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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, 18 Dec 2010 14:24:07 +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/18/t1292682125n2ccc4v663rbxja.htm/, Retrieved Tue, 30 Apr 2024 04:56:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111995, Retrieved Tue, 30 Apr 2024 04:56:32 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
0,59
0,6
0,59
0,6
0,61
0,56
0,53
0,52
0,52
0,47
0,5
0,51
0,54
0,54
0,56
0,58
0,57
0,59
0,61
0,67
0,66
0,68
0,68
0,74
0,76
0,87
0,92
0,93
0,81
0,79
0,71
0,62
0,5
0,47
0,45
0,41
0,45
0,46
0,5
0,48
0,53
0,5
0,5
0,53
0,52
0,57
0,54
0,59
0,64
0,65
0,64
0,62
0,63




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=111995&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=111995&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111995&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 Mean0.5964150943396230.016021335420365637.2263034691532
Geometric Mean0.586265664166524
Harmonic Mean0.577021032004555
Quadratic Mean0.607501844084475
Winsorized Mean ( 1 / 17 )0.5969811320754720.015794362743083837.7971015219897
Winsorized Mean ( 2 / 17 )0.5950943396226410.015091935585045139.4312801210423
Winsorized Mean ( 3 / 17 )0.5922641509433960.013877029681783942.6794612769942
Winsorized Mean ( 4 / 17 )0.5915094339622640.013296867780542544.484869950187
Winsorized Mean ( 5 / 17 )0.5886792452830190.012517151472119547.0298091857586
Winsorized Mean ( 6 / 17 )0.5875471698113210.011732707871145950.0777123460364
Winsorized Mean ( 7 / 17 )0.586226415094340.010332731592826856.7348923977965
Winsorized Mean ( 8 / 17 )0.5816981132075470.0093502087752379862.2123128146667
Winsorized Mean ( 9 / 17 )0.5816981132075470.0093502087752379862.2123128146667
Winsorized Mean ( 10 / 17 )0.5798113207547170.0089770331293446364.5883013241198
Winsorized Mean ( 11 / 17 )0.5777358490566040.0085851050232836467.295140535815
Winsorized Mean ( 12 / 17 )0.5777358490566040.0077872728841350974.1897526454502
Winsorized Mean ( 13 / 17 )0.5777358490566040.0069553912922702983.0630261878518
Winsorized Mean ( 14 / 17 )0.5777358490566040.0069553912922702983.0630261878518
Winsorized Mean ( 15 / 17 )0.5749056603773590.006479971607952688.7203980449236
Winsorized Mean ( 16 / 17 )0.5749056603773580.00551171493828525104.306130998171
Winsorized Mean ( 17 / 17 )0.5749056603773580.00551171493828525104.306130998171
Trimmed Mean ( 1 / 17 )0.5935294117647060.014831930392553440.0170035899505
Trimmed Mean ( 2 / 17 )0.5897959183673470.013569830093577843.4637658909585
Trimmed Mean ( 3 / 17 )0.5868085106382980.012440817837733547.1680011951051
Trimmed Mean ( 4 / 17 )0.5846666666666670.011645435226566750.2056518534289
Trimmed Mean ( 5 / 17 )0.5825581395348840.010860501872117453.6400754214232
Trimmed Mean ( 6 / 17 )0.5809756097560980.010144113263779557.2721927140269
Trimmed Mean ( 7 / 17 )0.579487179487180.0094800644436326261.1269240765972
Trimmed Mean ( 8 / 17 )0.5781081081081080.0090778898296594963.683093643558
Trimmed Mean ( 9 / 17 )0.5774285714285710.0088530757807844565.2234981069378
Trimmed Mean ( 10 / 17 )0.5766666666666670.0085243264492944867.649528686738
Trimmed Mean ( 11 / 17 )0.5761290322580650.0081738820794254470.4841379726097
Trimmed Mean ( 12 / 17 )0.5758620689655170.007792209722500873.9022805434326
Trimmed Mean ( 13 / 17 )0.5755555555555560.007498021264773176.7609926981146
Trimmed Mean ( 14 / 17 )0.57520.0073284832446193578.4882738760872
Trimmed Mean ( 15 / 17 )0.5747826086956520.0070253511922510381.815498324075
Trimmed Mean ( 16 / 17 )0.5747619047619050.006712427976701485.6265283973077
Trimmed Mean ( 17 / 17 )0.5747368421052630.0065947179400745687.1510877838644
Median0.58
Midrange0.67
Midmean - Weighted Average at Xnp0.575555555555555
Midmean - Weighted Average at X(n+1)p0.575555555555555
Midmean - Empirical Distribution Function0.575555555555555
Midmean - Empirical Distribution Function - Averaging0.575555555555555
Midmean - Empirical Distribution Function - Interpolation0.575555555555555
Midmean - Closest Observation0.573214285714286
Midmean - True Basic - Statistics Graphics Toolkit0.575555555555555
Midmean - MS Excel (old versions)0.575555555555555
Number of observations53

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.596415094339623 & 0.0160213354203656 & 37.2263034691532 \tabularnewline
Geometric Mean & 0.586265664166524 &  &  \tabularnewline
Harmonic Mean & 0.577021032004555 &  &  \tabularnewline
Quadratic Mean & 0.607501844084475 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 0.596981132075472 & 0.0157943627430838 & 37.7971015219897 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 0.595094339622641 & 0.0150919355850451 & 39.4312801210423 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 0.592264150943396 & 0.0138770296817839 & 42.6794612769942 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 0.591509433962264 & 0.0132968677805425 & 44.484869950187 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 0.588679245283019 & 0.0125171514721195 & 47.0298091857586 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 0.587547169811321 & 0.0117327078711459 & 50.0777123460364 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 0.58622641509434 & 0.0103327315928268 & 56.7348923977965 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 0.581698113207547 & 0.00935020877523798 & 62.2123128146667 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 0.581698113207547 & 0.00935020877523798 & 62.2123128146667 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 0.579811320754717 & 0.00897703312934463 & 64.5883013241198 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 0.577735849056604 & 0.00858510502328364 & 67.295140535815 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 0.577735849056604 & 0.00778727288413509 & 74.1897526454502 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 0.577735849056604 & 0.00695539129227029 & 83.0630261878518 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 0.577735849056604 & 0.00695539129227029 & 83.0630261878518 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 0.574905660377359 & 0.0064799716079526 & 88.7203980449236 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 0.574905660377358 & 0.00551171493828525 & 104.306130998171 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 0.574905660377358 & 0.00551171493828525 & 104.306130998171 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 0.593529411764706 & 0.0148319303925534 & 40.0170035899505 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 0.589795918367347 & 0.0135698300935778 & 43.4637658909585 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 0.586808510638298 & 0.0124408178377335 & 47.1680011951051 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 0.584666666666667 & 0.0116454352265667 & 50.2056518534289 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 0.582558139534884 & 0.0108605018721174 & 53.6400754214232 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 0.580975609756098 & 0.0101441132637795 & 57.2721927140269 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 0.57948717948718 & 0.00948006444363262 & 61.1269240765972 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 0.578108108108108 & 0.00907788982965949 & 63.683093643558 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 0.577428571428571 & 0.00885307578078445 & 65.2234981069378 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 0.576666666666667 & 0.00852432644929448 & 67.649528686738 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 0.576129032258065 & 0.00817388207942544 & 70.4841379726097 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 0.575862068965517 & 0.0077922097225008 & 73.9022805434326 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 0.575555555555556 & 0.0074980212647731 & 76.7609926981146 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 0.5752 & 0.00732848324461935 & 78.4882738760872 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 0.574782608695652 & 0.00702535119225103 & 81.815498324075 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 0.574761904761905 & 0.0067124279767014 & 85.6265283973077 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 0.574736842105263 & 0.00659471794007456 & 87.1510877838644 \tabularnewline
Median & 0.58 &  &  \tabularnewline
Midrange & 0.67 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.575555555555555 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.575555555555555 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.575555555555555 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.575555555555555 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.575555555555555 &  &  \tabularnewline
Midmean - Closest Observation & 0.573214285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.575555555555555 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.575555555555555 &  &  \tabularnewline
Number of observations & 53 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111995&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.596415094339623[/C][C]0.0160213354203656[/C][C]37.2263034691532[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.586265664166524[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.577021032004555[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.607501844084475[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]0.596981132075472[/C][C]0.0157943627430838[/C][C]37.7971015219897[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]0.595094339622641[/C][C]0.0150919355850451[/C][C]39.4312801210423[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]0.592264150943396[/C][C]0.0138770296817839[/C][C]42.6794612769942[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]0.591509433962264[/C][C]0.0132968677805425[/C][C]44.484869950187[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]0.588679245283019[/C][C]0.0125171514721195[/C][C]47.0298091857586[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]0.587547169811321[/C][C]0.0117327078711459[/C][C]50.0777123460364[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]0.58622641509434[/C][C]0.0103327315928268[/C][C]56.7348923977965[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]0.581698113207547[/C][C]0.00935020877523798[/C][C]62.2123128146667[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]0.581698113207547[/C][C]0.00935020877523798[/C][C]62.2123128146667[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]0.579811320754717[/C][C]0.00897703312934463[/C][C]64.5883013241198[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]0.577735849056604[/C][C]0.00858510502328364[/C][C]67.295140535815[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]0.577735849056604[/C][C]0.00778727288413509[/C][C]74.1897526454502[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]0.577735849056604[/C][C]0.00695539129227029[/C][C]83.0630261878518[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]0.577735849056604[/C][C]0.00695539129227029[/C][C]83.0630261878518[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]0.574905660377359[/C][C]0.0064799716079526[/C][C]88.7203980449236[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]0.574905660377358[/C][C]0.00551171493828525[/C][C]104.306130998171[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]0.574905660377358[/C][C]0.00551171493828525[/C][C]104.306130998171[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]0.593529411764706[/C][C]0.0148319303925534[/C][C]40.0170035899505[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]0.589795918367347[/C][C]0.0135698300935778[/C][C]43.4637658909585[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]0.586808510638298[/C][C]0.0124408178377335[/C][C]47.1680011951051[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]0.584666666666667[/C][C]0.0116454352265667[/C][C]50.2056518534289[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]0.582558139534884[/C][C]0.0108605018721174[/C][C]53.6400754214232[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]0.580975609756098[/C][C]0.0101441132637795[/C][C]57.2721927140269[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]0.57948717948718[/C][C]0.00948006444363262[/C][C]61.1269240765972[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]0.578108108108108[/C][C]0.00907788982965949[/C][C]63.683093643558[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]0.577428571428571[/C][C]0.00885307578078445[/C][C]65.2234981069378[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]0.576666666666667[/C][C]0.00852432644929448[/C][C]67.649528686738[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]0.576129032258065[/C][C]0.00817388207942544[/C][C]70.4841379726097[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]0.575862068965517[/C][C]0.0077922097225008[/C][C]73.9022805434326[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]0.575555555555556[/C][C]0.0074980212647731[/C][C]76.7609926981146[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]0.5752[/C][C]0.00732848324461935[/C][C]78.4882738760872[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]0.574782608695652[/C][C]0.00702535119225103[/C][C]81.815498324075[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]0.574761904761905[/C][C]0.0067124279767014[/C][C]85.6265283973077[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]0.574736842105263[/C][C]0.00659471794007456[/C][C]87.1510877838644[/C][/ROW]
[ROW][C]Median[/C][C]0.58[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.575555555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.575555555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.575555555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.575555555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.575555555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.573214285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.575555555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.575555555555555[/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=111995&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111995&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 Mean0.5964150943396230.016021335420365637.2263034691532
Geometric Mean0.586265664166524
Harmonic Mean0.577021032004555
Quadratic Mean0.607501844084475
Winsorized Mean ( 1 / 17 )0.5969811320754720.015794362743083837.7971015219897
Winsorized Mean ( 2 / 17 )0.5950943396226410.015091935585045139.4312801210423
Winsorized Mean ( 3 / 17 )0.5922641509433960.013877029681783942.6794612769942
Winsorized Mean ( 4 / 17 )0.5915094339622640.013296867780542544.484869950187
Winsorized Mean ( 5 / 17 )0.5886792452830190.012517151472119547.0298091857586
Winsorized Mean ( 6 / 17 )0.5875471698113210.011732707871145950.0777123460364
Winsorized Mean ( 7 / 17 )0.586226415094340.010332731592826856.7348923977965
Winsorized Mean ( 8 / 17 )0.5816981132075470.0093502087752379862.2123128146667
Winsorized Mean ( 9 / 17 )0.5816981132075470.0093502087752379862.2123128146667
Winsorized Mean ( 10 / 17 )0.5798113207547170.0089770331293446364.5883013241198
Winsorized Mean ( 11 / 17 )0.5777358490566040.0085851050232836467.295140535815
Winsorized Mean ( 12 / 17 )0.5777358490566040.0077872728841350974.1897526454502
Winsorized Mean ( 13 / 17 )0.5777358490566040.0069553912922702983.0630261878518
Winsorized Mean ( 14 / 17 )0.5777358490566040.0069553912922702983.0630261878518
Winsorized Mean ( 15 / 17 )0.5749056603773590.006479971607952688.7203980449236
Winsorized Mean ( 16 / 17 )0.5749056603773580.00551171493828525104.306130998171
Winsorized Mean ( 17 / 17 )0.5749056603773580.00551171493828525104.306130998171
Trimmed Mean ( 1 / 17 )0.5935294117647060.014831930392553440.0170035899505
Trimmed Mean ( 2 / 17 )0.5897959183673470.013569830093577843.4637658909585
Trimmed Mean ( 3 / 17 )0.5868085106382980.012440817837733547.1680011951051
Trimmed Mean ( 4 / 17 )0.5846666666666670.011645435226566750.2056518534289
Trimmed Mean ( 5 / 17 )0.5825581395348840.010860501872117453.6400754214232
Trimmed Mean ( 6 / 17 )0.5809756097560980.010144113263779557.2721927140269
Trimmed Mean ( 7 / 17 )0.579487179487180.0094800644436326261.1269240765972
Trimmed Mean ( 8 / 17 )0.5781081081081080.0090778898296594963.683093643558
Trimmed Mean ( 9 / 17 )0.5774285714285710.0088530757807844565.2234981069378
Trimmed Mean ( 10 / 17 )0.5766666666666670.0085243264492944867.649528686738
Trimmed Mean ( 11 / 17 )0.5761290322580650.0081738820794254470.4841379726097
Trimmed Mean ( 12 / 17 )0.5758620689655170.007792209722500873.9022805434326
Trimmed Mean ( 13 / 17 )0.5755555555555560.007498021264773176.7609926981146
Trimmed Mean ( 14 / 17 )0.57520.0073284832446193578.4882738760872
Trimmed Mean ( 15 / 17 )0.5747826086956520.0070253511922510381.815498324075
Trimmed Mean ( 16 / 17 )0.5747619047619050.006712427976701485.6265283973077
Trimmed Mean ( 17 / 17 )0.5747368421052630.0065947179400745687.1510877838644
Median0.58
Midrange0.67
Midmean - Weighted Average at Xnp0.575555555555555
Midmean - Weighted Average at X(n+1)p0.575555555555555
Midmean - Empirical Distribution Function0.575555555555555
Midmean - Empirical Distribution Function - Averaging0.575555555555555
Midmean - Empirical Distribution Function - Interpolation0.575555555555555
Midmean - Closest Observation0.573214285714286
Midmean - True Basic - Statistics Graphics Toolkit0.575555555555555
Midmean - MS Excel (old versions)0.575555555555555
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')