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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 computationSat, 25 Dec 2010 12:38:54 +0000
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/Dec/25/t1293280598xtyofjgoc6hxbdb.htm/, Retrieved Mon, 29 Apr 2024 03:48:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115375, Retrieved Mon, 29 Apr 2024 03:48:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2010-12-25 12:38:54] [55fca7c82a53ae69fe96aa1750b06058] [Current]
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Dataseries X:
0,57
0,60
0,62
0,69
0,74
0,74
0,75
0,78
0,80
0,87
0,94
1,05
1,13
1,24
1,31
1,38
1,50
1,70
1,98
2,20
2,51
3,15
3,64
4,05
4,43
4,69
5,06
5,51
6,07
6,41
6,74
7,02
7,32
7,35
7,51
7,69
8,12
8,50
9,00
9,39
9,79
10,17
9,76
9,97
10,18
10,74
11,52
11,86
12,29
12,57
13,12
13,50
13,89




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115375&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115375&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115375&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.568113207547170.5943520490787479.3683755548211
Geometric Mean3.53278267389454
Harmonic Mean2.00596672131297
Quadratic Mean7.02660026760842
Winsorized Mean ( 1 / 17 )5.561320754716980.5923216380587639.38902177023838
Winsorized Mean ( 2 / 17 )5.54773584905660.5885780040682499.42565948898987
Winsorized Mean ( 3 / 17 )5.520566037735850.580453779688949.51077627695743
Winsorized Mean ( 4 / 17 )5.503207547169810.5749848091376929.57104859069756
Winsorized Mean ( 5 / 17 )5.462641509433960.565970283837839.6518168275407
Winsorized Mean ( 6 / 17 )5.425283018867920.5575581483647719.73043445742728
Winsorized Mean ( 7 / 17 )5.326226415094340.5360677140804799.935734376823
Winsorized Mean ( 8 / 17 )5.244716981132080.5196381181733610.0930181942164
Winsorized Mean ( 9 / 17 )5.254905660377360.51738159724986710.1567309086943
Winsorized Mean ( 10 / 17 )5.230377358490570.50840332907241310.2878503333828
Winsorized Mean ( 11 / 17 )5.215849056603770.49806624855617110.4721993745287
Winsorized Mean ( 12 / 17 )5.227169811320750.49396571934070510.5820497387905
Winsorized Mean ( 13 / 17 )5.16339622641510.47387005189292510.8962282081118
Winsorized Mean ( 14 / 17 )5.07886792452830.45351495002564211.1988985682636
Winsorized Mean ( 15 / 17 )4.957169811320750.42727639968073211.6017870751224
Winsorized Mean ( 16 / 17 )4.878679245283020.40342627623667412.0931122553378
Winsorized Mean ( 17 / 17 )4.804905660377360.37216188935704412.9107944628034
Trimmed Mean ( 1 / 17 )5.502941176470590.5871558095060279.3721991460839
Trimmed Mean ( 2 / 17 )5.439795918367350.5798964464351279.3806333041151
Trimmed Mean ( 3 / 17 )5.378936170212770.5724722207078689.39597761365898
Trimmed Mean ( 4 / 17 )5.323333333333330.5661778640474869.40222794172479
Trimmed Mean ( 5 / 17 )5.267906976744190.5593413463755169.4180539502037
Trimmed Mean ( 6 / 17 )5.217560975609760.55269216727479.44026581982753
Trimmed Mean ( 7 / 17 )5.170512820512820.5456257100627729.47629982450418
Trimmed Mean ( 8 / 17 )5.138648648648650.5417058422648489.48604989594387
Trimmed Mean ( 9 / 17 )5.118571428571430.539697883562849.48414211814385
Trimmed Mean ( 10 / 17 )5.094242424242420.5356858090730439.5097580297256
Trimmed Mean ( 11 / 17 )5.070967741935480.5307546574613619.5542595258425
Trimmed Mean ( 12 / 17 )5.046896551724140.5246711621916499.61916132505227
Trimmed Mean ( 13 / 17 )5.017407407407410.5146684802989929.74881423570487
Trimmed Mean ( 14 / 17 )4.99360.5042251084585149.9035131655108
Trimmed Mean ( 15 / 17 )4.97956521739130.49287631968504310.1030725529142
Trimmed Mean ( 16 / 17 )4.983333333333330.48198613561038810.3391632355201
Trimmed Mean ( 17 / 17 )5.001578947368420.47013701073651510.6385560658859
Median5.06
Midrange7.23
Midmean - Weighted Average at Xnp4.84923076923077
Midmean - Weighted Average at X(n+1)p5.01740740740741
Midmean - Empirical Distribution Function5.01740740740741
Midmean - Empirical Distribution Function - Averaging5.01740740740741
Midmean - Empirical Distribution Function - Interpolation5.01740740740741
Midmean - Closest Observation4.87857142857143
Midmean - True Basic - Statistics Graphics Toolkit5.01740740740741
Midmean - MS Excel (old versions)5.01740740740741
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.56811320754717 & 0.594352049078747 & 9.3683755548211 \tabularnewline
Geometric Mean & 3.53278267389454 &  &  \tabularnewline
Harmonic Mean & 2.00596672131297 &  &  \tabularnewline
Quadratic Mean & 7.02660026760842 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 5.56132075471698 & 0.592321638058763 & 9.38902177023838 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 5.5477358490566 & 0.588578004068249 & 9.42565948898987 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 5.52056603773585 & 0.58045377968894 & 9.51077627695743 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 5.50320754716981 & 0.574984809137692 & 9.57104859069756 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 5.46264150943396 & 0.56597028383783 & 9.6518168275407 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 5.42528301886792 & 0.557558148364771 & 9.73043445742728 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 5.32622641509434 & 0.536067714080479 & 9.935734376823 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 5.24471698113208 & 0.51963811817336 & 10.0930181942164 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 5.25490566037736 & 0.517381597249867 & 10.1567309086943 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 5.23037735849057 & 0.508403329072413 & 10.2878503333828 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 5.21584905660377 & 0.498066248556171 & 10.4721993745287 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 5.22716981132075 & 0.493965719340705 & 10.5820497387905 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 5.1633962264151 & 0.473870051892925 & 10.8962282081118 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 5.0788679245283 & 0.453514950025642 & 11.1988985682636 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 4.95716981132075 & 0.427276399680732 & 11.6017870751224 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 4.87867924528302 & 0.403426276236674 & 12.0931122553378 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 4.80490566037736 & 0.372161889357044 & 12.9107944628034 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 5.50294117647059 & 0.587155809506027 & 9.3721991460839 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 5.43979591836735 & 0.579896446435127 & 9.3806333041151 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 5.37893617021277 & 0.572472220707868 & 9.39597761365898 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 5.32333333333333 & 0.566177864047486 & 9.40222794172479 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 5.26790697674419 & 0.559341346375516 & 9.4180539502037 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 5.21756097560976 & 0.5526921672747 & 9.44026581982753 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 5.17051282051282 & 0.545625710062772 & 9.47629982450418 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 5.13864864864865 & 0.541705842264848 & 9.48604989594387 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 5.11857142857143 & 0.53969788356284 & 9.48414211814385 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 5.09424242424242 & 0.535685809073043 & 9.5097580297256 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 5.07096774193548 & 0.530754657461361 & 9.5542595258425 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 5.04689655172414 & 0.524671162191649 & 9.61916132505227 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 5.01740740740741 & 0.514668480298992 & 9.74881423570487 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 4.9936 & 0.504225108458514 & 9.9035131655108 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 4.9795652173913 & 0.492876319685043 & 10.1030725529142 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 4.98333333333333 & 0.481986135610388 & 10.3391632355201 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 5.00157894736842 & 0.470137010736515 & 10.6385560658859 \tabularnewline
Median & 5.06 &  &  \tabularnewline
Midrange & 7.23 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.84923076923077 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.01740740740741 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.01740740740741 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.01740740740741 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.01740740740741 &  &  \tabularnewline
Midmean - Closest Observation & 4.87857142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.01740740740741 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.01740740740741 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115375&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]5.56811320754717[/C][C]0.594352049078747[/C][C]9.3683755548211[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.53278267389454[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.00596672131297[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.02660026760842[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]5.56132075471698[/C][C]0.592321638058763[/C][C]9.38902177023838[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]5.5477358490566[/C][C]0.588578004068249[/C][C]9.42565948898987[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]5.52056603773585[/C][C]0.58045377968894[/C][C]9.51077627695743[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]5.50320754716981[/C][C]0.574984809137692[/C][C]9.57104859069756[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]5.46264150943396[/C][C]0.56597028383783[/C][C]9.6518168275407[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]5.42528301886792[/C][C]0.557558148364771[/C][C]9.73043445742728[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]5.32622641509434[/C][C]0.536067714080479[/C][C]9.935734376823[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]5.24471698113208[/C][C]0.51963811817336[/C][C]10.0930181942164[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]5.25490566037736[/C][C]0.517381597249867[/C][C]10.1567309086943[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]5.23037735849057[/C][C]0.508403329072413[/C][C]10.2878503333828[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]5.21584905660377[/C][C]0.498066248556171[/C][C]10.4721993745287[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]5.22716981132075[/C][C]0.493965719340705[/C][C]10.5820497387905[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]5.1633962264151[/C][C]0.473870051892925[/C][C]10.8962282081118[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]5.0788679245283[/C][C]0.453514950025642[/C][C]11.1988985682636[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]4.95716981132075[/C][C]0.427276399680732[/C][C]11.6017870751224[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]4.87867924528302[/C][C]0.403426276236674[/C][C]12.0931122553378[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]4.80490566037736[/C][C]0.372161889357044[/C][C]12.9107944628034[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]5.50294117647059[/C][C]0.587155809506027[/C][C]9.3721991460839[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]5.43979591836735[/C][C]0.579896446435127[/C][C]9.3806333041151[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]5.37893617021277[/C][C]0.572472220707868[/C][C]9.39597761365898[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]5.32333333333333[/C][C]0.566177864047486[/C][C]9.40222794172479[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]5.26790697674419[/C][C]0.559341346375516[/C][C]9.4180539502037[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]5.21756097560976[/C][C]0.5526921672747[/C][C]9.44026581982753[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]5.17051282051282[/C][C]0.545625710062772[/C][C]9.47629982450418[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]5.13864864864865[/C][C]0.541705842264848[/C][C]9.48604989594387[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]5.11857142857143[/C][C]0.53969788356284[/C][C]9.48414211814385[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]5.09424242424242[/C][C]0.535685809073043[/C][C]9.5097580297256[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]5.07096774193548[/C][C]0.530754657461361[/C][C]9.5542595258425[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]5.04689655172414[/C][C]0.524671162191649[/C][C]9.61916132505227[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]5.01740740740741[/C][C]0.514668480298992[/C][C]9.74881423570487[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]4.9936[/C][C]0.504225108458514[/C][C]9.9035131655108[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]4.9795652173913[/C][C]0.492876319685043[/C][C]10.1030725529142[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]4.98333333333333[/C][C]0.481986135610388[/C][C]10.3391632355201[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]5.00157894736842[/C][C]0.470137010736515[/C][C]10.6385560658859[/C][/ROW]
[ROW][C]Median[/C][C]5.06[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.84923076923077[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.01740740740741[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.01740740740741[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.01740740740741[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.01740740740741[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.87857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.01740740740741[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.01740740740741[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]53[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115375&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115375&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 Mean5.568113207547170.5943520490787479.3683755548211
Geometric Mean3.53278267389454
Harmonic Mean2.00596672131297
Quadratic Mean7.02660026760842
Winsorized Mean ( 1 / 17 )5.561320754716980.5923216380587639.38902177023838
Winsorized Mean ( 2 / 17 )5.54773584905660.5885780040682499.42565948898987
Winsorized Mean ( 3 / 17 )5.520566037735850.580453779688949.51077627695743
Winsorized Mean ( 4 / 17 )5.503207547169810.5749848091376929.57104859069756
Winsorized Mean ( 5 / 17 )5.462641509433960.565970283837839.6518168275407
Winsorized Mean ( 6 / 17 )5.425283018867920.5575581483647719.73043445742728
Winsorized Mean ( 7 / 17 )5.326226415094340.5360677140804799.935734376823
Winsorized Mean ( 8 / 17 )5.244716981132080.5196381181733610.0930181942164
Winsorized Mean ( 9 / 17 )5.254905660377360.51738159724986710.1567309086943
Winsorized Mean ( 10 / 17 )5.230377358490570.50840332907241310.2878503333828
Winsorized Mean ( 11 / 17 )5.215849056603770.49806624855617110.4721993745287
Winsorized Mean ( 12 / 17 )5.227169811320750.49396571934070510.5820497387905
Winsorized Mean ( 13 / 17 )5.16339622641510.47387005189292510.8962282081118
Winsorized Mean ( 14 / 17 )5.07886792452830.45351495002564211.1988985682636
Winsorized Mean ( 15 / 17 )4.957169811320750.42727639968073211.6017870751224
Winsorized Mean ( 16 / 17 )4.878679245283020.40342627623667412.0931122553378
Winsorized Mean ( 17 / 17 )4.804905660377360.37216188935704412.9107944628034
Trimmed Mean ( 1 / 17 )5.502941176470590.5871558095060279.3721991460839
Trimmed Mean ( 2 / 17 )5.439795918367350.5798964464351279.3806333041151
Trimmed Mean ( 3 / 17 )5.378936170212770.5724722207078689.39597761365898
Trimmed Mean ( 4 / 17 )5.323333333333330.5661778640474869.40222794172479
Trimmed Mean ( 5 / 17 )5.267906976744190.5593413463755169.4180539502037
Trimmed Mean ( 6 / 17 )5.217560975609760.55269216727479.44026581982753
Trimmed Mean ( 7 / 17 )5.170512820512820.5456257100627729.47629982450418
Trimmed Mean ( 8 / 17 )5.138648648648650.5417058422648489.48604989594387
Trimmed Mean ( 9 / 17 )5.118571428571430.539697883562849.48414211814385
Trimmed Mean ( 10 / 17 )5.094242424242420.5356858090730439.5097580297256
Trimmed Mean ( 11 / 17 )5.070967741935480.5307546574613619.5542595258425
Trimmed Mean ( 12 / 17 )5.046896551724140.5246711621916499.61916132505227
Trimmed Mean ( 13 / 17 )5.017407407407410.5146684802989929.74881423570487
Trimmed Mean ( 14 / 17 )4.99360.5042251084585149.9035131655108
Trimmed Mean ( 15 / 17 )4.97956521739130.49287631968504310.1030725529142
Trimmed Mean ( 16 / 17 )4.983333333333330.48198613561038810.3391632355201
Trimmed Mean ( 17 / 17 )5.001578947368420.47013701073651510.6385560658859
Median5.06
Midrange7.23
Midmean - Weighted Average at Xnp4.84923076923077
Midmean - Weighted Average at X(n+1)p5.01740740740741
Midmean - Empirical Distribution Function5.01740740740741
Midmean - Empirical Distribution Function - Averaging5.01740740740741
Midmean - Empirical Distribution Function - Interpolation5.01740740740741
Midmean - Closest Observation4.87857142857143
Midmean - True Basic - Statistics Graphics Toolkit5.01740740740741
Midmean - MS Excel (old versions)5.01740740740741
Number of observations53



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')