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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, 26 Nov 2010 13:47:02 +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/Nov/26/t1290779595vfkprnit60j1oc2.htm/, Retrieved Fri, 03 May 2024 22:02:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101876, Retrieved Fri, 03 May 2024 22:02:56 +0000
QR Codes:

Original text written by user:link 1
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [mini tutorial cen...] [2010-11-26 13:47:02] [7b74daa7106fa81c528ad8096e75c3c0] [Current]
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Dataseries X:
8,7
8,7
8,7
8,6
8,5
8,5
8,4
8,4
8,3
8,2
8,1
8,0
8,1
8,1
8,0
7,8
7,7
7,7
7,7
7,6
7,5
7,3
7,1
7,1
7,2
7,2
7,2
6,9
6,8
6,8
6,8
6,9
7,0
7,2
7,2
7,2
7,0
7,0
7,2
7,4
7,8
8,0
7,8
7,8
7,9
7,9
8,0
8,0
8,0
8,0
8,2
8,4
8,6
8,6
8,5
8,5
8,4
8,4
8,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101876&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101876&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101876&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.81355932203390.076848261729916101.675160194185
Geometric Mean7.79133254151238
Harmonic Mean7.76884346815571
Quadratic Mean7.83544748486872
Winsorized Mean ( 1 / 19 )7.81355932203390.076848261729916101.675160194185
Winsorized Mean ( 2 / 19 )7.81355932203390.076848261729916101.675160194185
Winsorized Mean ( 3 / 19 )7.81355932203390.0747666397633327104.505958095309
Winsorized Mean ( 4 / 19 )7.81355932203390.0747666397633327104.505958095309
Winsorized Mean ( 5 / 19 )7.822033898305080.0730510576436312107.076258039462
Winsorized Mean ( 6 / 19 )7.811864406779660.0712698851336184109.60961129843
Winsorized Mean ( 7 / 19 )7.811864406779660.0712698851336184109.60961129843
Winsorized Mean ( 8 / 19 )7.825423728813560.0687023080566755113.903360020424
Winsorized Mean ( 9 / 19 )7.825423728813560.0687023080566755113.903360020424
Winsorized Mean ( 10 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 11 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 12 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 13 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 14 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 15 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 16 / 19 )7.798305084745760.0587962000060161132.632807629538
Winsorized Mean ( 17 / 19 )7.798305084745760.0496328734211795157.119758482853
Winsorized Mean ( 18 / 19 )7.828813559322030.0444494109213428176.128623463105
Winsorized Mean ( 19 / 19 )7.828813559322030.034618303373346226.146656434635
Trimmed Mean ( 1 / 19 )7.815789473684210.0759150310569472102.954439520959
Trimmed Mean ( 2 / 19 )7.818181818181820.0747201697329573104.632816629342
Trimmed Mean ( 3 / 19 )7.820754716981130.073199653936842106.841416541792
Trimmed Mean ( 4 / 19 )7.82352941176470.0722516427817371108.281682056678
Trimmed Mean ( 5 / 19 )7.82653061224490.0709972399461182110.237110881841
Trimmed Mean ( 6 / 19 )7.827659574468090.0699346945046822111.928129949063
Trimmed Mean ( 7 / 19 )7.831111111111110.0690353607403315113.436230753786
Trimmed Mean ( 8 / 19 )7.834883720930230.0677827714670514115.588128832099
Trimmed Mean ( 9 / 19 )7.836585365853660.0667865271904314117.337817903136
Trimmed Mean ( 10 / 19 )7.838461538461540.0653667515487414119.915115142546
Trimmed Mean ( 11 / 19 )7.840540540540540.0648930119110431120.822571023341
Trimmed Mean ( 12 / 19 )7.842857142857140.0640752858511202122.400657892969
Trimmed Mean ( 13 / 19 )7.845454545454550.0627783059860597124.970790820585
Trimmed Mean ( 14 / 19 )7.84838709677420.0607959689774955129.093872978312
Trimmed Mean ( 15 / 19 )7.851724137931030.0577962894591906135.851699328813
Trimmed Mean ( 16 / 19 )7.855555555555560.0531978335712664147.666832053074
Trimmed Mean ( 17 / 19 )7.8640.0475674959049419165.322976339038
Trimmed Mean ( 18 / 19 )7.873913043478260.0427407809925795184.224828386859
Trimmed Mean ( 19 / 19 )7.880952380952380.0375557031488197209.847019764828
Median7.9
Midrange7.75
Midmean - Weighted Average at Xnp7.83846153846154
Midmean - Weighted Average at X(n+1)p7.83846153846154
Midmean - Empirical Distribution Function7.83846153846154
Midmean - Empirical Distribution Function - Averaging7.83846153846154
Midmean - Empirical Distribution Function - Interpolation7.83846153846154
Midmean - Closest Observation7.83846153846154
Midmean - True Basic - Statistics Graphics Toolkit7.83846153846154
Midmean - MS Excel (old versions)7.83846153846154
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.8135593220339 & 0.076848261729916 & 101.675160194185 \tabularnewline
Geometric Mean & 7.79133254151238 &  &  \tabularnewline
Harmonic Mean & 7.76884346815571 &  &  \tabularnewline
Quadratic Mean & 7.83544748486872 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 7.8135593220339 & 0.076848261729916 & 101.675160194185 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 7.8135593220339 & 0.076848261729916 & 101.675160194185 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 7.8135593220339 & 0.0747666397633327 & 104.505958095309 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 7.8135593220339 & 0.0747666397633327 & 104.505958095309 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 7.82203389830508 & 0.0730510576436312 & 107.076258039462 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 7.81186440677966 & 0.0712698851336184 & 109.60961129843 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 7.81186440677966 & 0.0712698851336184 & 109.60961129843 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 7.82542372881356 & 0.0687023080566755 & 113.903360020424 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 7.82542372881356 & 0.0687023080566755 & 113.903360020424 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 7.82542372881356 & 0.0629302593001751 & 124.350730726955 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 7.82542372881356 & 0.0629302593001751 & 124.350730726955 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 7.82542372881356 & 0.0629302593001751 & 124.350730726955 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 7.82542372881356 & 0.0629302593001751 & 124.350730726955 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 7.82542372881356 & 0.0629302593001751 & 124.350730726955 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 7.82542372881356 & 0.0629302593001751 & 124.350730726955 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 7.79830508474576 & 0.0587962000060161 & 132.632807629538 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 7.79830508474576 & 0.0496328734211795 & 157.119758482853 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 7.82881355932203 & 0.0444494109213428 & 176.128623463105 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 7.82881355932203 & 0.034618303373346 & 226.146656434635 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 7.81578947368421 & 0.0759150310569472 & 102.954439520959 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 7.81818181818182 & 0.0747201697329573 & 104.632816629342 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 7.82075471698113 & 0.073199653936842 & 106.841416541792 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 7.8235294117647 & 0.0722516427817371 & 108.281682056678 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 7.8265306122449 & 0.0709972399461182 & 110.237110881841 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 7.82765957446809 & 0.0699346945046822 & 111.928129949063 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 7.83111111111111 & 0.0690353607403315 & 113.436230753786 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 7.83488372093023 & 0.0677827714670514 & 115.588128832099 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 7.83658536585366 & 0.0667865271904314 & 117.337817903136 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 7.83846153846154 & 0.0653667515487414 & 119.915115142546 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 7.84054054054054 & 0.0648930119110431 & 120.822571023341 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 7.84285714285714 & 0.0640752858511202 & 122.400657892969 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 7.84545454545455 & 0.0627783059860597 & 124.970790820585 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 7.8483870967742 & 0.0607959689774955 & 129.093872978312 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 7.85172413793103 & 0.0577962894591906 & 135.851699328813 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 7.85555555555556 & 0.0531978335712664 & 147.666832053074 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 7.864 & 0.0475674959049419 & 165.322976339038 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 7.87391304347826 & 0.0427407809925795 & 184.224828386859 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 7.88095238095238 & 0.0375557031488197 & 209.847019764828 \tabularnewline
Median & 7.9 &  &  \tabularnewline
Midrange & 7.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.83846153846154 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.83846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.83846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.83846153846154 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.83846153846154 &  &  \tabularnewline
Midmean - Closest Observation & 7.83846153846154 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.83846153846154 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.83846153846154 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101876&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]7.8135593220339[/C][C]0.076848261729916[/C][C]101.675160194185[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.79133254151238[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.76884346815571[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.83544748486872[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]7.8135593220339[/C][C]0.076848261729916[/C][C]101.675160194185[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]7.8135593220339[/C][C]0.076848261729916[/C][C]101.675160194185[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]7.8135593220339[/C][C]0.0747666397633327[/C][C]104.505958095309[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]7.8135593220339[/C][C]0.0747666397633327[/C][C]104.505958095309[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]7.82203389830508[/C][C]0.0730510576436312[/C][C]107.076258039462[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]7.81186440677966[/C][C]0.0712698851336184[/C][C]109.60961129843[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]7.81186440677966[/C][C]0.0712698851336184[/C][C]109.60961129843[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]7.82542372881356[/C][C]0.0687023080566755[/C][C]113.903360020424[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]7.82542372881356[/C][C]0.0687023080566755[/C][C]113.903360020424[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]7.82542372881356[/C][C]0.0629302593001751[/C][C]124.350730726955[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]7.82542372881356[/C][C]0.0629302593001751[/C][C]124.350730726955[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]7.82542372881356[/C][C]0.0629302593001751[/C][C]124.350730726955[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]7.82542372881356[/C][C]0.0629302593001751[/C][C]124.350730726955[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]7.82542372881356[/C][C]0.0629302593001751[/C][C]124.350730726955[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]7.82542372881356[/C][C]0.0629302593001751[/C][C]124.350730726955[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]7.79830508474576[/C][C]0.0587962000060161[/C][C]132.632807629538[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]7.79830508474576[/C][C]0.0496328734211795[/C][C]157.119758482853[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]7.82881355932203[/C][C]0.0444494109213428[/C][C]176.128623463105[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]7.82881355932203[/C][C]0.034618303373346[/C][C]226.146656434635[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]7.81578947368421[/C][C]0.0759150310569472[/C][C]102.954439520959[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]7.81818181818182[/C][C]0.0747201697329573[/C][C]104.632816629342[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]7.82075471698113[/C][C]0.073199653936842[/C][C]106.841416541792[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]7.8235294117647[/C][C]0.0722516427817371[/C][C]108.281682056678[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]7.8265306122449[/C][C]0.0709972399461182[/C][C]110.237110881841[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]7.82765957446809[/C][C]0.0699346945046822[/C][C]111.928129949063[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]7.83111111111111[/C][C]0.0690353607403315[/C][C]113.436230753786[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]7.83488372093023[/C][C]0.0677827714670514[/C][C]115.588128832099[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]7.83658536585366[/C][C]0.0667865271904314[/C][C]117.337817903136[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]7.83846153846154[/C][C]0.0653667515487414[/C][C]119.915115142546[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]7.84054054054054[/C][C]0.0648930119110431[/C][C]120.822571023341[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]7.84285714285714[/C][C]0.0640752858511202[/C][C]122.400657892969[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]7.84545454545455[/C][C]0.0627783059860597[/C][C]124.970790820585[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]7.8483870967742[/C][C]0.0607959689774955[/C][C]129.093872978312[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]7.85172413793103[/C][C]0.0577962894591906[/C][C]135.851699328813[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]7.85555555555556[/C][C]0.0531978335712664[/C][C]147.666832053074[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]7.864[/C][C]0.0475674959049419[/C][C]165.322976339038[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]7.87391304347826[/C][C]0.0427407809925795[/C][C]184.224828386859[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]7.88095238095238[/C][C]0.0375557031488197[/C][C]209.847019764828[/C][/ROW]
[ROW][C]Median[/C][C]7.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.83846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101876&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101876&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 Mean7.81355932203390.076848261729916101.675160194185
Geometric Mean7.79133254151238
Harmonic Mean7.76884346815571
Quadratic Mean7.83544748486872
Winsorized Mean ( 1 / 19 )7.81355932203390.076848261729916101.675160194185
Winsorized Mean ( 2 / 19 )7.81355932203390.076848261729916101.675160194185
Winsorized Mean ( 3 / 19 )7.81355932203390.0747666397633327104.505958095309
Winsorized Mean ( 4 / 19 )7.81355932203390.0747666397633327104.505958095309
Winsorized Mean ( 5 / 19 )7.822033898305080.0730510576436312107.076258039462
Winsorized Mean ( 6 / 19 )7.811864406779660.0712698851336184109.60961129843
Winsorized Mean ( 7 / 19 )7.811864406779660.0712698851336184109.60961129843
Winsorized Mean ( 8 / 19 )7.825423728813560.0687023080566755113.903360020424
Winsorized Mean ( 9 / 19 )7.825423728813560.0687023080566755113.903360020424
Winsorized Mean ( 10 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 11 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 12 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 13 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 14 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 15 / 19 )7.825423728813560.0629302593001751124.350730726955
Winsorized Mean ( 16 / 19 )7.798305084745760.0587962000060161132.632807629538
Winsorized Mean ( 17 / 19 )7.798305084745760.0496328734211795157.119758482853
Winsorized Mean ( 18 / 19 )7.828813559322030.0444494109213428176.128623463105
Winsorized Mean ( 19 / 19 )7.828813559322030.034618303373346226.146656434635
Trimmed Mean ( 1 / 19 )7.815789473684210.0759150310569472102.954439520959
Trimmed Mean ( 2 / 19 )7.818181818181820.0747201697329573104.632816629342
Trimmed Mean ( 3 / 19 )7.820754716981130.073199653936842106.841416541792
Trimmed Mean ( 4 / 19 )7.82352941176470.0722516427817371108.281682056678
Trimmed Mean ( 5 / 19 )7.82653061224490.0709972399461182110.237110881841
Trimmed Mean ( 6 / 19 )7.827659574468090.0699346945046822111.928129949063
Trimmed Mean ( 7 / 19 )7.831111111111110.0690353607403315113.436230753786
Trimmed Mean ( 8 / 19 )7.834883720930230.0677827714670514115.588128832099
Trimmed Mean ( 9 / 19 )7.836585365853660.0667865271904314117.337817903136
Trimmed Mean ( 10 / 19 )7.838461538461540.0653667515487414119.915115142546
Trimmed Mean ( 11 / 19 )7.840540540540540.0648930119110431120.822571023341
Trimmed Mean ( 12 / 19 )7.842857142857140.0640752858511202122.400657892969
Trimmed Mean ( 13 / 19 )7.845454545454550.0627783059860597124.970790820585
Trimmed Mean ( 14 / 19 )7.84838709677420.0607959689774955129.093872978312
Trimmed Mean ( 15 / 19 )7.851724137931030.0577962894591906135.851699328813
Trimmed Mean ( 16 / 19 )7.855555555555560.0531978335712664147.666832053074
Trimmed Mean ( 17 / 19 )7.8640.0475674959049419165.322976339038
Trimmed Mean ( 18 / 19 )7.873913043478260.0427407809925795184.224828386859
Trimmed Mean ( 19 / 19 )7.880952380952380.0375557031488197209.847019764828
Median7.9
Midrange7.75
Midmean - Weighted Average at Xnp7.83846153846154
Midmean - Weighted Average at X(n+1)p7.83846153846154
Midmean - Empirical Distribution Function7.83846153846154
Midmean - Empirical Distribution Function - Averaging7.83846153846154
Midmean - Empirical Distribution Function - Interpolation7.83846153846154
Midmean - Closest Observation7.83846153846154
Midmean - True Basic - Statistics Graphics Toolkit7.83846153846154
Midmean - MS Excel (old versions)7.83846153846154
Number of observations59



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')