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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 computationFri, 16 Oct 2009 06:59:56 -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/16/t1255698041l0w67237fr9vht9.htm/, Retrieved Tue, 30 Apr 2024 02:03:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46995, Retrieved Tue, 30 Apr 2024 02:03:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
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] [WS3] [2009-10-16 12:59:56] [78d370e6d5f4594e9982a5085e7604c6] [Current]
- RMP           [Histogram] [WS3] [2009-10-16 13:03:45] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMP             [Variability] [WS3] [2009-10-16 13:08:49] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMP             [Kernel Density Estimation] [WS3] [2009-10-16 13:11:33] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMPD            [Central Tendency] [WS3] [2009-10-16 13:44:32] [eaf42bcf5162b5692bb3c7f9d4636222]
-    D            [Histogram] [WS3] [2009-10-16 13:46:40] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMPD            [Variability] [WS3] [2009-10-16 13:48:36] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMPD            [Kernel Density Estimation] [WS3] [2009-10-16 13:50:32] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMPD            [Univariate Explorative Data Analysis] [WS3 vraag 3] [2009-10-19 07:50:09] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMP               [Histogram] [WS3] [2009-10-19 07:55:12] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMP               [Harrell-Davis Quantiles] [WS3] [2009-10-19 07:58:30] [eaf42bcf5162b5692bb3c7f9d4636222]
- RMP                 [Central Tendency] [WS3] [2009-10-20 15:06:41] [eaf42bcf5162b5692bb3c7f9d4636222]
-               [Central Tendency] [ws3 mediaan en ge...] [2009-10-20 18:44:38] [100eabcd48fc1a8fabbdc8e8267bd5e3]
- RMP           [Histogram] [WS3 histogram] [2009-10-20 18:47:39] [100eabcd48fc1a8fabbdc8e8267bd5e3]
- RM            [Variability] [WS3 ] [2009-10-20 18:51:43] [100eabcd48fc1a8fabbdc8e8267bd5e3]
- RMP           [Kernel Density Estimation] [WS3 Kernell Density] [2009-10-20 18:54:37] [100eabcd48fc1a8fabbdc8e8267bd5e3]
- RMPD          [Univariate Explorative Data Analysis] [WS3 vraag 3 Univa...] [2009-10-20 19:04:20] [100eabcd48fc1a8fabbdc8e8267bd5e3]
- RMP           [Histogram] [WS3 vraag 3 histo...] [2009-10-20 19:10:23] [100eabcd48fc1a8fabbdc8e8267bd5e3]
- RMPD          [Histogram] [WS3 vraag 3 histo...] [2009-10-20 19:13:29] [100eabcd48fc1a8fabbdc8e8267bd5e3]
- RMP           [Harrell-Davis Quantiles] [WS3 vraag 3 ] [2009-10-20 19:17:21] [100eabcd48fc1a8fabbdc8e8267bd5e3]
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Dataseries X:
2.86
2.55
2.27
2.26
2.57
3.07
2.76
2.51
2.87
3.14
3.11
3.16
2.47
2.57
2.89
2.63
2.38
1.69
1.96
2.19
1.87
1.6
1.63
1.22
1.21
1.49
1.64
1.66
1.77
1.82
1.78
1.28
1.29
1.37
1.12
1.51
2.24
2.94
3.09
3.46
3.64
4.39
4.15
5.21
5.8
5.91
5.39
5.46
4.72
3.14
2.63
2.32
1.93
0.62
0.6
-0.37
-1.1
-1.68
-0.78
-1.19




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46995&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46995&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.31150.20547311053406111.2496471873716
Geometric MeanNaN
Harmonic Mean2.91553861892959
Quadratic Mean2.79892211395744
Winsorized Mean ( 1 / 20 )2.317833333333330.2023885745846611.4523922019312
Winsorized Mean ( 2 / 20 )2.30950.19833137610010911.6446527292498
Winsorized Mean ( 3 / 20 )2.3220.19287459700409412.0389104426786
Winsorized Mean ( 4 / 20 )2.337333333333330.18248564167132712.8083136400566
Winsorized Mean ( 5 / 20 )2.377333333333330.15345123200103815.4924356248717
Winsorized Mean ( 6 / 20 )2.346333333333330.14482796470191316.2008306763309
Winsorized Mean ( 7 / 20 )2.376666666666670.12733572926429318.6645702694626
Winsorized Mean ( 8 / 20 )2.320666666666670.11031077482872921.0375339151573
Winsorized Mean ( 9 / 20 )2.295166666666670.10476675510636921.9073948060756
Winsorized Mean ( 10 / 20 )2.255166666666670.094205116893745323.9388978117854
Winsorized Mean ( 11 / 20 )2.253333333333330.09329004242182524.1540605496195
Winsorized Mean ( 12 / 20 )2.269333333333330.090542266768416425.0638007455424
Winsorized Mean ( 13 / 20 )2.288833333333330.08522422789744526.8566039235652
Winsorized Mean ( 14 / 20 )2.288833333333330.083726111077028227.3371509065744
Winsorized Mean ( 15 / 20 )2.306333333333330.079442253008638429.0315700523064
Winsorized Mean ( 16 / 20 )2.279666666666670.072735868671083431.3417122572011
Winsorized Mean ( 17 / 20 )2.268333333333330.070152040962641332.3345308590709
Winsorized Mean ( 18 / 20 )2.268333333333330.068345734027067733.1890990070423
Winsorized Mean ( 19 / 20 )2.274666666666670.066448002978356534.2322803502097
Winsorized Mean ( 20 / 20 )2.2680.057596296177213839.3775320729263
Trimmed Mean ( 1 / 20 )2.318275862068970.19097295031345112.1392891415454
Trimmed Mean ( 2 / 20 )2.318750.17667713279665513.1242224915929
Trimmed Mean ( 3 / 20 )2.323888888888890.16143235882454914.3954341360680
Trimmed Mean ( 4 / 20 )2.324615384615380.14472850266115016.0619044754298
Trimmed Mean ( 5 / 20 )2.32080.12771551293753618.1716374668994
Trimmed Mean ( 6 / 20 )2.306666666666670.11766731460653819.6032914865086
Trimmed Mean ( 7 / 20 )2.298043478260870.10778203966308121.3212097808167
Trimmed Mean ( 8 / 20 )2.282727272727270.10078778683077422.6488480847390
Trimmed Mean ( 9 / 20 )2.275952380952380.097066173247058923.4474308074295
Trimmed Mean ( 10 / 20 )2.272750.093736528946693824.2461506260006
Trimmed Mean ( 11 / 20 )2.275526315789470.092129614744686824.6991841016105
Trimmed Mean ( 12 / 20 )2.278888888888890.090039477918156825.309885636613
Trimmed Mean ( 13 / 20 )2.280294117647060.087789739587539925.9744946090569
Trimmed Mean ( 14 / 20 )2.27906250.085984994207307226.5053515559384
Trimmed Mean ( 15 / 20 )2.277666666666670.083632589112652927.2342000987038
Trimmed Mean ( 16 / 20 )2.273571428571430.081305834353534627.9632014928408
Trimmed Mean ( 17 / 20 )2.272692307692310.079800824542313728.4795592116624
Trimmed Mean ( 18 / 20 )2.273333333333330.077994952146831129.1471854364834
Trimmed Mean ( 19 / 20 )2.274090909090910.075388342625745230.1650206104187
Trimmed Mean ( 20 / 20 )2.2740.071474691877246831.8154571957505
Median2.295
Midrange2.115
Midmean - Weighted Average at Xnp2.25290322580645
Midmean - Weighted Average at X(n+1)p2.27766666666667
Midmean - Empirical Distribution Function2.25290322580645
Midmean - Empirical Distribution Function - Averaging2.27766666666667
Midmean - Empirical Distribution Function - Interpolation2.27766666666667
Midmean - Closest Observation2.25290322580645
Midmean - True Basic - Statistics Graphics Toolkit2.27766666666667
Midmean - MS Excel (old versions)2.2790625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.3115 & 0.205473110534061 & 11.2496471873716 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 2.91553861892959 &  &  \tabularnewline
Quadratic Mean & 2.79892211395744 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.31783333333333 & 0.20238857458466 & 11.4523922019312 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.3095 & 0.198331376100109 & 11.6446527292498 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.322 & 0.192874597004094 & 12.0389104426786 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.33733333333333 & 0.182485641671327 & 12.8083136400566 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.37733333333333 & 0.153451232001038 & 15.4924356248717 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.34633333333333 & 0.144827964701913 & 16.2008306763309 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.37666666666667 & 0.127335729264293 & 18.6645702694626 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.32066666666667 & 0.110310774828729 & 21.0375339151573 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.29516666666667 & 0.104766755106369 & 21.9073948060756 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.25516666666667 & 0.0942051168937453 & 23.9388978117854 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.25333333333333 & 0.093290042421825 & 24.1540605496195 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.26933333333333 & 0.0905422667684164 & 25.0638007455424 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.28883333333333 & 0.085224227897445 & 26.8566039235652 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.28883333333333 & 0.0837261110770282 & 27.3371509065744 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.30633333333333 & 0.0794422530086384 & 29.0315700523064 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.27966666666667 & 0.0727358686710834 & 31.3417122572011 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.26833333333333 & 0.0701520409626413 & 32.3345308590709 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.26833333333333 & 0.0683457340270677 & 33.1890990070423 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.27466666666667 & 0.0664480029783565 & 34.2322803502097 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.268 & 0.0575962961772138 & 39.3775320729263 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.31827586206897 & 0.190972950313451 & 12.1392891415454 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.31875 & 0.176677132796655 & 13.1242224915929 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.32388888888889 & 0.161432358824549 & 14.3954341360680 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.32461538461538 & 0.144728502661150 & 16.0619044754298 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.3208 & 0.127715512937536 & 18.1716374668994 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.30666666666667 & 0.117667314606538 & 19.6032914865086 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.29804347826087 & 0.107782039663081 & 21.3212097808167 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.28272727272727 & 0.100787786830774 & 22.6488480847390 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.27595238095238 & 0.0970661732470589 & 23.4474308074295 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.27275 & 0.0937365289466938 & 24.2461506260006 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.27552631578947 & 0.0921296147446868 & 24.6991841016105 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.27888888888889 & 0.0900394779181568 & 25.309885636613 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.28029411764706 & 0.0877897395875399 & 25.9744946090569 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.2790625 & 0.0859849942073072 & 26.5053515559384 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.27766666666667 & 0.0836325891126529 & 27.2342000987038 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.27357142857143 & 0.0813058343535346 & 27.9632014928408 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.27269230769231 & 0.0798008245423137 & 28.4795592116624 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.27333333333333 & 0.0779949521468311 & 29.1471854364834 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.27409090909091 & 0.0753883426257452 & 30.1650206104187 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.274 & 0.0714746918772468 & 31.8154571957505 \tabularnewline
Median & 2.295 &  &  \tabularnewline
Midrange & 2.115 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.25290322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.27766666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.25290322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.27766666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.27766666666667 &  &  \tabularnewline
Midmean - Closest Observation & 2.25290322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.27766666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.2790625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46995&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]2.3115[/C][C]0.205473110534061[/C][C]11.2496471873716[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.91553861892959[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.79892211395744[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.31783333333333[/C][C]0.20238857458466[/C][C]11.4523922019312[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.3095[/C][C]0.198331376100109[/C][C]11.6446527292498[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.322[/C][C]0.192874597004094[/C][C]12.0389104426786[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.33733333333333[/C][C]0.182485641671327[/C][C]12.8083136400566[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.37733333333333[/C][C]0.153451232001038[/C][C]15.4924356248717[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.34633333333333[/C][C]0.144827964701913[/C][C]16.2008306763309[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.37666666666667[/C][C]0.127335729264293[/C][C]18.6645702694626[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.32066666666667[/C][C]0.110310774828729[/C][C]21.0375339151573[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.29516666666667[/C][C]0.104766755106369[/C][C]21.9073948060756[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.25516666666667[/C][C]0.0942051168937453[/C][C]23.9388978117854[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.25333333333333[/C][C]0.093290042421825[/C][C]24.1540605496195[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.26933333333333[/C][C]0.0905422667684164[/C][C]25.0638007455424[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.28883333333333[/C][C]0.085224227897445[/C][C]26.8566039235652[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.28883333333333[/C][C]0.0837261110770282[/C][C]27.3371509065744[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.30633333333333[/C][C]0.0794422530086384[/C][C]29.0315700523064[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.27966666666667[/C][C]0.0727358686710834[/C][C]31.3417122572011[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.26833333333333[/C][C]0.0701520409626413[/C][C]32.3345308590709[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.26833333333333[/C][C]0.0683457340270677[/C][C]33.1890990070423[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.27466666666667[/C][C]0.0664480029783565[/C][C]34.2322803502097[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.268[/C][C]0.0575962961772138[/C][C]39.3775320729263[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.31827586206897[/C][C]0.190972950313451[/C][C]12.1392891415454[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.31875[/C][C]0.176677132796655[/C][C]13.1242224915929[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.32388888888889[/C][C]0.161432358824549[/C][C]14.3954341360680[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.32461538461538[/C][C]0.144728502661150[/C][C]16.0619044754298[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.3208[/C][C]0.127715512937536[/C][C]18.1716374668994[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.30666666666667[/C][C]0.117667314606538[/C][C]19.6032914865086[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.29804347826087[/C][C]0.107782039663081[/C][C]21.3212097808167[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.28272727272727[/C][C]0.100787786830774[/C][C]22.6488480847390[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.27595238095238[/C][C]0.0970661732470589[/C][C]23.4474308074295[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.27275[/C][C]0.0937365289466938[/C][C]24.2461506260006[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.27552631578947[/C][C]0.0921296147446868[/C][C]24.6991841016105[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.27888888888889[/C][C]0.0900394779181568[/C][C]25.309885636613[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.28029411764706[/C][C]0.0877897395875399[/C][C]25.9744946090569[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.2790625[/C][C]0.0859849942073072[/C][C]26.5053515559384[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.27766666666667[/C][C]0.0836325891126529[/C][C]27.2342000987038[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.27357142857143[/C][C]0.0813058343535346[/C][C]27.9632014928408[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.27269230769231[/C][C]0.0798008245423137[/C][C]28.4795592116624[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.27333333333333[/C][C]0.0779949521468311[/C][C]29.1471854364834[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.27409090909091[/C][C]0.0753883426257452[/C][C]30.1650206104187[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.274[/C][C]0.0714746918772468[/C][C]31.8154571957505[/C][/ROW]
[ROW][C]Median[/C][C]2.295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.25290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.27766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.25290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.27766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.27766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.25290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.27766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.2790625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46995&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 Mean2.31150.20547311053406111.2496471873716
Geometric MeanNaN
Harmonic Mean2.91553861892959
Quadratic Mean2.79892211395744
Winsorized Mean ( 1 / 20 )2.317833333333330.2023885745846611.4523922019312
Winsorized Mean ( 2 / 20 )2.30950.19833137610010911.6446527292498
Winsorized Mean ( 3 / 20 )2.3220.19287459700409412.0389104426786
Winsorized Mean ( 4 / 20 )2.337333333333330.18248564167132712.8083136400566
Winsorized Mean ( 5 / 20 )2.377333333333330.15345123200103815.4924356248717
Winsorized Mean ( 6 / 20 )2.346333333333330.14482796470191316.2008306763309
Winsorized Mean ( 7 / 20 )2.376666666666670.12733572926429318.6645702694626
Winsorized Mean ( 8 / 20 )2.320666666666670.11031077482872921.0375339151573
Winsorized Mean ( 9 / 20 )2.295166666666670.10476675510636921.9073948060756
Winsorized Mean ( 10 / 20 )2.255166666666670.094205116893745323.9388978117854
Winsorized Mean ( 11 / 20 )2.253333333333330.09329004242182524.1540605496195
Winsorized Mean ( 12 / 20 )2.269333333333330.090542266768416425.0638007455424
Winsorized Mean ( 13 / 20 )2.288833333333330.08522422789744526.8566039235652
Winsorized Mean ( 14 / 20 )2.288833333333330.083726111077028227.3371509065744
Winsorized Mean ( 15 / 20 )2.306333333333330.079442253008638429.0315700523064
Winsorized Mean ( 16 / 20 )2.279666666666670.072735868671083431.3417122572011
Winsorized Mean ( 17 / 20 )2.268333333333330.070152040962641332.3345308590709
Winsorized Mean ( 18 / 20 )2.268333333333330.068345734027067733.1890990070423
Winsorized Mean ( 19 / 20 )2.274666666666670.066448002978356534.2322803502097
Winsorized Mean ( 20 / 20 )2.2680.057596296177213839.3775320729263
Trimmed Mean ( 1 / 20 )2.318275862068970.19097295031345112.1392891415454
Trimmed Mean ( 2 / 20 )2.318750.17667713279665513.1242224915929
Trimmed Mean ( 3 / 20 )2.323888888888890.16143235882454914.3954341360680
Trimmed Mean ( 4 / 20 )2.324615384615380.14472850266115016.0619044754298
Trimmed Mean ( 5 / 20 )2.32080.12771551293753618.1716374668994
Trimmed Mean ( 6 / 20 )2.306666666666670.11766731460653819.6032914865086
Trimmed Mean ( 7 / 20 )2.298043478260870.10778203966308121.3212097808167
Trimmed Mean ( 8 / 20 )2.282727272727270.10078778683077422.6488480847390
Trimmed Mean ( 9 / 20 )2.275952380952380.097066173247058923.4474308074295
Trimmed Mean ( 10 / 20 )2.272750.093736528946693824.2461506260006
Trimmed Mean ( 11 / 20 )2.275526315789470.092129614744686824.6991841016105
Trimmed Mean ( 12 / 20 )2.278888888888890.090039477918156825.309885636613
Trimmed Mean ( 13 / 20 )2.280294117647060.087789739587539925.9744946090569
Trimmed Mean ( 14 / 20 )2.27906250.085984994207307226.5053515559384
Trimmed Mean ( 15 / 20 )2.277666666666670.083632589112652927.2342000987038
Trimmed Mean ( 16 / 20 )2.273571428571430.081305834353534627.9632014928408
Trimmed Mean ( 17 / 20 )2.272692307692310.079800824542313728.4795592116624
Trimmed Mean ( 18 / 20 )2.273333333333330.077994952146831129.1471854364834
Trimmed Mean ( 19 / 20 )2.274090909090910.075388342625745230.1650206104187
Trimmed Mean ( 20 / 20 )2.2740.071474691877246831.8154571957505
Median2.295
Midrange2.115
Midmean - Weighted Average at Xnp2.25290322580645
Midmean - Weighted Average at X(n+1)p2.27766666666667
Midmean - Empirical Distribution Function2.25290322580645
Midmean - Empirical Distribution Function - Averaging2.27766666666667
Midmean - Empirical Distribution Function - Interpolation2.27766666666667
Midmean - Closest Observation2.25290322580645
Midmean - True Basic - Statistics Graphics Toolkit2.27766666666667
Midmean - MS Excel (old versions)2.2790625
Number of observations60



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')