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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 computationSun, 14 Mar 2010 07:19:43 -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/2010/Mar/14/t1268572874cvzwf3ujiay14du.htm/, Retrieved Wed, 19 Jan 2022 11:02:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74388, Retrieved Wed, 19 Jan 2022 11:02:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten (fin...] [2010-03-14 13:19:43] [b58dfa1c2951471c561e0016df4afa08] [Current]
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Dataseries X:
1
1
3
3
1
1
-2
1
1
-1
-4
-2
-1
-5
-4
-5
0
-2
-4
-6
-2
-2
-2
1
-2
0
-1
2
3
2
3
4
5
5
4
5
6
4
6
6
3
5
5
5
3
5
5
6
6
5
4
4
0
2
3
3
2
3
5
6
6
5
4
7
5
6
5
6
5
6
6
6
6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74388&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74388&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74388&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.410958904109590.3920032151841966.15035492241235
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean4.10812759402226
Winsorized Mean ( 1 / 24 )2.410958904109590.3861350938066696.24382228598137
Winsorized Mean ( 2 / 24 )2.410958904109590.3861350938066696.24382228598137
Winsorized Mean ( 3 / 24 )2.452054794520550.3757494266360976.5257712206579
Winsorized Mean ( 4 / 24 )2.452054794520550.3757494266360976.5257712206579
Winsorized Mean ( 5 / 24 )2.452054794520550.3757494266360976.5257712206579
Winsorized Mean ( 6 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 7 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 8 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 9 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 10 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 11 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 12 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 13 / 24 )2.794520547945210.3084051527547139.06119927953279
Winsorized Mean ( 14 / 24 )2.60273972602740.2831786618029899.19115765805178
Winsorized Mean ( 15 / 24 )2.60273972602740.2831786618029899.19115765805178
Winsorized Mean ( 16 / 24 )2.821917808219180.24623687237831511.4601756469828
Winsorized Mean ( 17 / 24 )2.821917808219180.24623687237831511.4601756469828
Winsorized Mean ( 18 / 24 )2.821917808219180.24623687237831511.4601756469828
Winsorized Mean ( 19 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 20 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 21 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 22 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 23 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 24 / 24 )3.082191780821920.20713438076806514.8801554304649
Trimmed Mean ( 1 / 24 )2.464788732394370.3794685396733286.49537043180502
Trimmed Mean ( 2 / 24 )2.521739130434780.3714035816771266.78975447422319
Trimmed Mean ( 3 / 24 )2.582089552238810.3616318445791577.14010558236006
Trimmed Mean ( 4 / 24 )2.630769230769230.3546187218264467.41858528286263
Trimmed Mean ( 5 / 24 )2.682539682539680.3460148344444287.75267247384595
Trimmed Mean ( 6 / 24 )2.737704918032790.3354318962453078.1617310359497
Trimmed Mean ( 7 / 24 )2.762711864406780.3326557351618778.30501798822856
Trimmed Mean ( 8 / 24 )2.789473684210530.3289849602580338.47903102324999
Trimmed Mean ( 9 / 24 )2.818181818181820.3242093818715648.6924746036444
Trimmed Mean ( 10 / 24 )2.849056603773580.3180540277960828.95777558145007
Trimmed Mean ( 11 / 24 )2.882352941176470.3101512076815079.2933797121833
Trimmed Mean ( 12 / 24 )2.918367346938780.2999953722628869.72804121918724
Trimmed Mean ( 13 / 24 )2.957446808510640.28686549144788410.3095244868375
Trimmed Mean ( 14 / 24 )2.977777777777780.2779595364943810.7129901543708
Trimmed Mean ( 15 / 24 )3.023255813953490.27134946817585111.1415579115646
Trimmed Mean ( 16 / 24 )3.073170731707320.26223765962371911.7190289759181
Trimmed Mean ( 17 / 24 )3.10256410256410.25922877363074411.968440305101
Trimmed Mean ( 18 / 24 )3.135135135135140.25457425497197812.3152089180433
Trimmed Mean ( 19 / 24 )3.171428571428570.24762982092487312.8071351002218
Trimmed Mean ( 20 / 24 )3.181818181818180.2479252753326312.8337789583950
Trimmed Mean ( 21 / 24 )3.193548387096770.24721830863885712.9179283066854
Trimmed Mean ( 22 / 24 )3.206896551724140.2450460414405513.0869143319834
Trimmed Mean ( 23 / 24 )3.222222222222220.24068594598852513.387662536706
Trimmed Mean ( 24 / 24 )3.240.23295206946208213.9084405108811
Median3
Midrange0.5
Midmean - Weighted Average at Xnp3.16279069767442
Midmean - Weighted Average at X(n+1)p3.16279069767442
Midmean - Empirical Distribution Function3.16279069767442
Midmean - Empirical Distribution Function - Averaging3.16279069767442
Midmean - Empirical Distribution Function - Interpolation3.16279069767442
Midmean - Closest Observation3.16279069767442
Midmean - True Basic - Statistics Graphics Toolkit3.16279069767442
Midmean - MS Excel (old versions)3.16279069767442
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.41095890410959 & 0.392003215184196 & 6.15035492241235 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 4.10812759402226 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.41095890410959 & 0.386135093806669 & 6.24382228598137 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.41095890410959 & 0.386135093806669 & 6.24382228598137 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.45205479452055 & 0.375749426636097 & 6.5257712206579 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.45205479452055 & 0.375749426636097 & 6.5257712206579 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.45205479452055 & 0.375749426636097 & 6.5257712206579 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.61643835616438 & 0.3404660031631 & 7.68487406042412 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.61643835616438 & 0.3404660031631 & 7.68487406042412 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.61643835616438 & 0.3404660031631 & 7.68487406042412 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.61643835616438 & 0.3404660031631 & 7.68487406042412 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.61643835616438 & 0.3404660031631 & 7.68487406042412 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.61643835616438 & 0.3404660031631 & 7.68487406042412 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.61643835616438 & 0.3404660031631 & 7.68487406042412 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.79452054794521 & 0.308405152754713 & 9.06119927953279 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.6027397260274 & 0.283178661802989 & 9.19115765805178 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.6027397260274 & 0.283178661802989 & 9.19115765805178 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.82191780821918 & 0.246236872378315 & 11.4601756469828 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.82191780821918 & 0.246236872378315 & 11.4601756469828 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.82191780821918 & 0.246236872378315 & 11.4601756469828 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.08219178082192 & 0.207134380768065 & 14.8801554304649 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.08219178082192 & 0.207134380768065 & 14.8801554304649 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.08219178082192 & 0.207134380768065 & 14.8801554304649 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.08219178082192 & 0.207134380768065 & 14.8801554304649 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.08219178082192 & 0.207134380768065 & 14.8801554304649 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.08219178082192 & 0.207134380768065 & 14.8801554304649 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.46478873239437 & 0.379468539673328 & 6.49537043180502 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.52173913043478 & 0.371403581677126 & 6.78975447422319 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.58208955223881 & 0.361631844579157 & 7.14010558236006 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.63076923076923 & 0.354618721826446 & 7.41858528286263 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.68253968253968 & 0.346014834444428 & 7.75267247384595 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.73770491803279 & 0.335431896245307 & 8.1617310359497 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.76271186440678 & 0.332655735161877 & 8.30501798822856 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.78947368421053 & 0.328984960258033 & 8.47903102324999 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.81818181818182 & 0.324209381871564 & 8.6924746036444 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.84905660377358 & 0.318054027796082 & 8.95777558145007 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.88235294117647 & 0.310151207681507 & 9.2933797121833 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.91836734693878 & 0.299995372262886 & 9.72804121918724 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.95744680851064 & 0.286865491447884 & 10.3095244868375 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.97777777777778 & 0.27795953649438 & 10.7129901543708 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.02325581395349 & 0.271349468175851 & 11.1415579115646 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.07317073170732 & 0.262237659623719 & 11.7190289759181 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.1025641025641 & 0.259228773630744 & 11.968440305101 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.13513513513514 & 0.254574254971978 & 12.3152089180433 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.17142857142857 & 0.247629820924873 & 12.8071351002218 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.18181818181818 & 0.24792527533263 & 12.8337789583950 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.19354838709677 & 0.247218308638857 & 12.9179283066854 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.20689655172414 & 0.24504604144055 & 13.0869143319834 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.22222222222222 & 0.240685945988525 & 13.387662536706 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.24 & 0.232952069462082 & 13.9084405108811 \tabularnewline
Median & 3 &  &  \tabularnewline
Midrange & 0.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.16279069767442 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.16279069767442 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.16279069767442 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.16279069767442 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.16279069767442 &  &  \tabularnewline
Midmean - Closest Observation & 3.16279069767442 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.16279069767442 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.16279069767442 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74388&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]2.41095890410959[/C][C]0.392003215184196[/C][C]6.15035492241235[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.10812759402226[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.41095890410959[/C][C]0.386135093806669[/C][C]6.24382228598137[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.41095890410959[/C][C]0.386135093806669[/C][C]6.24382228598137[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.45205479452055[/C][C]0.375749426636097[/C][C]6.5257712206579[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.45205479452055[/C][C]0.375749426636097[/C][C]6.5257712206579[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.45205479452055[/C][C]0.375749426636097[/C][C]6.5257712206579[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.61643835616438[/C][C]0.3404660031631[/C][C]7.68487406042412[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.61643835616438[/C][C]0.3404660031631[/C][C]7.68487406042412[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.61643835616438[/C][C]0.3404660031631[/C][C]7.68487406042412[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.61643835616438[/C][C]0.3404660031631[/C][C]7.68487406042412[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.61643835616438[/C][C]0.3404660031631[/C][C]7.68487406042412[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.61643835616438[/C][C]0.3404660031631[/C][C]7.68487406042412[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.61643835616438[/C][C]0.3404660031631[/C][C]7.68487406042412[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.79452054794521[/C][C]0.308405152754713[/C][C]9.06119927953279[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.6027397260274[/C][C]0.283178661802989[/C][C]9.19115765805178[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.6027397260274[/C][C]0.283178661802989[/C][C]9.19115765805178[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.82191780821918[/C][C]0.246236872378315[/C][C]11.4601756469828[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.82191780821918[/C][C]0.246236872378315[/C][C]11.4601756469828[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.82191780821918[/C][C]0.246236872378315[/C][C]11.4601756469828[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.08219178082192[/C][C]0.207134380768065[/C][C]14.8801554304649[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.08219178082192[/C][C]0.207134380768065[/C][C]14.8801554304649[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.08219178082192[/C][C]0.207134380768065[/C][C]14.8801554304649[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.08219178082192[/C][C]0.207134380768065[/C][C]14.8801554304649[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.08219178082192[/C][C]0.207134380768065[/C][C]14.8801554304649[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.08219178082192[/C][C]0.207134380768065[/C][C]14.8801554304649[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.46478873239437[/C][C]0.379468539673328[/C][C]6.49537043180502[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.52173913043478[/C][C]0.371403581677126[/C][C]6.78975447422319[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.58208955223881[/C][C]0.361631844579157[/C][C]7.14010558236006[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.63076923076923[/C][C]0.354618721826446[/C][C]7.41858528286263[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.68253968253968[/C][C]0.346014834444428[/C][C]7.75267247384595[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.73770491803279[/C][C]0.335431896245307[/C][C]8.1617310359497[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.76271186440678[/C][C]0.332655735161877[/C][C]8.30501798822856[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.78947368421053[/C][C]0.328984960258033[/C][C]8.47903102324999[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.81818181818182[/C][C]0.324209381871564[/C][C]8.6924746036444[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.84905660377358[/C][C]0.318054027796082[/C][C]8.95777558145007[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.88235294117647[/C][C]0.310151207681507[/C][C]9.2933797121833[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.91836734693878[/C][C]0.299995372262886[/C][C]9.72804121918724[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.95744680851064[/C][C]0.286865491447884[/C][C]10.3095244868375[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.97777777777778[/C][C]0.27795953649438[/C][C]10.7129901543708[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.02325581395349[/C][C]0.271349468175851[/C][C]11.1415579115646[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.07317073170732[/C][C]0.262237659623719[/C][C]11.7190289759181[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.1025641025641[/C][C]0.259228773630744[/C][C]11.968440305101[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.13513513513514[/C][C]0.254574254971978[/C][C]12.3152089180433[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.17142857142857[/C][C]0.247629820924873[/C][C]12.8071351002218[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.18181818181818[/C][C]0.24792527533263[/C][C]12.8337789583950[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.19354838709677[/C][C]0.247218308638857[/C][C]12.9179283066854[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.20689655172414[/C][C]0.24504604144055[/C][C]13.0869143319834[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.22222222222222[/C][C]0.240685945988525[/C][C]13.387662536706[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.24[/C][C]0.232952069462082[/C][C]13.9084405108811[/C][/ROW]
[ROW][C]Median[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.16279069767442[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74388&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74388&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 Mean2.410958904109590.3920032151841966.15035492241235
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean4.10812759402226
Winsorized Mean ( 1 / 24 )2.410958904109590.3861350938066696.24382228598137
Winsorized Mean ( 2 / 24 )2.410958904109590.3861350938066696.24382228598137
Winsorized Mean ( 3 / 24 )2.452054794520550.3757494266360976.5257712206579
Winsorized Mean ( 4 / 24 )2.452054794520550.3757494266360976.5257712206579
Winsorized Mean ( 5 / 24 )2.452054794520550.3757494266360976.5257712206579
Winsorized Mean ( 6 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 7 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 8 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 9 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 10 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 11 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 12 / 24 )2.616438356164380.34046600316317.68487406042412
Winsorized Mean ( 13 / 24 )2.794520547945210.3084051527547139.06119927953279
Winsorized Mean ( 14 / 24 )2.60273972602740.2831786618029899.19115765805178
Winsorized Mean ( 15 / 24 )2.60273972602740.2831786618029899.19115765805178
Winsorized Mean ( 16 / 24 )2.821917808219180.24623687237831511.4601756469828
Winsorized Mean ( 17 / 24 )2.821917808219180.24623687237831511.4601756469828
Winsorized Mean ( 18 / 24 )2.821917808219180.24623687237831511.4601756469828
Winsorized Mean ( 19 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 20 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 21 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 22 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 23 / 24 )3.082191780821920.20713438076806514.8801554304649
Winsorized Mean ( 24 / 24 )3.082191780821920.20713438076806514.8801554304649
Trimmed Mean ( 1 / 24 )2.464788732394370.3794685396733286.49537043180502
Trimmed Mean ( 2 / 24 )2.521739130434780.3714035816771266.78975447422319
Trimmed Mean ( 3 / 24 )2.582089552238810.3616318445791577.14010558236006
Trimmed Mean ( 4 / 24 )2.630769230769230.3546187218264467.41858528286263
Trimmed Mean ( 5 / 24 )2.682539682539680.3460148344444287.75267247384595
Trimmed Mean ( 6 / 24 )2.737704918032790.3354318962453078.1617310359497
Trimmed Mean ( 7 / 24 )2.762711864406780.3326557351618778.30501798822856
Trimmed Mean ( 8 / 24 )2.789473684210530.3289849602580338.47903102324999
Trimmed Mean ( 9 / 24 )2.818181818181820.3242093818715648.6924746036444
Trimmed Mean ( 10 / 24 )2.849056603773580.3180540277960828.95777558145007
Trimmed Mean ( 11 / 24 )2.882352941176470.3101512076815079.2933797121833
Trimmed Mean ( 12 / 24 )2.918367346938780.2999953722628869.72804121918724
Trimmed Mean ( 13 / 24 )2.957446808510640.28686549144788410.3095244868375
Trimmed Mean ( 14 / 24 )2.977777777777780.2779595364943810.7129901543708
Trimmed Mean ( 15 / 24 )3.023255813953490.27134946817585111.1415579115646
Trimmed Mean ( 16 / 24 )3.073170731707320.26223765962371911.7190289759181
Trimmed Mean ( 17 / 24 )3.10256410256410.25922877363074411.968440305101
Trimmed Mean ( 18 / 24 )3.135135135135140.25457425497197812.3152089180433
Trimmed Mean ( 19 / 24 )3.171428571428570.24762982092487312.8071351002218
Trimmed Mean ( 20 / 24 )3.181818181818180.2479252753326312.8337789583950
Trimmed Mean ( 21 / 24 )3.193548387096770.24721830863885712.9179283066854
Trimmed Mean ( 22 / 24 )3.206896551724140.2450460414405513.0869143319834
Trimmed Mean ( 23 / 24 )3.222222222222220.24068594598852513.387662536706
Trimmed Mean ( 24 / 24 )3.240.23295206946208213.9084405108811
Median3
Midrange0.5
Midmean - Weighted Average at Xnp3.16279069767442
Midmean - Weighted Average at X(n+1)p3.16279069767442
Midmean - Empirical Distribution Function3.16279069767442
Midmean - Empirical Distribution Function - Averaging3.16279069767442
Midmean - Empirical Distribution Function - Interpolation3.16279069767442
Midmean - Closest Observation3.16279069767442
Midmean - True Basic - Statistics Graphics Toolkit3.16279069767442
Midmean - MS Excel (old versions)3.16279069767442
Number of observations73



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')