302158087051993.2517396230508
Trimmed Mean ( 11 / 26 )84.34482758620690.86152965586556197.901246941369
Trimmed Mean ( 12 / 26 )84.49464285714290.814783931373065103.701901330766
Trimmed Mean ( 13 / 26 )84.63333333333330.765028785489496110.627645571770
Trimmed Mean ( 14 / 26 )84.73846153846150.725277051376263116.835988919909
Trimmed Mean ( 15 / 26 )84.7840.703294637359603120.552604123795
Trimmed Mean ( 16 / 26 )84.818750.687906270997223123.299864496136
Trimmed Mean ( 17 / 26 )84.83260869565220.677014291715268125.304014603181
Trimmed Mean ( 18 / 26 )84.85681818181820.664601787711332127.680695043023
Trimmed Mean ( 19 / 26 )84.8976190476190.651305203422396130.349978169236
Trimmed Mean ( 20 / 26 )84.95250.635458521109979133.686931841925
Trimmed Mean ( 21 / 26 )85.01578947368420.618842657654588137.378683292283
Trimmed Mean ( 22 / 26 )85.08611111111110.603838945964186140.908617570616
Trimmed Mean ( 23 / 26 )85.14411764705880.591369768240766143.977799034857
Trimmed Mean ( 24 / 26 )85.2093750.578292804766197147.346420874889
Trimmed Mean ( 25 / 26 )85.29333333333330.560417195444779152.196138924038
Trimmed Mean ( 26 / 26 )85.40.535066627903756159.606291154008
Median85.95
Midrange81.35
Midmean - Weighted Average at Xnp84.2113636363637
Midmean - Weighted Average at X(n+1)p84.9525
Midmean - Empirical Distribution Function84.2113636363637
Midmean - Empirical Distribution Function - Averaging84.9525
Midmean - Empirical Distribution Function - Interpolation84.9525
Midmean - Closest Observation84.2113636363637
Midmean - True Basic - Statistics Graphics Toolkit84.9525
Midmean - MS Excel (old versions)84.3577777777778
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 83.36125 & 1.13046211810688 & 73.7408610733464 \tabularnewline
Geometric Mean & 82.7190524039892 &  &  \tabularnewline
Harmonic Mean & 82.0408445607866 &  &  \tabularnewline
Quadratic Mean & 83.9646093601346 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 83.3525 & 1.12604659474833 & 74.022247737119 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 83.3375 & 1.12364035278423 & 74.1674146834448 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 83.3375 & 1.11946299145640 & 74.4441760344214 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 83.3775 & 1.11103779601651 & 75.0447017184655 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 83.39625 & 1.10493204406139 & 75.4763611465746 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 83.31375 & 1.09258105708339 & 76.254067796492 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 83.2875 & 1.08275956486953 & 76.9215093565448 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 83.2675 & 1.07654036681975 & 77.3473086252991 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 83.25625 & 1.07115790263314 & 77.7254686683805 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 83.21875 & 1.06186499080746 & 78.3703679096896 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 83.19125 & 1.03983809862919 & 80.0040411191614 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 83.37125 & 1.00375591135923 & 83.0592866816624 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 83.745 & 0.910961552079498 & 91.930334281212 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 84.34 & 0.79013017674465 & 106.741904666244 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 84.47125 & 0.729893337426084 & 115.730950905624 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 84.69125 & 0.685150343267627 & 123.609731546057 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 84.60625 & 0.673507124914152 & 125.620423111017 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 84.47125 & 0.655606767343105 & 128.84438387103 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 84.37625 & 0.64343137623038 & 131.134808026193 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 84.35125 & 0.619789658455067 & 136.096575425702 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 84.35125 & 0.584472048226627 & 144.320417470663 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 84.54375 & 0.549487228603845 & 153.85935395589 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 84.54375 & 0.526971415379034 & 160.433274998778 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 84.45375 & 0.516377179602201 & 163.550507915668 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 84.36 & 0.505594023358362 & 166.853238176445 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 84.3275 & 0.501913979089109 & 168.011857635526 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 83.4128205128205 & 1.11232815421464 & 74.9893996630109 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 83.4763157894737 & 1.09607732538894 & 76.159148497897 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 83.5513513513514 & 1.07828906402807 & 77.4851142783883 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 83.6305555555556 & 1.05898539834135 & 78.9723405880222 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 83.7028571428571 & 1.03899730973767 & 80.5611875587923 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 83.775 & 1.01695757027351 & 82.3780681208444 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 83.8681818181818 & 0.99372426817993 & 84.3978400283931 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 83.971875 & 0.968052344153882 & 86.743114158145 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 84.0854838709677 & 0.938268730903797 & 89.617698108698 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 84.2083333333333 & 0.903021580870519 & 93.2517396230508 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 84.3448275862069 & 0.861529655865561 & 97.901246941369 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 84.4946428571429 & 0.814783931373065 & 103.701901330766 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 84.6333333333333 & 0.765028785489496 & 110.627645571770 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 84.7384615384615 & 0.725277051376263 & 116.835988919909 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 84.784 & 0.703294637359603 & 120.552604123795 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 84.81875 & 0.687906270997223 & 123.299864496136 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 84.8326086956522 & 0.677014291715268 & 125.304014603181 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 84.8568181818182 & 0.664601787711332 & 127.680695043023 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 84.897619047619 & 0.651305203422396 & 130.349978169236 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 84.9525 & 0.635458521109979 & 133.686931841925 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 85.0157894736842 & 0.618842657654588 & 137.378683292283 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 85.0861111111111 & 0.603838945964186 & 140.908617570616 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 85.1441176470588 & 0.591369768240766 & 143.977799034857 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 85.209375 & 0.578292804766197 & 147.346420874889 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 85.2933333333333 & 0.560417195444779 & 152.196138924038 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 85.4 & 0.535066627903756 & 159.606291154008 \tabularnewline
Median & 85.95 &  &  \tabularnewline
Midrange & 81.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 84.2113636363637 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 84.9525 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 84.2113636363637 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 84.9525 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 84.9525 &  &  \tabularnewline
Midmean - Closest Observation & 84.2113636363637 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 84.9525 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 84.3577777777778 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5379&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]83.36125[/C][C]1.13046211810688[/C][C]73.7408610733464[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]82.7190524039892[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]82.0408445607866[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]83.9646093601346[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]83.3525[/C][C]1.12604659474833[/C][C]74.022247737119[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]83.3375[/C][C]1.12364035278423[/C][C]74.1674146834448[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]83.3375[/C][C]1.11946299145640[/C][C]74.4441760344214[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]83.3775[/C][C]1.11103779601651[/C][C]75.0447017184655[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]83.39625[/C][C]1.10493204406139[/C][C]75.4763611465746[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]83.31375[/C][C]1.09258105708339[/C][C]76.254067796492[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]83.2875[/C][C]1.08275956486953[/C][C]76.9215093565448[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]83.2675[/C][C]1.07654036681975[/C][C]77.3473086252991[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]83.25625[/C][C]1.07115790263314[/C][C]77.7254686683805[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]83.21875[/C][C]1.06186499080746[/C][C]78.3703679096896[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]83.19125[/C][C]1.03983809862919[/C][C]80.0040411191614[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]83.37125[/C][C]1.00375591135923[/C][C]83.0592866816624[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]83.745[/C][C]0.910961552079498[/C][C]91.930334281212[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]84.34[/C][C]0.79013017674465[/C][C]106.741904666244[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]84.47125[/C][C]0.729893337426084[/C][C]115.730950905624[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]84.69125[/C][C]0.685150343267627[/C][C]123.609731546057[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]84.60625[/C][C]0.673507124914152[/C][C]125.620423111017[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]84.47125[/C][C]0.655606767343105[/C][C]128.84438387103[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]84.37625[/C][C]0.64343137623038[/C][C]131.134808026193[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]84.35125[/C][C]0.619789658455067[/C][C]136.096575425702[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]84.35125[/C][C]0.584472048226627[/C][C]144.320417470663[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]84.54375[/C][C]0.549487228603845[/C][C]153.85935395589[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]84.54375[/C][C]0.526971415379034[/C][C]160.433274998778[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]84.45375[/C][C]0.516377179602201[/C][C]163.550507915668[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]84.36[/C][C]0.505594023358362[/C][C]166.853238176445[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]84.3275[/C][C]0.501913979089109[/C][C]168.011857635526[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]83.4128205128205[/C][C]1.11232815421464[/C][C]74.9893996630109[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]83.4763157894737[/C][C]1.09607732538894[/C][C]76.159148497897[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]83.5513513513514[/C][C]1.07828906402807[/C][C]77.4851142783883[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]83.6305555555556[/C][C]1.05898539834135[/C][C]78.9723405880222[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]83.7028571428571[/C][C]1.03899730973767[/C][C]80.5611875587923[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]83.775[/C][C]1.01695757027351[/C][C]82.3780681208444[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]83.8681818181818[/C][C]0.99372426817993[/C][C]84.3978400283931[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]83.971875[/C][C]0.968052344153882[/C][C]86.743114158145[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]84.0854838709677[/C][C]0.938268730903797[/C][C]89.617698108698[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]84.2083333333333[/C][C]0.903021580870519[/C][C]93.2517396230508[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]84.3448275862069[/C][C]0.861529655865561[/C][C]97.901246941369[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]84.4946428571429[/C][C]0.814783931373065[/C][C]103.701901330766[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]84.6333333333333[/C][C]0.765028785489496[/C][C]110.627645571770[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]84.7384615384615[/C][C]0.725277051376263[/C][C]116.835988919909[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]84.784[/C][C]0.703294637359603[/C][C]120.552604123795[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]84.81875[/C][C]0.687906270997223[/C][C]123.299864496136[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]84.8326086956522[/C][C]0.677014291715268[/C][C]125.304014603181[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]84.8568181818182[/C][C]0.664601787711332[/C][C]127.680695043023[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]84.897619047619[/C][C]0.651305203422396[/C][C]130.349978169236[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]84.9525[/C][C]0.635458521109979[/C][C]133.686931841925[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]85.0157894736842[/C][C]0.618842657654588[/C][C]137.378683292283[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]85.0861111111111[/C][C]0.603838945964186[/C][C]140.908617570616[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]85.1441176470588[/C][C]0.591369768240766[/C][C]143.977799034857[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]85.209375[/C][C]0.578292804766197[/C][C]147.346420874889[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]85.2933333333333[/C][C]0.560417195444779[/C][C]152.196138924038[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]85.4[/C][C]0.535066627903756[/C][C]159.606291154008[/C][/ROW]
[ROW][C]Median[/C][C]85.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]81.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]84.2113636363637[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]84.9525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]84.2113636363637[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]84.9525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]84.9525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]84.2113636363637[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]84.9525[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]84.3577777777778[/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=5379&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5379&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 Mean83.361251.1304621181068873.7408610733464
Geometric Mean82.7190524039892
Harmonic Mean82.0408445607866
Quadratic Mean83.9646093601346
Winsorized Mean ( 1 / 26 )83.35251.1260465947483374.022247737119
Winsorized Mean ( 2 / 26 )83.33751.1236403527842374.1674146834448
Winsorized Mean ( 3 / 26 )83.33751.1194629914564074.4441760344214
Winsorized Mean ( 4 / 26 )83.37751.1110377960165175.0447017184655
Winsorized Mean ( 5 / 26 )83.396251.1049320440613975.4763611465746
Winsorized Mean ( 6 / 26 )83.313751.0925810570833976.254067796492
Winsorized Mean ( 7 / 26 )83.28751.0827595648695376.9215093565448
Winsorized Mean ( 8 / 26 )83.26751.0765403668197577.3473086252991
Winsorized Mean ( 9 / 26 )83.256251.0711579026331477.7254686683805
Winsorized Mean ( 10 / 26 )83.218751.0618649908074678.3703679096896
Winsorized Mean ( 11 / 26 )83.191251.0398380986291980.0040411191614
Winsorized Mean ( 12 / 26 )83.371251.0037559113592383.0592866816624
Winsorized Mean ( 13 / 26 )83.7450.91096155207949891.930334281212
Winsorized Mean ( 14 / 26 )84.340.79013017674465106.741904666244
Winsorized Mean ( 15 / 26 )84.471250.729893337426084115.730950905624
Winsorized Mean ( 16 / 26 )84.691250.685150343267627123.609731546057
Winsorized Mean ( 17 / 26 )84.606250.673507124914152125.620423111017
Winsorized Mean ( 18 / 26 )84.471250.655606767343105128.84438387103
Winsorized Mean ( 19 / 26 )84.376250.64343137623038131.134808026193
Winsorized Mean ( 20 / 26 )84.351250.619789658455067136.096575425702
Winsorized Mean ( 21 / 26 )84.351250.584472048226627144.320417470663
Winsorized Mean ( 22 / 26 )84.543750.549487228603845153.85935395589
Winsorized Mean ( 23 / 26 )84.543750.526971415379034160.433274998778
Winsorized Mean ( 24 / 26 )84.453750.516377179602201163.550507915668
Winsorized Mean ( 25 / 26 )84.360.505594023358362166.853238176445
Winsorized Mean ( 26 / 26 )84.32750.501913979089109168.011857635526
Trimmed Mean ( 1 / 26 )83.41282051282051.1123281542146474.9893996630109
Trimmed Mean ( 2 / 26 )83.47631578947371.0960773253889476.159148497897
Trimmed Mean ( 3 / 26 )83.55135135135141.0782890640280777.4851142783883
Trimmed Mean ( 4 / 26 )83.63055555555561.0589853983413578.9723405880222
Trimmed Mean ( 5 / 26 )83.70285714285711.0389973097376780.5611875587923
Trimmed Mean ( 6 / 26 )83.7751.0169575702735182.3780681208444
Trimmed Mean ( 7 / 26 )83.86818181818180.9937242681799384.3978400283931
Trimmed Mean ( 8 / 26 )83.9718750.96805234415388286.743114158145
Trimmed Mean ( 9 / 26 )84.08548387096770.93826873090379789.617698108698
Trimmed Mean ( 10 / 26 )84.20833333333330.90302158087051993.2517396230508
Trimmed Mean ( 11 / 26 )84.34482758620690.86152965586556197.901246941369
Trimmed Mean ( 12 / 26 )84.49464285714290.814783931373065103.701901330766
Trimmed Mean ( 13 / 26 )84.63333333333330.765028785489496110.627645571770
Trimmed Mean ( 14 / 26 )84.73846153846150.725277051376263116.835988919909
Trimmed Mean ( 15 / 26 )84.7840.703294637359603120.552604123795
Trimmed Mean ( 16 / 26 )84.818750.687906270997223123.299864496136
Trimmed Mean ( 17 / 26 )84.83260869565220.677014291715268125.304014603181
Trimmed Mean ( 18 / 26 )84.85681818181820.664601787711332127.680695043023
Trimmed Mean ( 19 / 26 )84.8976190476190.651305203422396130.349978169236
Trimmed Mean ( 20 / 26 )84.95250.635458521109979133.686931841925
Trimmed Mean ( 21 / 26 )85.01578947368420.618842657654588137.378683292283
Trimmed Mean ( 22 / 26 )85.08611111111110.603838945964186140.908617570616
Trimmed Mean ( 23 / 26 )85.14411764705880.591369768240766143.977799034857
Trimmed Mean ( 24 / 26 )85.2093750.578292804766197147.346420874889
Trimmed Mean ( 25 / 26 )85.29333333333330.560417195444779152.196138924038
Trimmed Mean ( 26 / 26 )85.40.535066627903756159.606291154008
Median85.95
Midrange81.35
Midmean - Weighted Average at Xnp84.2113636363637
Midmean - Weighted Average at X(n+1)p84.9525
Midmean - Empirical Distribution Function84.2113636363637
Midmean - Empirical Distribution Function - Averaging84.9525
Midmean - Empirical Distribution Function - Interpolation84.9525
Midmean - Closest Observation84.2113636363637
Midmean - True Basic - Statistics Graphics Toolkit84.9525
Midmean - MS Excel (old versions)84.3577777777778
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')