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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 13:26:13 -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/2009/Oct/20/t12560668791vn2yn6riq7vqgo.htm/, Retrieved Fri, 03 May 2024 00:02:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49061, Retrieved Fri, 03 May 2024 00:02:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [e[t] in Y[t]-X[t]...] [2009-10-20 19:26:13] [9a3898f49d4e2f0208d1968305d88f0a] [Current]
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Dataseries X:
500.82
-318.38
253.72
128.42
-212.78
303.52
-163.08
-46.08
209.32
356.72
248.22
-62.28
793.12
-327.98
766.82
401.12
-23.38
-63.28
-156.58
479.72
150.92
336.42
609.82
113.12
757.22
-248.18
532.72
-57.18
11.92
323.22
-192.88
461.52
612.02
-44.38
33.02
417.32
609.12
189.12
257.32
-249.18
-608.98
272.82
-1169.48
501.82
-232.08
-484.18
-120.48
-406.48
-102.88
-1140.48
-661.08
-866.98
-996.38
-901.98
-1445.38
-312.18
-223.88
77.42
219.82
322.92
587.22




Summary of computational 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 computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49061&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49061&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.0029508196721332764.1123964123527-4.60257272736217e-05
Geometric MeanNaN
Harmonic Mean12454.9646321734
Quadratic Mean496.612487189747
Winsorized Mean ( 1 / 20 )4.0888524590163962.46436267223970.0654589638650640
Winsorized Mean ( 2 / 20 )4.7249180327868962.10557367110980.0760788082855246
Winsorized Mean ( 3 / 20 )4.6708196721311558.66646446296580.0796165188219188
Winsorized Mean ( 4 / 20 )10.716721311475456.93340942812450.188232558336502
Winsorized Mean ( 5 / 20 )13.528196721311556.16520247293320.240864380891904
Winsorized Mean ( 6 / 20 )31.626557377049250.81511660703020.622384823430154
Winsorized Mean ( 7 / 20 )31.351147540983648.36500131999350.648219718501763
Winsorized Mean ( 8 / 20 )43.665901639344344.22332925198980.987395168521366
Winsorized Mean ( 9 / 20 )54.982295081967242.0054422810151.30893265482452
Winsorized Mean ( 10 / 20 )64.39213114754139.13667840204471.64531415993077
Winsorized Mean ( 11 / 20 )62.841311475409838.27314736692351.64191648188617
Winsorized Mean ( 12 / 20 )55.365901639344336.59758954511081.51282918704521
Winsorized Mean ( 13 / 20 )65.339672131147633.8616167134161.92960875684532
Winsorized Mean ( 14 / 20 )55.379016393442632.18755464758901.72051020960646
Winsorized Mean ( 15 / 20 )54.346229508196730.79888188141851.76455202878598
Winsorized Mean ( 16 / 20 )53.034754098360729.94175984658791.77126375904737
Winsorized Mean ( 17 / 20 )56.044590163934429.45545332123111.90268978557999
Winsorized Mean ( 18 / 20 )56.19213114754127.71060667015662.02782031502970
Winsorized Mean ( 19 / 20 )55.911803278688524.92954972918492.24279234426897
Winsorized Mean ( 20 / 20 )52.960983606557423.8868214091592.21716329265351
Trimmed Mean ( 1 / 20 )11.052203389830559.99876315891940.184207187080780
Trimmed Mean ( 2 / 20 )18.504210526315856.94467458501450.32495067644456
Trimmed Mean ( 3 / 20 )26.145454545454553.3665575944590.489922073372955
Trimmed Mean ( 4 / 20 )34.384150943396250.6350240551140.679058647349917
Trimmed Mean ( 5 / 20 )41.461176470588247.92013561606970.865214088765736
Trimmed Mean ( 6 / 20 )48.415918367346944.72988421815921.08240652113495
Trimmed Mean ( 7 / 20 )52.047659574468142.53463133858591.22365371313921
Trimmed Mean ( 8 / 20 )56.055555555555640.46917384719261.38514207794840
Trimmed Mean ( 9 / 20 )58.252558139534939.03589677744841.49228179569294
Trimmed Mean ( 10 / 20 )58.793170731707337.77444904028971.55642695592990
Trimmed Mean ( 11 / 20 )57.917435897435936.85811847155091.57136170534966
Trimmed Mean ( 12 / 20 )57.179459459459535.81749104217731.59641163564827
Trimmed Mean ( 13 / 20 )57.442857142857134.81865362267811.64977249739040
Trimmed Mean ( 14 / 20 )56.3234.13583910443151.64987888030819
Trimmed Mean ( 15 / 20 )56.452258064516133.56183296514921.68203739417738
Trimmed Mean ( 16 / 20 )56.747586206896533.0306906459071.71802602661983
Trimmed Mean ( 17 / 20 )57.271851851851832.38274327221081.76859172709434
Trimmed Mean ( 18 / 20 )57.44831.42846402016281.82789715600306
Trimmed Mean ( 19 / 20 )57.633043478260930.45870288110641.89216998843410
Trimmed Mean ( 20 / 20 )57.896190476190529.85726194249811.93909912394821
Median33.02
Midrange-326.13
Midmean - Weighted Average at Xnp47.12
Midmean - Weighted Average at X(n+1)p56.4522580645161
Midmean - Empirical Distribution Function56.4522580645161
Midmean - Empirical Distribution Function - Averaging56.4522580645161
Midmean - Empirical Distribution Function - Interpolation56.4522580645161
Midmean - Closest Observation46.9325
Midmean - True Basic - Statistics Graphics Toolkit56.4522580645161
Midmean - MS Excel (old versions)56.4522580645161
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.00295081967213327 & 64.1123964123527 & -4.60257272736217e-05 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 12454.9646321734 &  &  \tabularnewline
Quadratic Mean & 496.612487189747 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4.08885245901639 & 62.4643626722397 & 0.0654589638650640 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4.72491803278689 & 62.1055736711098 & 0.0760788082855246 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4.67081967213115 & 58.6664644629658 & 0.0796165188219188 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 10.7167213114754 & 56.9334094281245 & 0.188232558336502 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 13.5281967213115 & 56.1652024729332 & 0.240864380891904 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 31.6265573770492 & 50.8151166070302 & 0.622384823430154 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 31.3511475409836 & 48.3650013199935 & 0.648219718501763 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 43.6659016393443 & 44.2233292519898 & 0.987395168521366 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 54.9822950819672 & 42.005442281015 & 1.30893265482452 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 64.392131147541 & 39.1366784020447 & 1.64531415993077 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 62.8413114754098 & 38.2731473669235 & 1.64191648188617 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 55.3659016393443 & 36.5975895451108 & 1.51282918704521 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 65.3396721311476 & 33.861616713416 & 1.92960875684532 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 55.3790163934426 & 32.1875546475890 & 1.72051020960646 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 54.3462295081967 & 30.7988818814185 & 1.76455202878598 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 53.0347540983607 & 29.9417598465879 & 1.77126375904737 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 56.0445901639344 & 29.4554533212311 & 1.90268978557999 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 56.192131147541 & 27.7106066701566 & 2.02782031502970 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 55.9118032786885 & 24.9295497291849 & 2.24279234426897 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 52.9609836065574 & 23.886821409159 & 2.21716329265351 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 11.0522033898305 & 59.9987631589194 & 0.184207187080780 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18.5042105263158 & 56.9446745850145 & 0.32495067644456 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 26.1454545454545 & 53.366557594459 & 0.489922073372955 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 34.3841509433962 & 50.635024055114 & 0.679058647349917 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 41.4611764705882 & 47.9201356160697 & 0.865214088765736 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 48.4159183673469 & 44.7298842181592 & 1.08240652113495 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 52.0476595744681 & 42.5346313385859 & 1.22365371313921 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 56.0555555555556 & 40.4691738471926 & 1.38514207794840 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 58.2525581395349 & 39.0358967774484 & 1.49228179569294 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 58.7931707317073 & 37.7744490402897 & 1.55642695592990 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 57.9174358974359 & 36.8581184715509 & 1.57136170534966 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 57.1794594594595 & 35.8174910421773 & 1.59641163564827 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 57.4428571428571 & 34.8186536226781 & 1.64977249739040 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 56.32 & 34.1358391044315 & 1.64987888030819 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 56.4522580645161 & 33.5618329651492 & 1.68203739417738 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 56.7475862068965 & 33.030690645907 & 1.71802602661983 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 57.2718518518518 & 32.3827432722108 & 1.76859172709434 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 57.448 & 31.4284640201628 & 1.82789715600306 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 57.6330434782609 & 30.4587028811064 & 1.89216998843410 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 57.8961904761905 & 29.8572619424981 & 1.93909912394821 \tabularnewline
Median & 33.02 &  &  \tabularnewline
Midrange & -326.13 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 47.12 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 56.4522580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 56.4522580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 56.4522580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 56.4522580645161 &  &  \tabularnewline
Midmean - Closest Observation & 46.9325 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 56.4522580645161 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 56.4522580645161 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49061&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]-0.00295081967213327[/C][C]64.1123964123527[/C][C]-4.60257272736217e-05[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12454.9646321734[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]496.612487189747[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4.08885245901639[/C][C]62.4643626722397[/C][C]0.0654589638650640[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4.72491803278689[/C][C]62.1055736711098[/C][C]0.0760788082855246[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4.67081967213115[/C][C]58.6664644629658[/C][C]0.0796165188219188[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]10.7167213114754[/C][C]56.9334094281245[/C][C]0.188232558336502[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]13.5281967213115[/C][C]56.1652024729332[/C][C]0.240864380891904[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]31.6265573770492[/C][C]50.8151166070302[/C][C]0.622384823430154[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]31.3511475409836[/C][C]48.3650013199935[/C][C]0.648219718501763[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]43.6659016393443[/C][C]44.2233292519898[/C][C]0.987395168521366[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]54.9822950819672[/C][C]42.005442281015[/C][C]1.30893265482452[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]64.392131147541[/C][C]39.1366784020447[/C][C]1.64531415993077[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]62.8413114754098[/C][C]38.2731473669235[/C][C]1.64191648188617[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]55.3659016393443[/C][C]36.5975895451108[/C][C]1.51282918704521[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]65.3396721311476[/C][C]33.861616713416[/C][C]1.92960875684532[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]55.3790163934426[/C][C]32.1875546475890[/C][C]1.72051020960646[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]54.3462295081967[/C][C]30.7988818814185[/C][C]1.76455202878598[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]53.0347540983607[/C][C]29.9417598465879[/C][C]1.77126375904737[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]56.0445901639344[/C][C]29.4554533212311[/C][C]1.90268978557999[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]56.192131147541[/C][C]27.7106066701566[/C][C]2.02782031502970[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]55.9118032786885[/C][C]24.9295497291849[/C][C]2.24279234426897[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]52.9609836065574[/C][C]23.886821409159[/C][C]2.21716329265351[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]11.0522033898305[/C][C]59.9987631589194[/C][C]0.184207187080780[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18.5042105263158[/C][C]56.9446745850145[/C][C]0.32495067644456[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]26.1454545454545[/C][C]53.366557594459[/C][C]0.489922073372955[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]34.3841509433962[/C][C]50.635024055114[/C][C]0.679058647349917[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]41.4611764705882[/C][C]47.9201356160697[/C][C]0.865214088765736[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]48.4159183673469[/C][C]44.7298842181592[/C][C]1.08240652113495[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]52.0476595744681[/C][C]42.5346313385859[/C][C]1.22365371313921[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]56.0555555555556[/C][C]40.4691738471926[/C][C]1.38514207794840[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]58.2525581395349[/C][C]39.0358967774484[/C][C]1.49228179569294[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]58.7931707317073[/C][C]37.7744490402897[/C][C]1.55642695592990[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]57.9174358974359[/C][C]36.8581184715509[/C][C]1.57136170534966[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]57.1794594594595[/C][C]35.8174910421773[/C][C]1.59641163564827[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]57.4428571428571[/C][C]34.8186536226781[/C][C]1.64977249739040[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]56.32[/C][C]34.1358391044315[/C][C]1.64987888030819[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]56.4522580645161[/C][C]33.5618329651492[/C][C]1.68203739417738[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]56.7475862068965[/C][C]33.030690645907[/C][C]1.71802602661983[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]57.2718518518518[/C][C]32.3827432722108[/C][C]1.76859172709434[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]57.448[/C][C]31.4284640201628[/C][C]1.82789715600306[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]57.6330434782609[/C][C]30.4587028811064[/C][C]1.89216998843410[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]57.8961904761905[/C][C]29.8572619424981[/C][C]1.93909912394821[/C][/ROW]
[ROW][C]Median[/C][C]33.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-326.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]47.12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]56.4522580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]56.4522580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]56.4522580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]56.4522580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]46.9325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]56.4522580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]56.4522580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49061&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 Mean-0.0029508196721332764.1123964123527-4.60257272736217e-05
Geometric MeanNaN
Harmonic Mean12454.9646321734
Quadratic Mean496.612487189747
Winsorized Mean ( 1 / 20 )4.0888524590163962.46436267223970.0654589638650640
Winsorized Mean ( 2 / 20 )4.7249180327868962.10557367110980.0760788082855246
Winsorized Mean ( 3 / 20 )4.6708196721311558.66646446296580.0796165188219188
Winsorized Mean ( 4 / 20 )10.716721311475456.93340942812450.188232558336502
Winsorized Mean ( 5 / 20 )13.528196721311556.16520247293320.240864380891904
Winsorized Mean ( 6 / 20 )31.626557377049250.81511660703020.622384823430154
Winsorized Mean ( 7 / 20 )31.351147540983648.36500131999350.648219718501763
Winsorized Mean ( 8 / 20 )43.665901639344344.22332925198980.987395168521366
Winsorized Mean ( 9 / 20 )54.982295081967242.0054422810151.30893265482452
Winsorized Mean ( 10 / 20 )64.39213114754139.13667840204471.64531415993077
Winsorized Mean ( 11 / 20 )62.841311475409838.27314736692351.64191648188617
Winsorized Mean ( 12 / 20 )55.365901639344336.59758954511081.51282918704521
Winsorized Mean ( 13 / 20 )65.339672131147633.8616167134161.92960875684532
Winsorized Mean ( 14 / 20 )55.379016393442632.18755464758901.72051020960646
Winsorized Mean ( 15 / 20 )54.346229508196730.79888188141851.76455202878598
Winsorized Mean ( 16 / 20 )53.034754098360729.94175984658791.77126375904737
Winsorized Mean ( 17 / 20 )56.044590163934429.45545332123111.90268978557999
Winsorized Mean ( 18 / 20 )56.19213114754127.71060667015662.02782031502970
Winsorized Mean ( 19 / 20 )55.911803278688524.92954972918492.24279234426897
Winsorized Mean ( 20 / 20 )52.960983606557423.8868214091592.21716329265351
Trimmed Mean ( 1 / 20 )11.052203389830559.99876315891940.184207187080780
Trimmed Mean ( 2 / 20 )18.504210526315856.94467458501450.32495067644456
Trimmed Mean ( 3 / 20 )26.145454545454553.3665575944590.489922073372955
Trimmed Mean ( 4 / 20 )34.384150943396250.6350240551140.679058647349917
Trimmed Mean ( 5 / 20 )41.461176470588247.92013561606970.865214088765736
Trimmed Mean ( 6 / 20 )48.415918367346944.72988421815921.08240652113495
Trimmed Mean ( 7 / 20 )52.047659574468142.53463133858591.22365371313921
Trimmed Mean ( 8 / 20 )56.055555555555640.46917384719261.38514207794840
Trimmed Mean ( 9 / 20 )58.252558139534939.03589677744841.49228179569294
Trimmed Mean ( 10 / 20 )58.793170731707337.77444904028971.55642695592990
Trimmed Mean ( 11 / 20 )57.917435897435936.85811847155091.57136170534966
Trimmed Mean ( 12 / 20 )57.179459459459535.81749104217731.59641163564827
Trimmed Mean ( 13 / 20 )57.442857142857134.81865362267811.64977249739040
Trimmed Mean ( 14 / 20 )56.3234.13583910443151.64987888030819
Trimmed Mean ( 15 / 20 )56.452258064516133.56183296514921.68203739417738
Trimmed Mean ( 16 / 20 )56.747586206896533.0306906459071.71802602661983
Trimmed Mean ( 17 / 20 )57.271851851851832.38274327221081.76859172709434
Trimmed Mean ( 18 / 20 )57.44831.42846402016281.82789715600306
Trimmed Mean ( 19 / 20 )57.633043478260930.45870288110641.89216998843410
Trimmed Mean ( 20 / 20 )57.896190476190529.85726194249811.93909912394821
Median33.02
Midrange-326.13
Midmean - Weighted Average at Xnp47.12
Midmean - Weighted Average at X(n+1)p56.4522580645161
Midmean - Empirical Distribution Function56.4522580645161
Midmean - Empirical Distribution Function - Averaging56.4522580645161
Midmean - Empirical Distribution Function - Interpolation56.4522580645161
Midmean - Closest Observation46.9325
Midmean - True Basic - Statistics Graphics Toolkit56.4522580645161
Midmean - MS Excel (old versions)56.4522580645161
Number of observations61



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')