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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 computationSat, 13 Oct 2012 05:46:19 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/13/t1350121594ge9v7mesr0g56ep.htm/, Retrieved Fri, 03 May 2024 10:05:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175609, Retrieved Fri, 03 May 2024 10:05:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-13 09:46:19] [5af040df2efe5a417a92383fa6aaebd4] [Current]
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Dataseries X:
99.42
99.42
99.42
99.42
99.42
109.26
110.00
110.00
109.26
100.07
100.07
100.05
100.05
100.05
100.05
100.05
100.05
108.77
111.32
111.60
108.52
103.13
102.87
102.75
102.75
102.75
102.75
102.75
102.75
115.22
115.53
115.40
111.99
107.93
107.43
106.98
106.98
106.98
106.98
106.98
106.98
113.71
118.77
118.54
116.16
110.52
110.06
109.90
109.90
110.72
110.09
110.07
112.45
113.06
119.83
119.84
113.73
110.50
110.12
109.86
110.36
110.36
110.59
112.52
112.10
115.90
122.96
121.26
114.55
111.57
110.65
109.77




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175609&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175609&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175609&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.6745833333330.712269564018479152.575076660883
Geometric Mean108.508985271629
Harmonic Mean108.343561687374
Quadratic Mean108.840182588203
Winsorized Mean ( 1 / 24 )108.6509722222220.705963285998989153.904564694853
Winsorized Mean ( 2 / 24 )108.6115277777780.696520714424873155.934382895504
Winsorized Mean ( 3 / 24 )108.6111111111110.696426142733802155.954959824973
Winsorized Mean ( 4 / 24 )108.5522222222220.683541770060283158.808469323899
Winsorized Mean ( 5 / 24 )108.580.672165700749805161.537549266317
Winsorized Mean ( 6 / 24 )108.3816666666670.634236537827563170.885245807352
Winsorized Mean ( 7 / 24 )108.3563888888890.629921415769626172.015724781322
Winsorized Mean ( 8 / 24 )108.3152777777780.623101497527912173.832478669217
Winsorized Mean ( 9 / 24 )108.2990277777780.62046675725557174.54444820993
Winsorized Mean ( 10 / 24 )108.2740277777780.616468076757016175.636065937693
Winsorized Mean ( 11 / 24 )108.1747222222220.600104026331027180.25995073486
Winsorized Mean ( 12 / 24 )108.0380555555560.58042816608222186.13510141107
Winsorized Mean ( 13 / 24 )108.5183333333330.492671488537903220.265097246407
Winsorized Mean ( 14 / 24 )108.3919444444440.474524662866515228.422151526686
Winsorized Mean ( 15 / 24 )108.2794444444440.459410381496028235.692202017382
Winsorized Mean ( 16 / 24 )108.2638888888890.457396633762527236.695858468206
Winsorized Mean ( 17 / 24 )108.181250.446965553138593242.034871010419
Winsorized Mean ( 18 / 24 )108.153750.443592728197149243.813171689173
Winsorized Mean ( 19 / 24 )108.08250.42588739860564253.781868996038
Winsorized Mean ( 20 / 24 )108.1463888888890.412505053108688262.169852402739
Winsorized Mean ( 21 / 24 )109.1963888888890.223767298363115487.990826575973
Winsorized Mean ( 22 / 24 )109.0130555555560.200451235770949543.838281347003
Winsorized Mean ( 23 / 24 )108.9906944444440.197789063276995551.045101476657
Winsorized Mean ( 24 / 24 )108.9706944444440.195440428587142557.564753783054
Trimmed Mean ( 1 / 24 )108.6027142857140.690572179163571157.264826997889
Trimmed Mean ( 2 / 24 )108.5516176470590.672204927752234161.485899858011
Trimmed Mean ( 3 / 24 )108.5189393939390.65629233809616165.351525676412
Trimmed Mean ( 4 / 24 )108.4843750.637178952578573170.257310855889
Trimmed Mean ( 5 / 24 )108.4646774193550.618975233255336175.232661327843
Trimmed Mean ( 6 / 24 )108.4370.600525678381433180.570130310272
Trimmed Mean ( 7 / 24 )108.4484482758620.588927876451329184.145550944768
Trimmed Mean ( 8 / 24 )108.4653571428570.575631892447742188.428331657638
Trimmed Mean ( 9 / 24 )108.490370370370.560710837343201193.487200790388
Trimmed Mean ( 10 / 24 )108.5198076923080.542595606076367200.001265172491
Trimmed Mean ( 11 / 24 )108.55520.520628524389668208.507976252855
Trimmed Mean ( 12 / 24 )108.6070833333330.49644882160839218.767934590859
Trimmed Mean ( 13 / 24 )108.6813043478260.469678439561528231.395131633648
Trimmed Mean ( 14 / 24 )108.7018181818180.457582843240249237.55658628299
Trimmed Mean ( 15 / 24 )108.7397619047620.445439204116462244.118076944865
Trimmed Mean ( 16 / 24 )108.7950.432185115846178251.732408199643
Trimmed Mean ( 17 / 24 )108.8578947368420.414299552483997262.751658996897
Trimmed Mean ( 18 / 24 )108.93750.391665020259964278.139467057063
Trimmed Mean ( 19 / 24 )109.0297058823530.35997858059029302.878314880755
Trimmed Mean ( 20 / 24 )109.1418750.318202625360461342.994891624051
Trimmed Mean ( 21 / 24 )109.2613333333330.258146235547224423.253638007615
Trimmed Mean ( 22 / 24 )109.2692857142860.253368798985431431.265752341388
Trimmed Mean ( 23 / 24 )109.3015384615380.251639358733695434.357880307628
Trimmed Mean ( 24 / 24 )109.3420833333330.247861125187527441.142527899876
Median109.9
Midrange111.19
Midmean - Weighted Average at Xnp108.182926829268
Midmean - Weighted Average at X(n+1)p108.182926829268
Midmean - Empirical Distribution Function108.182926829268
Midmean - Empirical Distribution Function - Averaging108.182926829268
Midmean - Empirical Distribution Function - Interpolation108.182926829268
Midmean - Closest Observation108.182926829268
Midmean - True Basic - Statistics Graphics Toolkit108.182926829268
Midmean - MS Excel (old versions)108.276190476191
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.674583333333 & 0.712269564018479 & 152.575076660883 \tabularnewline
Geometric Mean & 108.508985271629 &  &  \tabularnewline
Harmonic Mean & 108.343561687374 &  &  \tabularnewline
Quadratic Mean & 108.840182588203 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 108.650972222222 & 0.705963285998989 & 153.904564694853 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 108.611527777778 & 0.696520714424873 & 155.934382895504 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 108.611111111111 & 0.696426142733802 & 155.954959824973 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 108.552222222222 & 0.683541770060283 & 158.808469323899 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 108.58 & 0.672165700749805 & 161.537549266317 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 108.381666666667 & 0.634236537827563 & 170.885245807352 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 108.356388888889 & 0.629921415769626 & 172.015724781322 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 108.315277777778 & 0.623101497527912 & 173.832478669217 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 108.299027777778 & 0.62046675725557 & 174.54444820993 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 108.274027777778 & 0.616468076757016 & 175.636065937693 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 108.174722222222 & 0.600104026331027 & 180.25995073486 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 108.038055555556 & 0.58042816608222 & 186.13510141107 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 108.518333333333 & 0.492671488537903 & 220.265097246407 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 108.391944444444 & 0.474524662866515 & 228.422151526686 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 108.279444444444 & 0.459410381496028 & 235.692202017382 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 108.263888888889 & 0.457396633762527 & 236.695858468206 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 108.18125 & 0.446965553138593 & 242.034871010419 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.15375 & 0.443592728197149 & 243.813171689173 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.0825 & 0.42588739860564 & 253.781868996038 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.146388888889 & 0.412505053108688 & 262.169852402739 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 109.196388888889 & 0.223767298363115 & 487.990826575973 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 109.013055555556 & 0.200451235770949 & 543.838281347003 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.990694444444 & 0.197789063276995 & 551.045101476657 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.970694444444 & 0.195440428587142 & 557.564753783054 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 108.602714285714 & 0.690572179163571 & 157.264826997889 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 108.551617647059 & 0.672204927752234 & 161.485899858011 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 108.518939393939 & 0.65629233809616 & 165.351525676412 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 108.484375 & 0.637178952578573 & 170.257310855889 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 108.464677419355 & 0.618975233255336 & 175.232661327843 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 108.437 & 0.600525678381433 & 180.570130310272 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 108.448448275862 & 0.588927876451329 & 184.145550944768 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 108.465357142857 & 0.575631892447742 & 188.428331657638 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 108.49037037037 & 0.560710837343201 & 193.487200790388 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 108.519807692308 & 0.542595606076367 & 200.001265172491 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.5552 & 0.520628524389668 & 208.507976252855 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.607083333333 & 0.49644882160839 & 218.767934590859 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.681304347826 & 0.469678439561528 & 231.395131633648 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.701818181818 & 0.457582843240249 & 237.55658628299 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.739761904762 & 0.445439204116462 & 244.118076944865 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.795 & 0.432185115846178 & 251.732408199643 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.857894736842 & 0.414299552483997 & 262.751658996897 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.9375 & 0.391665020259964 & 278.139467057063 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 109.029705882353 & 0.35997858059029 & 302.878314880755 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 109.141875 & 0.318202625360461 & 342.994891624051 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 109.261333333333 & 0.258146235547224 & 423.253638007615 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 109.269285714286 & 0.253368798985431 & 431.265752341388 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 109.301538461538 & 0.251639358733695 & 434.357880307628 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 109.342083333333 & 0.247861125187527 & 441.142527899876 \tabularnewline
Median & 109.9 &  &  \tabularnewline
Midrange & 111.19 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.182926829268 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.182926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.182926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.182926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.182926829268 &  &  \tabularnewline
Midmean - Closest Observation & 108.182926829268 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.182926829268 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.276190476191 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175609&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]108.674583333333[/C][C]0.712269564018479[/C][C]152.575076660883[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.508985271629[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.343561687374[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.840182588203[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]108.650972222222[/C][C]0.705963285998989[/C][C]153.904564694853[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]108.611527777778[/C][C]0.696520714424873[/C][C]155.934382895504[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]108.611111111111[/C][C]0.696426142733802[/C][C]155.954959824973[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]108.552222222222[/C][C]0.683541770060283[/C][C]158.808469323899[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]108.58[/C][C]0.672165700749805[/C][C]161.537549266317[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]108.381666666667[/C][C]0.634236537827563[/C][C]170.885245807352[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]108.356388888889[/C][C]0.629921415769626[/C][C]172.015724781322[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]108.315277777778[/C][C]0.623101497527912[/C][C]173.832478669217[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]108.299027777778[/C][C]0.62046675725557[/C][C]174.54444820993[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]108.274027777778[/C][C]0.616468076757016[/C][C]175.636065937693[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]108.174722222222[/C][C]0.600104026331027[/C][C]180.25995073486[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]108.038055555556[/C][C]0.58042816608222[/C][C]186.13510141107[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]108.518333333333[/C][C]0.492671488537903[/C][C]220.265097246407[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]108.391944444444[/C][C]0.474524662866515[/C][C]228.422151526686[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]108.279444444444[/C][C]0.459410381496028[/C][C]235.692202017382[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]108.263888888889[/C][C]0.457396633762527[/C][C]236.695858468206[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]108.18125[/C][C]0.446965553138593[/C][C]242.034871010419[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.15375[/C][C]0.443592728197149[/C][C]243.813171689173[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.0825[/C][C]0.42588739860564[/C][C]253.781868996038[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.146388888889[/C][C]0.412505053108688[/C][C]262.169852402739[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]109.196388888889[/C][C]0.223767298363115[/C][C]487.990826575973[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]109.013055555556[/C][C]0.200451235770949[/C][C]543.838281347003[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.990694444444[/C][C]0.197789063276995[/C][C]551.045101476657[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.970694444444[/C][C]0.195440428587142[/C][C]557.564753783054[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]108.602714285714[/C][C]0.690572179163571[/C][C]157.264826997889[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]108.551617647059[/C][C]0.672204927752234[/C][C]161.485899858011[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]108.518939393939[/C][C]0.65629233809616[/C][C]165.351525676412[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]108.484375[/C][C]0.637178952578573[/C][C]170.257310855889[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]108.464677419355[/C][C]0.618975233255336[/C][C]175.232661327843[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]108.437[/C][C]0.600525678381433[/C][C]180.570130310272[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]108.448448275862[/C][C]0.588927876451329[/C][C]184.145550944768[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]108.465357142857[/C][C]0.575631892447742[/C][C]188.428331657638[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]108.49037037037[/C][C]0.560710837343201[/C][C]193.487200790388[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]108.519807692308[/C][C]0.542595606076367[/C][C]200.001265172491[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.5552[/C][C]0.520628524389668[/C][C]208.507976252855[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.607083333333[/C][C]0.49644882160839[/C][C]218.767934590859[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.681304347826[/C][C]0.469678439561528[/C][C]231.395131633648[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.701818181818[/C][C]0.457582843240249[/C][C]237.55658628299[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.739761904762[/C][C]0.445439204116462[/C][C]244.118076944865[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.795[/C][C]0.432185115846178[/C][C]251.732408199643[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.857894736842[/C][C]0.414299552483997[/C][C]262.751658996897[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.9375[/C][C]0.391665020259964[/C][C]278.139467057063[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]109.029705882353[/C][C]0.35997858059029[/C][C]302.878314880755[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]109.141875[/C][C]0.318202625360461[/C][C]342.994891624051[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]109.261333333333[/C][C]0.258146235547224[/C][C]423.253638007615[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]109.269285714286[/C][C]0.253368798985431[/C][C]431.265752341388[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]109.301538461538[/C][C]0.251639358733695[/C][C]434.357880307628[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]109.342083333333[/C][C]0.247861125187527[/C][C]441.142527899876[/C][/ROW]
[ROW][C]Median[/C][C]109.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.19[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.182926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.182926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.182926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.182926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.182926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.182926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.182926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.276190476191[/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=175609&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175609&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 Mean108.6745833333330.712269564018479152.575076660883
Geometric Mean108.508985271629
Harmonic Mean108.343561687374
Quadratic Mean108.840182588203
Winsorized Mean ( 1 / 24 )108.6509722222220.705963285998989153.904564694853
Winsorized Mean ( 2 / 24 )108.6115277777780.696520714424873155.934382895504
Winsorized Mean ( 3 / 24 )108.6111111111110.696426142733802155.954959824973
Winsorized Mean ( 4 / 24 )108.5522222222220.683541770060283158.808469323899
Winsorized Mean ( 5 / 24 )108.580.672165700749805161.537549266317
Winsorized Mean ( 6 / 24 )108.3816666666670.634236537827563170.885245807352
Winsorized Mean ( 7 / 24 )108.3563888888890.629921415769626172.015724781322
Winsorized Mean ( 8 / 24 )108.3152777777780.623101497527912173.832478669217
Winsorized Mean ( 9 / 24 )108.2990277777780.62046675725557174.54444820993
Winsorized Mean ( 10 / 24 )108.2740277777780.616468076757016175.636065937693
Winsorized Mean ( 11 / 24 )108.1747222222220.600104026331027180.25995073486
Winsorized Mean ( 12 / 24 )108.0380555555560.58042816608222186.13510141107
Winsorized Mean ( 13 / 24 )108.5183333333330.492671488537903220.265097246407
Winsorized Mean ( 14 / 24 )108.3919444444440.474524662866515228.422151526686
Winsorized Mean ( 15 / 24 )108.2794444444440.459410381496028235.692202017382
Winsorized Mean ( 16 / 24 )108.2638888888890.457396633762527236.695858468206
Winsorized Mean ( 17 / 24 )108.181250.446965553138593242.034871010419
Winsorized Mean ( 18 / 24 )108.153750.443592728197149243.813171689173
Winsorized Mean ( 19 / 24 )108.08250.42588739860564253.781868996038
Winsorized Mean ( 20 / 24 )108.1463888888890.412505053108688262.169852402739
Winsorized Mean ( 21 / 24 )109.1963888888890.223767298363115487.990826575973
Winsorized Mean ( 22 / 24 )109.0130555555560.200451235770949543.838281347003
Winsorized Mean ( 23 / 24 )108.9906944444440.197789063276995551.045101476657
Winsorized Mean ( 24 / 24 )108.9706944444440.195440428587142557.564753783054
Trimmed Mean ( 1 / 24 )108.6027142857140.690572179163571157.264826997889
Trimmed Mean ( 2 / 24 )108.5516176470590.672204927752234161.485899858011
Trimmed Mean ( 3 / 24 )108.5189393939390.65629233809616165.351525676412
Trimmed Mean ( 4 / 24 )108.4843750.637178952578573170.257310855889
Trimmed Mean ( 5 / 24 )108.4646774193550.618975233255336175.232661327843
Trimmed Mean ( 6 / 24 )108.4370.600525678381433180.570130310272
Trimmed Mean ( 7 / 24 )108.4484482758620.588927876451329184.145550944768
Trimmed Mean ( 8 / 24 )108.4653571428570.575631892447742188.428331657638
Trimmed Mean ( 9 / 24 )108.490370370370.560710837343201193.487200790388
Trimmed Mean ( 10 / 24 )108.5198076923080.542595606076367200.001265172491
Trimmed Mean ( 11 / 24 )108.55520.520628524389668208.507976252855
Trimmed Mean ( 12 / 24 )108.6070833333330.49644882160839218.767934590859
Trimmed Mean ( 13 / 24 )108.6813043478260.469678439561528231.395131633648
Trimmed Mean ( 14 / 24 )108.7018181818180.457582843240249237.55658628299
Trimmed Mean ( 15 / 24 )108.7397619047620.445439204116462244.118076944865
Trimmed Mean ( 16 / 24 )108.7950.432185115846178251.732408199643
Trimmed Mean ( 17 / 24 )108.8578947368420.414299552483997262.751658996897
Trimmed Mean ( 18 / 24 )108.93750.391665020259964278.139467057063
Trimmed Mean ( 19 / 24 )109.0297058823530.35997858059029302.878314880755
Trimmed Mean ( 20 / 24 )109.1418750.318202625360461342.994891624051
Trimmed Mean ( 21 / 24 )109.2613333333330.258146235547224423.253638007615
Trimmed Mean ( 22 / 24 )109.2692857142860.253368798985431431.265752341388
Trimmed Mean ( 23 / 24 )109.3015384615380.251639358733695434.357880307628
Trimmed Mean ( 24 / 24 )109.3420833333330.247861125187527441.142527899876
Median109.9
Midrange111.19
Midmean - Weighted Average at Xnp108.182926829268
Midmean - Weighted Average at X(n+1)p108.182926829268
Midmean - Empirical Distribution Function108.182926829268
Midmean - Empirical Distribution Function - Averaging108.182926829268
Midmean - Empirical Distribution Function - Interpolation108.182926829268
Midmean - Closest Observation108.182926829268
Midmean - True Basic - Statistics Graphics Toolkit108.182926829268
Midmean - MS Excel (old versions)108.276190476191
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')