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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 11:56:24 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/10/t11973121447lob4cvlep03pri.htm/, Retrieved Mon, 06 May 2024 14:30:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3019, Retrieved Mon, 06 May 2024 14:30:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-12-10 18:56:24] [40a229849a2b804e343854d9b3fa1a24] [Current]
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Dataseries X:
-0.905505201072139 
-2.84125906727696 
-1.73989240963297 
-4.73986800255703 
-2.59806291953585 
-3.62985545468938 
1.9691521211208 
-0.908612977417503 
2.36118200055135 
-1.75994094290335 
0.309767477712872 
-0.380472879874446 
-2.26580525336983 
2.05252057785798 
0.656247119753716 
-1.34557400672799 
-2.73669284952533 
2.97381956437437 
0.809868264771043 
1.16355665740363 
1.60813484055000 
-3.82222169480132 
-1.53025931659421 
0.613050669890987 
-1.17201966125335 
0.0796793187334257 
-0.283459949979886 
0.80547629701484 
-0.0341566291768046 
-0.57554811011592 
-0.854951887435694 
-1.39617782250000 
-3.07900917009265 
1.98238041034064 
1.78373651296124 
1.43258717211950 
-3.02613203678431 
2.54922080810211 
4.13455177544102 
-1.59398520020844 
-0.745296883228396 
-1.33072909421033 
-2.39557044440736 
1.28845823649155 
-3.94712151483964 
1.07761969844871 
2.06434276134405 
1.60356924734568 




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3019&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3019&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.3816512468308660.300071739531345-1.27186667903793
Geometric MeanNaN
Harmonic Mean-2.27087618669487
Quadratic Mean2.09229084280360
Winsorized Mean ( 1 / 16 )-0.3893176160673090.288456946323542-1.34965588809444
Winsorized Mean ( 2 / 16 )-0.4018050717437230.282945177504454-1.42008100398671
Winsorized Mean ( 3 / 16 )-0.4015346072086490.277359793262971-1.44770300873402
Winsorized Mean ( 4 / 16 )-0.3803673534261970.261532020147509-1.45438158284275
Winsorized Mean ( 5 / 16 )-0.3760907961530440.26008553290105-1.44602735860794
Winsorized Mean ( 6 / 16 )-0.3617491959042930.253440422441084-1.42735398094748
Winsorized Mean ( 7 / 16 )-0.348429081326740.249922684597838-1.39414748159981
Winsorized Mean ( 8 / 16 )-0.3562266943550870.239278847601188-1.48875129551284
Winsorized Mean ( 9 / 16 )-0.3511846688456020.225655010257279-1.55629014594093
Winsorized Mean ( 10 / 16 )-0.3251014192970170.220339001148604-1.47546016639041
Winsorized Mean ( 11 / 16 )-0.2483575737211150.192418252823198-1.29071733100765
Winsorized Mean ( 12 / 16 )-0.2793776743105070.184978864373607-1.51032214008104
Winsorized Mean ( 13 / 16 )-0.2736886494276750.172384097696710-1.58766761600712
Winsorized Mean ( 14 / 16 )-0.2801668797353770.164952127870274-1.69847387452748
Winsorized Mean ( 15 / 16 )-0.3219387358552070.143892095858719-2.23736219792993
Winsorized Mean ( 16 / 16 )-0.3065347865166040.140984410071819-2.17424597769677
Trimmed Mean ( 1 / 16 )-0.3850857308862080.281255323179413-1.36916779577026
Trimmed Mean ( 2 / 16 )-0.3804691288704610.271803108467127-1.39979682725548
Trimmed Mean ( 3 / 16 )-0.3682771615143120.263255068817678-1.39893664030214
Trimmed Mean ( 4 / 16 )-0.3549741832365760.254756350638595-1.39338698464932
Trimmed Mean ( 5 / 16 )-0.3469552873872220.250134161138545-1.38707678234741
Trimmed Mean ( 6 / 16 )-0.3391858183830030.244026564676644-1.38995448644066
Trimmed Mean ( 7 / 16 )-0.3338767883779940.237674218609783-1.40476653433816
Trimmed Mean ( 8 / 16 )-0.3307584398889770.229618631073893-1.44046865161624
Trimmed Mean ( 9 / 16 )-0.3256647889957560.221516147521015-1.47016275174639
Trimmed Mean ( 10 / 16 )-0.3208038595005470.214135486926759-1.49813496167625
Trimmed Mean ( 11 / 16 )-0.3200104638458140.204485735702212-1.56495250266179
Trimmed Mean ( 12 / 16 )-0.3330382620503040.199774777380558-1.66706861805626
Trimmed Mean ( 13 / 16 )-0.3427947325484490.194177782637984-1.76536536719826
Trimmed Mean ( 14 / 16 )-0.3555527786630540.189055044585651-1.88068390051328
Trimmed Mean ( 15 / 16 )-0.3699119975064210.182074623673367-2.03165048507817
Trimmed Mean ( 16 / 16 )-0.3795066498366640.179091243723132-2.11906870457255
Median-0.478010494995183
Midrange-0.302658113558005
Midmean - Weighted Average at Xnp-0.390114369284426
Midmean - Weighted Average at X(n+1)p-0.333038262050304
Midmean - Empirical Distribution Function-0.390114369284426
Midmean - Empirical Distribution Function - Averaging-0.333038262050304
Midmean - Empirical Distribution Function - Interpolation-0.333038262050304
Midmean - Closest Observation-0.390114369284426
Midmean - True Basic - Statistics Graphics Toolkit-0.333038262050304
Midmean - MS Excel (old versions)-0.320010463845814
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.381651246830866 & 0.300071739531345 & -1.27186667903793 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -2.27087618669487 &  &  \tabularnewline
Quadratic Mean & 2.09229084280360 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -0.389317616067309 & 0.288456946323542 & -1.34965588809444 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -0.401805071743723 & 0.282945177504454 & -1.42008100398671 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -0.401534607208649 & 0.277359793262971 & -1.44770300873402 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -0.380367353426197 & 0.261532020147509 & -1.45438158284275 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -0.376090796153044 & 0.26008553290105 & -1.44602735860794 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -0.361749195904293 & 0.253440422441084 & -1.42735398094748 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -0.34842908132674 & 0.249922684597838 & -1.39414748159981 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -0.356226694355087 & 0.239278847601188 & -1.48875129551284 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -0.351184668845602 & 0.225655010257279 & -1.55629014594093 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -0.325101419297017 & 0.220339001148604 & -1.47546016639041 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -0.248357573721115 & 0.192418252823198 & -1.29071733100765 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -0.279377674310507 & 0.184978864373607 & -1.51032214008104 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -0.273688649427675 & 0.172384097696710 & -1.58766761600712 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -0.280166879735377 & 0.164952127870274 & -1.69847387452748 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -0.321938735855207 & 0.143892095858719 & -2.23736219792993 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -0.306534786516604 & 0.140984410071819 & -2.17424597769677 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -0.385085730886208 & 0.281255323179413 & -1.36916779577026 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -0.380469128870461 & 0.271803108467127 & -1.39979682725548 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -0.368277161514312 & 0.263255068817678 & -1.39893664030214 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -0.354974183236576 & 0.254756350638595 & -1.39338698464932 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -0.346955287387222 & 0.250134161138545 & -1.38707678234741 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -0.339185818383003 & 0.244026564676644 & -1.38995448644066 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -0.333876788377994 & 0.237674218609783 & -1.40476653433816 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -0.330758439888977 & 0.229618631073893 & -1.44046865161624 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -0.325664788995756 & 0.221516147521015 & -1.47016275174639 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -0.320803859500547 & 0.214135486926759 & -1.49813496167625 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -0.320010463845814 & 0.204485735702212 & -1.56495250266179 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -0.333038262050304 & 0.199774777380558 & -1.66706861805626 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -0.342794732548449 & 0.194177782637984 & -1.76536536719826 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -0.355552778663054 & 0.189055044585651 & -1.88068390051328 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -0.369911997506421 & 0.182074623673367 & -2.03165048507817 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -0.379506649836664 & 0.179091243723132 & -2.11906870457255 \tabularnewline
Median & -0.478010494995183 &  &  \tabularnewline
Midrange & -0.302658113558005 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -0.390114369284426 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.333038262050304 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.390114369284426 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.333038262050304 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.333038262050304 &  &  \tabularnewline
Midmean - Closest Observation & -0.390114369284426 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.333038262050304 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.320010463845814 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3019&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]-0.381651246830866[/C][C]0.300071739531345[/C][C]-1.27186667903793[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-2.27087618669487[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.09229084280360[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-0.389317616067309[/C][C]0.288456946323542[/C][C]-1.34965588809444[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-0.401805071743723[/C][C]0.282945177504454[/C][C]-1.42008100398671[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-0.401534607208649[/C][C]0.277359793262971[/C][C]-1.44770300873402[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-0.380367353426197[/C][C]0.261532020147509[/C][C]-1.45438158284275[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-0.376090796153044[/C][C]0.26008553290105[/C][C]-1.44602735860794[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-0.361749195904293[/C][C]0.253440422441084[/C][C]-1.42735398094748[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-0.34842908132674[/C][C]0.249922684597838[/C][C]-1.39414748159981[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-0.356226694355087[/C][C]0.239278847601188[/C][C]-1.48875129551284[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-0.351184668845602[/C][C]0.225655010257279[/C][C]-1.55629014594093[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-0.325101419297017[/C][C]0.220339001148604[/C][C]-1.47546016639041[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-0.248357573721115[/C][C]0.192418252823198[/C][C]-1.29071733100765[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-0.279377674310507[/C][C]0.184978864373607[/C][C]-1.51032214008104[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-0.273688649427675[/C][C]0.172384097696710[/C][C]-1.58766761600712[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-0.280166879735377[/C][C]0.164952127870274[/C][C]-1.69847387452748[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-0.321938735855207[/C][C]0.143892095858719[/C][C]-2.23736219792993[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-0.306534786516604[/C][C]0.140984410071819[/C][C]-2.17424597769677[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-0.385085730886208[/C][C]0.281255323179413[/C][C]-1.36916779577026[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-0.380469128870461[/C][C]0.271803108467127[/C][C]-1.39979682725548[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-0.368277161514312[/C][C]0.263255068817678[/C][C]-1.39893664030214[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-0.354974183236576[/C][C]0.254756350638595[/C][C]-1.39338698464932[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-0.346955287387222[/C][C]0.250134161138545[/C][C]-1.38707678234741[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-0.339185818383003[/C][C]0.244026564676644[/C][C]-1.38995448644066[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-0.333876788377994[/C][C]0.237674218609783[/C][C]-1.40476653433816[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-0.330758439888977[/C][C]0.229618631073893[/C][C]-1.44046865161624[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-0.325664788995756[/C][C]0.221516147521015[/C][C]-1.47016275174639[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-0.320803859500547[/C][C]0.214135486926759[/C][C]-1.49813496167625[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-0.320010463845814[/C][C]0.204485735702212[/C][C]-1.56495250266179[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-0.333038262050304[/C][C]0.199774777380558[/C][C]-1.66706861805626[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-0.342794732548449[/C][C]0.194177782637984[/C][C]-1.76536536719826[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-0.355552778663054[/C][C]0.189055044585651[/C][C]-1.88068390051328[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-0.369911997506421[/C][C]0.182074623673367[/C][C]-2.03165048507817[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-0.379506649836664[/C][C]0.179091243723132[/C][C]-2.11906870457255[/C][/ROW]
[ROW][C]Median[/C][C]-0.478010494995183[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.302658113558005[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-0.390114369284426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.333038262050304[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.390114369284426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.333038262050304[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.333038262050304[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-0.390114369284426[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.333038262050304[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.320010463845814[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3019&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 Mean-0.3816512468308660.300071739531345-1.27186667903793
Geometric MeanNaN
Harmonic Mean-2.27087618669487
Quadratic Mean2.09229084280360
Winsorized Mean ( 1 / 16 )-0.3893176160673090.288456946323542-1.34965588809444
Winsorized Mean ( 2 / 16 )-0.4018050717437230.282945177504454-1.42008100398671
Winsorized Mean ( 3 / 16 )-0.4015346072086490.277359793262971-1.44770300873402
Winsorized Mean ( 4 / 16 )-0.3803673534261970.261532020147509-1.45438158284275
Winsorized Mean ( 5 / 16 )-0.3760907961530440.26008553290105-1.44602735860794
Winsorized Mean ( 6 / 16 )-0.3617491959042930.253440422441084-1.42735398094748
Winsorized Mean ( 7 / 16 )-0.348429081326740.249922684597838-1.39414748159981
Winsorized Mean ( 8 / 16 )-0.3562266943550870.239278847601188-1.48875129551284
Winsorized Mean ( 9 / 16 )-0.3511846688456020.225655010257279-1.55629014594093
Winsorized Mean ( 10 / 16 )-0.3251014192970170.220339001148604-1.47546016639041
Winsorized Mean ( 11 / 16 )-0.2483575737211150.192418252823198-1.29071733100765
Winsorized Mean ( 12 / 16 )-0.2793776743105070.184978864373607-1.51032214008104
Winsorized Mean ( 13 / 16 )-0.2736886494276750.172384097696710-1.58766761600712
Winsorized Mean ( 14 / 16 )-0.2801668797353770.164952127870274-1.69847387452748
Winsorized Mean ( 15 / 16 )-0.3219387358552070.143892095858719-2.23736219792993
Winsorized Mean ( 16 / 16 )-0.3065347865166040.140984410071819-2.17424597769677
Trimmed Mean ( 1 / 16 )-0.3850857308862080.281255323179413-1.36916779577026
Trimmed Mean ( 2 / 16 )-0.3804691288704610.271803108467127-1.39979682725548
Trimmed Mean ( 3 / 16 )-0.3682771615143120.263255068817678-1.39893664030214
Trimmed Mean ( 4 / 16 )-0.3549741832365760.254756350638595-1.39338698464932
Trimmed Mean ( 5 / 16 )-0.3469552873872220.250134161138545-1.38707678234741
Trimmed Mean ( 6 / 16 )-0.3391858183830030.244026564676644-1.38995448644066
Trimmed Mean ( 7 / 16 )-0.3338767883779940.237674218609783-1.40476653433816
Trimmed Mean ( 8 / 16 )-0.3307584398889770.229618631073893-1.44046865161624
Trimmed Mean ( 9 / 16 )-0.3256647889957560.221516147521015-1.47016275174639
Trimmed Mean ( 10 / 16 )-0.3208038595005470.214135486926759-1.49813496167625
Trimmed Mean ( 11 / 16 )-0.3200104638458140.204485735702212-1.56495250266179
Trimmed Mean ( 12 / 16 )-0.3330382620503040.199774777380558-1.66706861805626
Trimmed Mean ( 13 / 16 )-0.3427947325484490.194177782637984-1.76536536719826
Trimmed Mean ( 14 / 16 )-0.3555527786630540.189055044585651-1.88068390051328
Trimmed Mean ( 15 / 16 )-0.3699119975064210.182074623673367-2.03165048507817
Trimmed Mean ( 16 / 16 )-0.3795066498366640.179091243723132-2.11906870457255
Median-0.478010494995183
Midrange-0.302658113558005
Midmean - Weighted Average at Xnp-0.390114369284426
Midmean - Weighted Average at X(n+1)p-0.333038262050304
Midmean - Empirical Distribution Function-0.390114369284426
Midmean - Empirical Distribution Function - Averaging-0.333038262050304
Midmean - Empirical Distribution Function - Interpolation-0.333038262050304
Midmean - Closest Observation-0.390114369284426
Midmean - True Basic - Statistics Graphics Toolkit-0.333038262050304
Midmean - MS Excel (old versions)-0.320010463845814
Number of observations48



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')