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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 computationThu, 17 Apr 2008 09:52:50 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/17/t1208447685papujcmka8auq26.htm/, Retrieved Thu, 31 Oct 2024 22:49:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10174, Retrieved Thu, 31 Oct 2024 22:49:06 +0000
QR Codes:

Original text written by user:Centrummaten
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact338
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2008-04-17 15:52:50] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1,74
1,73
1,74
1,73
1,74
1,73
1,73
1,74
1,75
1,73
1,74
1,74
1,74
1,74
1,76
1,76
1,78
1,77
1,78
1,79
1,83
1,82
1,84
1,83
1,83
1,84
1,83
1,83
1,83
1,83
1,83
1,84
1,83
1,84
1,84
1,83
1,84
1,85
1,85
1,85
1,85
1,84
1,84
1,85
1,84
1,84
1,84
1,84
1,85
1,84
1,85
1,84
1,84
1,84
1,84
1,84
1,83
1,83
1,82
1,83
1,83
1,83
1,87
1,87
1,86
1,87
1,87
1,89
1,89
1,88
1,88
1,87




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=10174&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=10174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10174&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.817638888888890.00552591368448146328.930018214617
Geometric Mean1.81703438536713
Harmonic Mean1.81642180738002
Quadratic Mean1.81823517914121
Winsorized Mean ( 1 / 24 )1.817638888888890.00552591368448146328.930018214617
Winsorized Mean ( 2 / 24 )1.817361111111110.00547791502619883331.761464429322
Winsorized Mean ( 3 / 24 )1.817361111111110.00547791502619883331.761464429322
Winsorized Mean ( 4 / 24 )1.816805555555560.00539455178153528336.785265788754
Winsorized Mean ( 5 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 6 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 7 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 8 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 9 / 24 )1.816250.0050793296016185357.576716309424
Winsorized Mean ( 10 / 24 )1.814861111111110.00492507658065687368.493988142020
Winsorized Mean ( 11 / 24 )1.814861111111110.00492507658065687368.493988142020
Winsorized Mean ( 12 / 24 )1.814861111111110.00492507658065687368.493988142020
Winsorized Mean ( 13 / 24 )1.816666666666670.00454502772217125399.704199339582
Winsorized Mean ( 14 / 24 )1.818611111111110.00415046406306491438.170547552737
Winsorized Mean ( 15 / 24 )1.818611111111110.00415046406306491438.170547552737
Winsorized Mean ( 16 / 24 )1.820833333333330.00371495097139583490.136571748398
Winsorized Mean ( 17 / 24 )1.820833333333330.00302409468598398602.108572119946
Winsorized Mean ( 18 / 24 )1.820833333333330.00302409468598398602.108572119946
Winsorized Mean ( 19 / 24 )1.823472222222220.00252653927595031721.727241519473
Winsorized Mean ( 20 / 24 )1.831805555555560.001033976569615411771.61224865753
Winsorized Mean ( 21 / 24 )1.831805555555560.001033976569615411771.61224865753
Winsorized Mean ( 22 / 24 )1.834861111111110.0005931618532716563093.35656194125
Winsorized Mean ( 23 / 24 )1.834861111111110.0005931618532716563093.35656194125
Winsorized Mean ( 24 / 24 )1.834861111111110.0005931618532716563093.35656194125
Trimmed Mean ( 1 / 24 )1.817857142857140.00544459333367171333.882997581239
Trimmed Mean ( 2 / 24 )1.818088235294120.00534686796697294340.02863854583
Trimmed Mean ( 3 / 24 )1.818484848484850.00525899129825971345.785863742847
Trimmed Mean ( 4 / 24 )1.818906250.00515203952670418353.045864763304
Trimmed Mean ( 5 / 24 )1.819516129032260.00505091694611525360.23481447892
Trimmed Mean ( 6 / 24 )1.820.00497451130382317365.865084797624
Trimmed Mean ( 7 / 24 )1.820517241379310.00487857653433844373.165661861689
Trimmed Mean ( 8 / 24 )1.821071428571430.00475830491637306382.714319611008
Trimmed Mean ( 9 / 24 )1.821666666666670.00460721337625464395.394464700821
Trimmed Mean ( 10 / 24 )1.82250.00445248926259056409.321593498831
Trimmed Mean ( 11 / 24 )1.82360.00428342796157947425.733785266594
Trimmed Mean ( 12 / 24 )1.824791666666670.00406059579849691449.39012825215
Trimmed Mean ( 13 / 24 )1.826086956521740.00376197939559813485.405889957407
Trimmed Mean ( 14 / 24 )1.827272727272730.003476949714854525.539014690483
Trimmed Mean ( 15 / 24 )1.828333333333330.00321358662333468568.93855608476
Trimmed Mean ( 16 / 24 )1.82950.00284086480151957643.994039780212
Trimmed Mean ( 17 / 24 )1.830526315789470.00247167074013923740.60281819186
Trimmed Mean ( 18 / 24 )1.831666666666670.00216391767000034846.45857467691
Trimmed Mean ( 19 / 24 )1.832941176470590.001663780661615411101.67236508864
Trimmed Mean ( 20 / 24 )1.83406250.001086888036937901687.44381911418
Trimmed Mean ( 21 / 24 )1.834333333333330.001037607031823911767.84975146991
Trimmed Mean ( 22 / 24 )1.834642857142860.0009597925890831611911.49929475429
Trimmed Mean ( 23 / 24 )1.834615384615380.0009970370305242871840.06744829794
Trimmed Mean ( 24 / 24 )1.834583333333330.001038945721662301765.81249153039
Median1.83
Midrange1.81
Midmean - Weighted Average at Xnp1.83052631578947
Midmean - Weighted Average at X(n+1)p1.83052631578947
Midmean - Empirical Distribution Function1.83052631578947
Midmean - Empirical Distribution Function - Averaging1.83052631578947
Midmean - Empirical Distribution Function - Interpolation1.83052631578947
Midmean - Closest Observation1.83052631578947
Midmean - True Basic - Statistics Graphics Toolkit1.83052631578947
Midmean - MS Excel (old versions)1.83052631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.81763888888889 & 0.00552591368448146 & 328.930018214617 \tabularnewline
Geometric Mean & 1.81703438536713 &  &  \tabularnewline
Harmonic Mean & 1.81642180738002 &  &  \tabularnewline
Quadratic Mean & 1.81823517914121 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.81763888888889 & 0.00552591368448146 & 328.930018214617 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.81736111111111 & 0.00547791502619883 & 331.761464429322 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.81736111111111 & 0.00547791502619883 & 331.761464429322 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.81680555555556 & 0.00539455178153528 & 336.785265788754 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.8175 & 0.00524348466722266 & 346.620637867276 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.8175 & 0.00524348466722266 & 346.620637867276 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.8175 & 0.00524348466722266 & 346.620637867276 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.8175 & 0.00524348466722266 & 346.620637867276 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.81625 & 0.0050793296016185 & 357.576716309424 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.81486111111111 & 0.00492507658065687 & 368.493988142020 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.81486111111111 & 0.00492507658065687 & 368.493988142020 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.81486111111111 & 0.00492507658065687 & 368.493988142020 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.81666666666667 & 0.00454502772217125 & 399.704199339582 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.81861111111111 & 0.00415046406306491 & 438.170547552737 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.81861111111111 & 0.00415046406306491 & 438.170547552737 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.82083333333333 & 0.00371495097139583 & 490.136571748398 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.82083333333333 & 0.00302409468598398 & 602.108572119946 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.82083333333333 & 0.00302409468598398 & 602.108572119946 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.82347222222222 & 0.00252653927595031 & 721.727241519473 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.83180555555556 & 0.00103397656961541 & 1771.61224865753 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.83180555555556 & 0.00103397656961541 & 1771.61224865753 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.83486111111111 & 0.000593161853271656 & 3093.35656194125 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.83486111111111 & 0.000593161853271656 & 3093.35656194125 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.83486111111111 & 0.000593161853271656 & 3093.35656194125 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.81785714285714 & 0.00544459333367171 & 333.882997581239 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.81808823529412 & 0.00534686796697294 & 340.02863854583 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.81848484848485 & 0.00525899129825971 & 345.785863742847 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.81890625 & 0.00515203952670418 & 353.045864763304 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.81951612903226 & 0.00505091694611525 & 360.23481447892 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.82 & 0.00497451130382317 & 365.865084797624 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.82051724137931 & 0.00487857653433844 & 373.165661861689 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.82107142857143 & 0.00475830491637306 & 382.714319611008 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.82166666666667 & 0.00460721337625464 & 395.394464700821 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.8225 & 0.00445248926259056 & 409.321593498831 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.8236 & 0.00428342796157947 & 425.733785266594 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.82479166666667 & 0.00406059579849691 & 449.39012825215 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.82608695652174 & 0.00376197939559813 & 485.405889957407 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.82727272727273 & 0.003476949714854 & 525.539014690483 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.82833333333333 & 0.00321358662333468 & 568.93855608476 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.8295 & 0.00284086480151957 & 643.994039780212 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.83052631578947 & 0.00247167074013923 & 740.60281819186 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.83166666666667 & 0.00216391767000034 & 846.45857467691 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.83294117647059 & 0.00166378066161541 & 1101.67236508864 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.8340625 & 0.00108688803693790 & 1687.44381911418 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.83433333333333 & 0.00103760703182391 & 1767.84975146991 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.83464285714286 & 0.000959792589083161 & 1911.49929475429 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.83461538461538 & 0.000997037030524287 & 1840.06744829794 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.83458333333333 & 0.00103894572166230 & 1765.81249153039 \tabularnewline
Median & 1.83 &  &  \tabularnewline
Midrange & 1.81 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.83052631578947 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.83052631578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.83052631578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.83052631578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.83052631578947 &  &  \tabularnewline
Midmean - Closest Observation & 1.83052631578947 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.83052631578947 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.83052631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10174&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]1.81763888888889[/C][C]0.00552591368448146[/C][C]328.930018214617[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.81703438536713[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.81642180738002[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.81823517914121[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.81763888888889[/C][C]0.00552591368448146[/C][C]328.930018214617[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.81736111111111[/C][C]0.00547791502619883[/C][C]331.761464429322[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.81736111111111[/C][C]0.00547791502619883[/C][C]331.761464429322[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.81680555555556[/C][C]0.00539455178153528[/C][C]336.785265788754[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.8175[/C][C]0.00524348466722266[/C][C]346.620637867276[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.8175[/C][C]0.00524348466722266[/C][C]346.620637867276[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.8175[/C][C]0.00524348466722266[/C][C]346.620637867276[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.8175[/C][C]0.00524348466722266[/C][C]346.620637867276[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.81625[/C][C]0.0050793296016185[/C][C]357.576716309424[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.81486111111111[/C][C]0.00492507658065687[/C][C]368.493988142020[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.81486111111111[/C][C]0.00492507658065687[/C][C]368.493988142020[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.81486111111111[/C][C]0.00492507658065687[/C][C]368.493988142020[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.81666666666667[/C][C]0.00454502772217125[/C][C]399.704199339582[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.81861111111111[/C][C]0.00415046406306491[/C][C]438.170547552737[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.81861111111111[/C][C]0.00415046406306491[/C][C]438.170547552737[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.82083333333333[/C][C]0.00371495097139583[/C][C]490.136571748398[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.82083333333333[/C][C]0.00302409468598398[/C][C]602.108572119946[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.82083333333333[/C][C]0.00302409468598398[/C][C]602.108572119946[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.82347222222222[/C][C]0.00252653927595031[/C][C]721.727241519473[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.83180555555556[/C][C]0.00103397656961541[/C][C]1771.61224865753[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.83180555555556[/C][C]0.00103397656961541[/C][C]1771.61224865753[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.83486111111111[/C][C]0.000593161853271656[/C][C]3093.35656194125[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.83486111111111[/C][C]0.000593161853271656[/C][C]3093.35656194125[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.83486111111111[/C][C]0.000593161853271656[/C][C]3093.35656194125[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.81785714285714[/C][C]0.00544459333367171[/C][C]333.882997581239[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.81808823529412[/C][C]0.00534686796697294[/C][C]340.02863854583[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.81848484848485[/C][C]0.00525899129825971[/C][C]345.785863742847[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.81890625[/C][C]0.00515203952670418[/C][C]353.045864763304[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.81951612903226[/C][C]0.00505091694611525[/C][C]360.23481447892[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.82[/C][C]0.00497451130382317[/C][C]365.865084797624[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.82051724137931[/C][C]0.00487857653433844[/C][C]373.165661861689[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.82107142857143[/C][C]0.00475830491637306[/C][C]382.714319611008[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.82166666666667[/C][C]0.00460721337625464[/C][C]395.394464700821[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.8225[/C][C]0.00445248926259056[/C][C]409.321593498831[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.8236[/C][C]0.00428342796157947[/C][C]425.733785266594[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.82479166666667[/C][C]0.00406059579849691[/C][C]449.39012825215[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.82608695652174[/C][C]0.00376197939559813[/C][C]485.405889957407[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.82727272727273[/C][C]0.003476949714854[/C][C]525.539014690483[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.82833333333333[/C][C]0.00321358662333468[/C][C]568.93855608476[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.8295[/C][C]0.00284086480151957[/C][C]643.994039780212[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.83052631578947[/C][C]0.00247167074013923[/C][C]740.60281819186[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.83166666666667[/C][C]0.00216391767000034[/C][C]846.45857467691[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.83294117647059[/C][C]0.00166378066161541[/C][C]1101.67236508864[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.8340625[/C][C]0.00108688803693790[/C][C]1687.44381911418[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.83433333333333[/C][C]0.00103760703182391[/C][C]1767.84975146991[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.83464285714286[/C][C]0.000959792589083161[/C][C]1911.49929475429[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.83461538461538[/C][C]0.000997037030524287[/C][C]1840.06744829794[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.83458333333333[/C][C]0.00103894572166230[/C][C]1765.81249153039[/C][/ROW]
[ROW][C]Median[/C][C]1.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.83052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.83052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.83052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.83052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.83052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.83052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.83052631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.83052631578947[/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=10174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10174&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.817638888888890.00552591368448146328.930018214617
Geometric Mean1.81703438536713
Harmonic Mean1.81642180738002
Quadratic Mean1.81823517914121
Winsorized Mean ( 1 / 24 )1.817638888888890.00552591368448146328.930018214617
Winsorized Mean ( 2 / 24 )1.817361111111110.00547791502619883331.761464429322
Winsorized Mean ( 3 / 24 )1.817361111111110.00547791502619883331.761464429322
Winsorized Mean ( 4 / 24 )1.816805555555560.00539455178153528336.785265788754
Winsorized Mean ( 5 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 6 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 7 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 8 / 24 )1.81750.00524348466722266346.620637867276
Winsorized Mean ( 9 / 24 )1.816250.0050793296016185357.576716309424
Winsorized Mean ( 10 / 24 )1.814861111111110.00492507658065687368.493988142020
Winsorized Mean ( 11 / 24 )1.814861111111110.00492507658065687368.493988142020
Winsorized Mean ( 12 / 24 )1.814861111111110.00492507658065687368.493988142020
Winsorized Mean ( 13 / 24 )1.816666666666670.00454502772217125399.704199339582
Winsorized Mean ( 14 / 24 )1.818611111111110.00415046406306491438.170547552737
Winsorized Mean ( 15 / 24 )1.818611111111110.00415046406306491438.170547552737
Winsorized Mean ( 16 / 24 )1.820833333333330.00371495097139583490.136571748398
Winsorized Mean ( 17 / 24 )1.820833333333330.00302409468598398602.108572119946
Winsorized Mean ( 18 / 24 )1.820833333333330.00302409468598398602.108572119946
Winsorized Mean ( 19 / 24 )1.823472222222220.00252653927595031721.727241519473
Winsorized Mean ( 20 / 24 )1.831805555555560.001033976569615411771.61224865753
Winsorized Mean ( 21 / 24 )1.831805555555560.001033976569615411771.61224865753
Winsorized Mean ( 22 / 24 )1.834861111111110.0005931618532716563093.35656194125
Winsorized Mean ( 23 / 24 )1.834861111111110.0005931618532716563093.35656194125
Winsorized Mean ( 24 / 24 )1.834861111111110.0005931618532716563093.35656194125
Trimmed Mean ( 1 / 24 )1.817857142857140.00544459333367171333.882997581239
Trimmed Mean ( 2 / 24 )1.818088235294120.00534686796697294340.02863854583
Trimmed Mean ( 3 / 24 )1.818484848484850.00525899129825971345.785863742847
Trimmed Mean ( 4 / 24 )1.818906250.00515203952670418353.045864763304
Trimmed Mean ( 5 / 24 )1.819516129032260.00505091694611525360.23481447892
Trimmed Mean ( 6 / 24 )1.820.00497451130382317365.865084797624
Trimmed Mean ( 7 / 24 )1.820517241379310.00487857653433844373.165661861689
Trimmed Mean ( 8 / 24 )1.821071428571430.00475830491637306382.714319611008
Trimmed Mean ( 9 / 24 )1.821666666666670.00460721337625464395.394464700821
Trimmed Mean ( 10 / 24 )1.82250.00445248926259056409.321593498831
Trimmed Mean ( 11 / 24 )1.82360.00428342796157947425.733785266594
Trimmed Mean ( 12 / 24 )1.824791666666670.00406059579849691449.39012825215
Trimmed Mean ( 13 / 24 )1.826086956521740.00376197939559813485.405889957407
Trimmed Mean ( 14 / 24 )1.827272727272730.003476949714854525.539014690483
Trimmed Mean ( 15 / 24 )1.828333333333330.00321358662333468568.93855608476
Trimmed Mean ( 16 / 24 )1.82950.00284086480151957643.994039780212
Trimmed Mean ( 17 / 24 )1.830526315789470.00247167074013923740.60281819186
Trimmed Mean ( 18 / 24 )1.831666666666670.00216391767000034846.45857467691
Trimmed Mean ( 19 / 24 )1.832941176470590.001663780661615411101.67236508864
Trimmed Mean ( 20 / 24 )1.83406250.001086888036937901687.44381911418
Trimmed Mean ( 21 / 24 )1.834333333333330.001037607031823911767.84975146991
Trimmed Mean ( 22 / 24 )1.834642857142860.0009597925890831611911.49929475429
Trimmed Mean ( 23 / 24 )1.834615384615380.0009970370305242871840.06744829794
Trimmed Mean ( 24 / 24 )1.834583333333330.001038945721662301765.81249153039
Median1.83
Midrange1.81
Midmean - Weighted Average at Xnp1.83052631578947
Midmean - Weighted Average at X(n+1)p1.83052631578947
Midmean - Empirical Distribution Function1.83052631578947
Midmean - Empirical Distribution Function - Averaging1.83052631578947
Midmean - Empirical Distribution Function - Interpolation1.83052631578947
Midmean - Closest Observation1.83052631578947
Midmean - True Basic - Statistics Graphics Toolkit1.83052631578947
Midmean - MS Excel (old versions)1.83052631578947
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')