Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 24 Dec 2007 02:30:51 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/24/t1198487525mcqewkp1vicnxjg.htm/, Retrieved Sun, 05 May 2024 16:14:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4849, Retrieved Sun, 05 May 2024 16:14:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKlaas Van Pelt
Estimated Impact280
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency 2] [2007-12-24 09:30:51] [6abd901c2e17b7d5559c695bbff3d863] [Current]
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Dataseries X:
124,9
120,4
141,2
95,4
111,4
113,3
78
77,7
110,1
109,6
111
97
90,9
94,7
113,5
107,1
103,7
107,7
75,2
74,1
115,7
116,2
95,4
95,9
89,9
102,4
130,2
98,9
102,1
117,3
87,8
66,6
106,3
104,5
113,1
95,1
96,9
107,1
135,4
120,3
105,5
128,4
78,2
85,8
128,7
131,2
128,9
112,3
115
116
140,2
121,2
104,1
128,8
76,1
86,9
127,6
108
113,5
117,4
102,4
117,9
132
95
120,8
128,9
88,4
81,1
120,7
131
123,6
139
109,6
108
130,3
111,7
105,9
128,7
89,9
101




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4849&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4849&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.421251.9499859572279255.6010414321807
Geometric Mean106.956138360016
Harmonic Mean105.406958132597
Quadratic Mean109.797817032034
Winsorized Mean ( 1 / 26 )108.50251.9240030913617656.3941401586858
Winsorized Mean ( 2 / 26 )108.51.9117011444843556.7557331401117
Winsorized Mean ( 3 / 26 )108.398751.8783809128180757.7086091858617
Winsorized Mean ( 4 / 26 )108.308751.8318094686917159.1266460028481
Winsorized Mean ( 5 / 26 )108.27751.8197727071522459.5005626661162
Winsorized Mean ( 6 / 26 )108.27751.8142343077501759.6822028651167
Winsorized Mean ( 7 / 26 )108.471.7528208729525861.8831060684972
Winsorized Mean ( 8 / 26 )108.931.6632745649714665.4912918733107
Winsorized Mean ( 9 / 26 )108.90751.6184525104188367.2911310643378
Winsorized Mean ( 10 / 26 )109.021.5993218499560568.1663919010398
Winsorized Mean ( 11 / 26 )109.088751.5834058326450768.8950032587463
Winsorized Mean ( 12 / 26 )109.298751.5445304617618070.7650335852399
Winsorized Mean ( 13 / 26 )109.298751.5445304617618070.7650335852399
Winsorized Mean ( 14 / 26 )109.421251.5086645257006672.5285496781879
Winsorized Mean ( 15 / 26 )109.983751.3790205244316779.7549768487508
Winsorized Mean ( 16 / 26 )109.503751.2858534620209085.1603648738475
Winsorized Mean ( 17 / 26 )109.248751.2416480393570687.9868904368181
Winsorized Mean ( 18 / 26 )108.776251.1554880657518494.1387914112487
Winsorized Mean ( 19 / 26 )108.681251.1426458494142295.1136785345308
Winsorized Mean ( 20 / 26 )108.781251.1209979360492197.03965235064
Winsorized Mean ( 21 / 26 )108.9651.07259755096174101.589827332999
Winsorized Mean ( 22 / 26 )108.9651.06497622841480102.316837777866
Winsorized Mean ( 23 / 26 )108.821250.896963396495029121.321840361858
Winsorized Mean ( 24 / 26 )109.301250.791586481337768138.078722384549
Winsorized Mean ( 25 / 26 )109.613750.742664003432017147.595345261720
Winsorized Mean ( 26 / 26 )109.353750.684054238887901159.861227053839
Trimmed Mean ( 1 / 26 )108.5371794871791.8790847250307857.7606629660626
Trimmed Mean ( 2 / 26 )108.5736842105261.8266250812474659.4395014746967
Trimmed Mean ( 3 / 26 )108.6135135135141.7728623228310561.2644942107353
Trimmed Mean ( 4 / 26 )108.6930555555561.7245583299634663.02660435838
Trimmed Mean ( 5 / 26 )108.8028571428571.6841103363387564.6055396699209
Trimmed Mean ( 6 / 26 )108.9264705882351.6395766729801366.4357284311982
Trimmed Mean ( 7 / 26 )109.0575757575761.5877592082947568.6864703336872
Trimmed Mean ( 8 / 26 )109.16251.541540374492570.8139091302997
Trimmed Mean ( 9 / 26 )109.21.5073379478582172.445598649701
Trimmed Mean ( 10 / 26 )109.2433333333331.4755509679891574.0356217462336
Trimmed Mean ( 11 / 26 )109.2741379310341.4406184402156475.8522415655584
Trimmed Mean ( 12 / 26 )109.2982142857141.4008566281642178.0224129209758
Trimmed Mean ( 13 / 26 )109.2981481481481.3597320890100380.382120148186
Trimmed Mean ( 14 / 26 )109.2980769230771.3082217398238183.5470575024975
Trimmed Mean ( 15 / 26 )109.2841.2511818413004687.3446180184426
Trimmed Mean ( 16 / 26 )109.206251.2070471496032290.4738891400378
Trimmed Mean ( 17 / 26 )109.1739130434781.1710577191046093.2267566853605
Trimmed Mean ( 18 / 26 )109.1659090909091.1338904905801596.2755310127476
Trimmed Mean ( 19 / 26 )109.2071428571431.1038334262703498.9344408840152
Trimmed Mean ( 20 / 26 )109.26251.06608971275452102.489029481104
Trimmed Mean ( 21 / 26 )109.3131578947371.02025832121108107.142628118905
Trimmed Mean ( 22 / 26 )109.350.970391019207582112.686533403096
Trimmed Mean ( 23 / 26 )109.3911764705880.902564850421694121.200350777541
Trimmed Mean ( 24 / 26 )109.4531250.858672366719074127.467855310417
Trimmed Mean ( 25 / 26 )109.470.828239373472497132.171934233256
Trimmed Mean ( 26 / 26 )109.4535714285710.797789309001485137.196086978859
Median109.6
Midrange103.9
Midmean - Weighted Average at Xnp108.602380952381
Midmean - Weighted Average at X(n+1)p109.2625
Midmean - Empirical Distribution Function108.602380952381
Midmean - Empirical Distribution Function - Averaging109.2625
Midmean - Empirical Distribution Function - Interpolation109.2625
Midmean - Closest Observation108.602380952381
Midmean - True Basic - Statistics Graphics Toolkit109.2625
Midmean - MS Excel (old versions)108.886046511628
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.42125 & 1.94998595722792 & 55.6010414321807 \tabularnewline
Geometric Mean & 106.956138360016 &  &  \tabularnewline
Harmonic Mean & 105.406958132597 &  &  \tabularnewline
Quadratic Mean & 109.797817032034 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 108.5025 & 1.92400309136176 & 56.3941401586858 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 108.5 & 1.91170114448435 & 56.7557331401117 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 108.39875 & 1.87838091281807 & 57.7086091858617 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 108.30875 & 1.83180946869171 & 59.1266460028481 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 108.2775 & 1.81977270715224 & 59.5005626661162 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 108.2775 & 1.81423430775017 & 59.6822028651167 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 108.47 & 1.75282087295258 & 61.8831060684972 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 108.93 & 1.66327456497146 & 65.4912918733107 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 108.9075 & 1.61845251041883 & 67.2911310643378 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 109.02 & 1.59932184995605 & 68.1663919010398 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 109.08875 & 1.58340583264507 & 68.8950032587463 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 109.29875 & 1.54453046176180 & 70.7650335852399 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 109.29875 & 1.54453046176180 & 70.7650335852399 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 109.42125 & 1.50866452570066 & 72.5285496781879 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 109.98375 & 1.37902052443167 & 79.7549768487508 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 109.50375 & 1.28585346202090 & 85.1603648738475 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 109.24875 & 1.24164803935706 & 87.9868904368181 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 108.77625 & 1.15548806575184 & 94.1387914112487 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 108.68125 & 1.14264584941422 & 95.1136785345308 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 108.78125 & 1.12099793604921 & 97.03965235064 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 108.965 & 1.07259755096174 & 101.589827332999 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 108.965 & 1.06497622841480 & 102.316837777866 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 108.82125 & 0.896963396495029 & 121.321840361858 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 109.30125 & 0.791586481337768 & 138.078722384549 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 109.61375 & 0.742664003432017 & 147.595345261720 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 109.35375 & 0.684054238887901 & 159.861227053839 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 108.537179487179 & 1.87908472503078 & 57.7606629660626 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 108.573684210526 & 1.82662508124746 & 59.4395014746967 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 108.613513513514 & 1.77286232283105 & 61.2644942107353 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 108.693055555556 & 1.72455832996346 & 63.02660435838 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 108.802857142857 & 1.68411033633875 & 64.6055396699209 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 108.926470588235 & 1.63957667298013 & 66.4357284311982 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 109.057575757576 & 1.58775920829475 & 68.6864703336872 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 109.1625 & 1.5415403744925 & 70.8139091302997 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 109.2 & 1.50733794785821 & 72.445598649701 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 109.243333333333 & 1.47555096798915 & 74.0356217462336 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 109.274137931034 & 1.44061844021564 & 75.8522415655584 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 109.298214285714 & 1.40085662816421 & 78.0224129209758 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 109.298148148148 & 1.35973208901003 & 80.382120148186 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 109.298076923077 & 1.30822173982381 & 83.5470575024975 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 109.284 & 1.25118184130046 & 87.3446180184426 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 109.20625 & 1.20704714960322 & 90.4738891400378 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 109.173913043478 & 1.17105771910460 & 93.2267566853605 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 109.165909090909 & 1.13389049058015 & 96.2755310127476 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 109.207142857143 & 1.10383342627034 & 98.9344408840152 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 109.2625 & 1.06608971275452 & 102.489029481104 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 109.313157894737 & 1.02025832121108 & 107.142628118905 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 109.35 & 0.970391019207582 & 112.686533403096 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 109.391176470588 & 0.902564850421694 & 121.200350777541 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 109.453125 & 0.858672366719074 & 127.467855310417 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 109.47 & 0.828239373472497 & 132.171934233256 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 109.453571428571 & 0.797789309001485 & 137.196086978859 \tabularnewline
Median & 109.6 &  &  \tabularnewline
Midrange & 103.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.602380952381 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.2625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.602380952381 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.2625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.2625 &  &  \tabularnewline
Midmean - Closest Observation & 108.602380952381 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.2625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.886046511628 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4849&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]108.42125[/C][C]1.94998595722792[/C][C]55.6010414321807[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]106.956138360016[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.406958132597[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.797817032034[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]108.5025[/C][C]1.92400309136176[/C][C]56.3941401586858[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]108.5[/C][C]1.91170114448435[/C][C]56.7557331401117[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]108.39875[/C][C]1.87838091281807[/C][C]57.7086091858617[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]108.30875[/C][C]1.83180946869171[/C][C]59.1266460028481[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]108.2775[/C][C]1.81977270715224[/C][C]59.5005626661162[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]108.2775[/C][C]1.81423430775017[/C][C]59.6822028651167[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]108.47[/C][C]1.75282087295258[/C][C]61.8831060684972[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]108.93[/C][C]1.66327456497146[/C][C]65.4912918733107[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]108.9075[/C][C]1.61845251041883[/C][C]67.2911310643378[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]109.02[/C][C]1.59932184995605[/C][C]68.1663919010398[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]109.08875[/C][C]1.58340583264507[/C][C]68.8950032587463[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]109.29875[/C][C]1.54453046176180[/C][C]70.7650335852399[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]109.29875[/C][C]1.54453046176180[/C][C]70.7650335852399[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]109.42125[/C][C]1.50866452570066[/C][C]72.5285496781879[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]109.98375[/C][C]1.37902052443167[/C][C]79.7549768487508[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]109.50375[/C][C]1.28585346202090[/C][C]85.1603648738475[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]109.24875[/C][C]1.24164803935706[/C][C]87.9868904368181[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]108.77625[/C][C]1.15548806575184[/C][C]94.1387914112487[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]108.68125[/C][C]1.14264584941422[/C][C]95.1136785345308[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]108.78125[/C][C]1.12099793604921[/C][C]97.03965235064[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]108.965[/C][C]1.07259755096174[/C][C]101.589827332999[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]108.965[/C][C]1.06497622841480[/C][C]102.316837777866[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]108.82125[/C][C]0.896963396495029[/C][C]121.321840361858[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]109.30125[/C][C]0.791586481337768[/C][C]138.078722384549[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]109.61375[/C][C]0.742664003432017[/C][C]147.595345261720[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]109.35375[/C][C]0.684054238887901[/C][C]159.861227053839[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]108.537179487179[/C][C]1.87908472503078[/C][C]57.7606629660626[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]108.573684210526[/C][C]1.82662508124746[/C][C]59.4395014746967[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]108.613513513514[/C][C]1.77286232283105[/C][C]61.2644942107353[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]108.693055555556[/C][C]1.72455832996346[/C][C]63.02660435838[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]108.802857142857[/C][C]1.68411033633875[/C][C]64.6055396699209[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]108.926470588235[/C][C]1.63957667298013[/C][C]66.4357284311982[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]109.057575757576[/C][C]1.58775920829475[/C][C]68.6864703336872[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]109.1625[/C][C]1.5415403744925[/C][C]70.8139091302997[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]109.2[/C][C]1.50733794785821[/C][C]72.445598649701[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]109.243333333333[/C][C]1.47555096798915[/C][C]74.0356217462336[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]109.274137931034[/C][C]1.44061844021564[/C][C]75.8522415655584[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]109.298214285714[/C][C]1.40085662816421[/C][C]78.0224129209758[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]109.298148148148[/C][C]1.35973208901003[/C][C]80.382120148186[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]109.298076923077[/C][C]1.30822173982381[/C][C]83.5470575024975[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]109.284[/C][C]1.25118184130046[/C][C]87.3446180184426[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]109.20625[/C][C]1.20704714960322[/C][C]90.4738891400378[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]109.173913043478[/C][C]1.17105771910460[/C][C]93.2267566853605[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]109.165909090909[/C][C]1.13389049058015[/C][C]96.2755310127476[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]109.207142857143[/C][C]1.10383342627034[/C][C]98.9344408840152[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]109.2625[/C][C]1.06608971275452[/C][C]102.489029481104[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]109.313157894737[/C][C]1.02025832121108[/C][C]107.142628118905[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]109.35[/C][C]0.970391019207582[/C][C]112.686533403096[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]109.391176470588[/C][C]0.902564850421694[/C][C]121.200350777541[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]109.453125[/C][C]0.858672366719074[/C][C]127.467855310417[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]109.47[/C][C]0.828239373472497[/C][C]132.171934233256[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]109.453571428571[/C][C]0.797789309001485[/C][C]137.196086978859[/C][/ROW]
[ROW][C]Median[/C][C]109.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.602380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.2625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.602380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.2625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.2625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.602380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.2625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.886046511628[/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=4849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4849&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 Mean108.421251.9499859572279255.6010414321807
Geometric Mean106.956138360016
Harmonic Mean105.406958132597
Quadratic Mean109.797817032034
Winsorized Mean ( 1 / 26 )108.50251.9240030913617656.3941401586858
Winsorized Mean ( 2 / 26 )108.51.9117011444843556.7557331401117
Winsorized Mean ( 3 / 26 )108.398751.8783809128180757.7086091858617
Winsorized Mean ( 4 / 26 )108.308751.8318094686917159.1266460028481
Winsorized Mean ( 5 / 26 )108.27751.8197727071522459.5005626661162
Winsorized Mean ( 6 / 26 )108.27751.8142343077501759.6822028651167
Winsorized Mean ( 7 / 26 )108.471.7528208729525861.8831060684972
Winsorized Mean ( 8 / 26 )108.931.6632745649714665.4912918733107
Winsorized Mean ( 9 / 26 )108.90751.6184525104188367.2911310643378
Winsorized Mean ( 10 / 26 )109.021.5993218499560568.1663919010398
Winsorized Mean ( 11 / 26 )109.088751.5834058326450768.8950032587463
Winsorized Mean ( 12 / 26 )109.298751.5445304617618070.7650335852399
Winsorized Mean ( 13 / 26 )109.298751.5445304617618070.7650335852399
Winsorized Mean ( 14 / 26 )109.421251.5086645257006672.5285496781879
Winsorized Mean ( 15 / 26 )109.983751.3790205244316779.7549768487508
Winsorized Mean ( 16 / 26 )109.503751.2858534620209085.1603648738475
Winsorized Mean ( 17 / 26 )109.248751.2416480393570687.9868904368181
Winsorized Mean ( 18 / 26 )108.776251.1554880657518494.1387914112487
Winsorized Mean ( 19 / 26 )108.681251.1426458494142295.1136785345308
Winsorized Mean ( 20 / 26 )108.781251.1209979360492197.03965235064
Winsorized Mean ( 21 / 26 )108.9651.07259755096174101.589827332999
Winsorized Mean ( 22 / 26 )108.9651.06497622841480102.316837777866
Winsorized Mean ( 23 / 26 )108.821250.896963396495029121.321840361858
Winsorized Mean ( 24 / 26 )109.301250.791586481337768138.078722384549
Winsorized Mean ( 25 / 26 )109.613750.742664003432017147.595345261720
Winsorized Mean ( 26 / 26 )109.353750.684054238887901159.861227053839
Trimmed Mean ( 1 / 26 )108.5371794871791.8790847250307857.7606629660626
Trimmed Mean ( 2 / 26 )108.5736842105261.8266250812474659.4395014746967
Trimmed Mean ( 3 / 26 )108.6135135135141.7728623228310561.2644942107353
Trimmed Mean ( 4 / 26 )108.6930555555561.7245583299634663.02660435838
Trimmed Mean ( 5 / 26 )108.8028571428571.6841103363387564.6055396699209
Trimmed Mean ( 6 / 26 )108.9264705882351.6395766729801366.4357284311982
Trimmed Mean ( 7 / 26 )109.0575757575761.5877592082947568.6864703336872
Trimmed Mean ( 8 / 26 )109.16251.541540374492570.8139091302997
Trimmed Mean ( 9 / 26 )109.21.5073379478582172.445598649701
Trimmed Mean ( 10 / 26 )109.2433333333331.4755509679891574.0356217462336
Trimmed Mean ( 11 / 26 )109.2741379310341.4406184402156475.8522415655584
Trimmed Mean ( 12 / 26 )109.2982142857141.4008566281642178.0224129209758
Trimmed Mean ( 13 / 26 )109.2981481481481.3597320890100380.382120148186
Trimmed Mean ( 14 / 26 )109.2980769230771.3082217398238183.5470575024975
Trimmed Mean ( 15 / 26 )109.2841.2511818413004687.3446180184426
Trimmed Mean ( 16 / 26 )109.206251.2070471496032290.4738891400378
Trimmed Mean ( 17 / 26 )109.1739130434781.1710577191046093.2267566853605
Trimmed Mean ( 18 / 26 )109.1659090909091.1338904905801596.2755310127476
Trimmed Mean ( 19 / 26 )109.2071428571431.1038334262703498.9344408840152
Trimmed Mean ( 20 / 26 )109.26251.06608971275452102.489029481104
Trimmed Mean ( 21 / 26 )109.3131578947371.02025832121108107.142628118905
Trimmed Mean ( 22 / 26 )109.350.970391019207582112.686533403096
Trimmed Mean ( 23 / 26 )109.3911764705880.902564850421694121.200350777541
Trimmed Mean ( 24 / 26 )109.4531250.858672366719074127.467855310417
Trimmed Mean ( 25 / 26 )109.470.828239373472497132.171934233256
Trimmed Mean ( 26 / 26 )109.4535714285710.797789309001485137.196086978859
Median109.6
Midrange103.9
Midmean - Weighted Average at Xnp108.602380952381
Midmean - Weighted Average at X(n+1)p109.2625
Midmean - Empirical Distribution Function108.602380952381
Midmean - Empirical Distribution Function - Averaging109.2625
Midmean - Empirical Distribution Function - Interpolation109.2625
Midmean - Closest Observation108.602380952381
Midmean - True Basic - Statistics Graphics Toolkit109.2625
Midmean - MS Excel (old versions)108.886046511628
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')