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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Oct 2009 16:17:27 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t1256163629cvq1lub0n8qgegj.htm/, Retrieved Fri, 03 May 2024 01:51:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49623, Retrieved Fri, 03 May 2024 01:51:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsIlseWS3P2
Estimated Impact157

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [WS2 Tijdseries] [2009-10-12 22:20:05] [8733f8ed033058987ec00f5e71b74854]
-   PD  [Univariate Data Series] [WS2 Tijdseries] [2009-10-12 23:06:53] [8733f8ed033058987ec00f5e71b74854]
- RMP       [Central Tendency] [WS3 Y(t) = c + e(t)] [2009-10-21 22:17:27] [c6e373ff11c42d4585d53e9e88ed5606] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.7
2.3
1.9
2.0
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3.0
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2.0
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5
4.8
3.2
2.7
2.1
1.9
0.6
0.7
-0.2
-1.0
-1.7
-0.7
-1.0

Tables (Output of Computation)





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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49623&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49623&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49623&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

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






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.3650.19894957201107511.8874344694159
Geometric MeanNaN
Harmonic Mean3.62823660038811
Quadratic Mean2.81575922266091
Winsorized Mean ( 1 / 20 )2.3750.19471295692177312.1974420066671
Winsorized Mean ( 2 / 20 )2.3650.19183657416259512.328201805749
Winsorized Mean ( 3 / 20 )2.3750.18612347824103912.7603461016577
Winsorized Mean ( 4 / 20 )2.388333333333330.17174892439842313.9059580238936
Winsorized Mean ( 5 / 20 )2.430.14950577714968116.2535525136742
Winsorized Mean ( 6 / 20 )2.40.13708012420470517.5080086476725
Winsorized Mean ( 7 / 20 )2.423333333333330.11713063513608320.6891504559664
Winsorized Mean ( 8 / 20 )2.370.099583879983370723.7990325381554
Winsorized Mean ( 9 / 20 )2.3550.096504588456820724.4029847456808
Winsorized Mean ( 10 / 20 )2.3050.08708801314703626.4674771728726
Winsorized Mean ( 11 / 20 )2.3050.080409439533562828.6657886607690
Winsorized Mean ( 12 / 20 )2.3450.066316524003691635.3607194470787
Winsorized Mean ( 13 / 20 )2.323333333333330.062813807303388936.9876215608409
Winsorized Mean ( 14 / 20 )2.346666666666670.059015781987028639.7633749423578
Winsorized Mean ( 15 / 20 )2.321666666666670.055188002599162142.0683220505233
Winsorized Mean ( 16 / 20 )2.321666666666670.055188002599162142.0683220505233
Winsorized Mean ( 17 / 20 )2.350.050784801320845446.2736869866498
Winsorized Mean ( 18 / 20 )2.350.050784801320845446.2736869866498
Winsorized Mean ( 19 / 20 )2.350.050784801320845446.2736869866498
Winsorized Mean ( 20 / 20 )2.350.040928489380110957.4172180696699
Trimmed Mean ( 1 / 20 )2.374137931034480.18331095411165012.9514242208813
Trimmed Mean ( 2 / 20 )2.373214285714290.16900186488305914.0425331244506
Trimmed Mean ( 3 / 20 )2.377777777777780.15279064173019915.5623260093148
Trimmed Mean ( 4 / 20 )2.378846153846150.13482396037076217.6440904665936
Trimmed Mean ( 5 / 20 )2.3760.11806466578160720.1245646550601
Trimmed Mean ( 6 / 20 )2.36250.10550557949684222.3921806909814
Trimmed Mean ( 7 / 20 )2.354347826086960.093751986606410725.1125113323835
Trimmed Mean ( 8 / 20 )2.340909090909090.085423839564507627.4034637502024
Trimmed Mean ( 9 / 20 )2.335714285714290.080418578915221229.0444610837583
Trimmed Mean ( 10 / 20 )2.33250.074712054085274831.2198617553432
Trimmed Mean ( 11 / 20 )2.336842105263160.069995026508094433.3858307060277
Trimmed Mean ( 12 / 20 )2.341666666666670.065631849604743635.6788157086681
Trimmed Mean ( 13 / 20 )2.341176470588240.063906913009942136.6341661695350
Trimmed Mean ( 14 / 20 )2.343750.062368813934633237.5788772006537
Trimmed Mean ( 15 / 20 )2.343333333333330.061154286385297838.3183824363405
Trimmed Mean ( 16 / 20 )2.346428571428570.060308322198345438.9072102472277
Trimmed Mean ( 17 / 20 )2.350.058769432138197139.9867739826709
Trimmed Mean ( 18 / 20 )2.350.057735026918962640.7031939778686
Trimmed Mean ( 19 / 20 )2.350.055732042902271342.1660480689867
Trimmed Mean ( 20 / 20 )2.350.052062715217221245.1378686300762
Median2.3
Midrange2.1
Midmean - Weighted Average at Xnp2.32580645161290
Midmean - Weighted Average at X(n+1)p2.32580645161290
Midmean - Empirical Distribution Function2.32580645161290
Midmean - Empirical Distribution Function - Averaging2.32580645161290
Midmean - Empirical Distribution Function - Interpolation2.32580645161290
Midmean - Closest Observation2.32580645161290
Midmean - True Basic - Statistics Graphics Toolkit2.32580645161290
Midmean - MS Excel (old versions)2.36060606060606
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.365 & 0.198949572011075 & 11.8874344694159 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 3.62823660038811 &  &  \tabularnewline
Quadratic Mean & 2.81575922266091 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.375 & 0.194712956921773 & 12.1974420066671 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.365 & 0.191836574162595 & 12.328201805749 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.375 & 0.186123478241039 & 12.7603461016577 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.38833333333333 & 0.171748924398423 & 13.9059580238936 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.43 & 0.149505777149681 & 16.2535525136742 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.4 & 0.137080124204705 & 17.5080086476725 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.42333333333333 & 0.117130635136083 & 20.6891504559664 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.37 & 0.0995838799833707 & 23.7990325381554 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.355 & 0.0965045884568207 & 24.4029847456808 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.305 & 0.087088013147036 & 26.4674771728726 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.305 & 0.0804094395335628 & 28.6657886607690 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.345 & 0.0663165240036916 & 35.3607194470787 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.32333333333333 & 0.0628138073033889 & 36.9876215608409 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.34666666666667 & 0.0590157819870286 & 39.7633749423578 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.32166666666667 & 0.0551880025991621 & 42.0683220505233 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.32166666666667 & 0.0551880025991621 & 42.0683220505233 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.35 & 0.0507848013208454 & 46.2736869866498 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.35 & 0.0507848013208454 & 46.2736869866498 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.35 & 0.0507848013208454 & 46.2736869866498 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.35 & 0.0409284893801109 & 57.4172180696699 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.37413793103448 & 0.183310954111650 & 12.9514242208813 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.37321428571429 & 0.169001864883059 & 14.0425331244506 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.37777777777778 & 0.152790641730199 & 15.5623260093148 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.37884615384615 & 0.134823960370762 & 17.6440904665936 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.376 & 0.118064665781607 & 20.1245646550601 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.3625 & 0.105505579496842 & 22.3921806909814 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.35434782608696 & 0.0937519866064107 & 25.1125113323835 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.34090909090909 & 0.0854238395645076 & 27.4034637502024 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.33571428571429 & 0.0804185789152212 & 29.0444610837583 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.3325 & 0.0747120540852748 & 31.2198617553432 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.33684210526316 & 0.0699950265080944 & 33.3858307060277 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.34166666666667 & 0.0656318496047436 & 35.6788157086681 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.34117647058824 & 0.0639069130099421 & 36.6341661695350 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.34375 & 0.0623688139346332 & 37.5788772006537 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.34333333333333 & 0.0611542863852978 & 38.3183824363405 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.34642857142857 & 0.0603083221983454 & 38.9072102472277 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.35 & 0.0587694321381971 & 39.9867739826709 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.35 & 0.0577350269189626 & 40.7031939778686 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.35 & 0.0557320429022713 & 42.1660480689867 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.35 & 0.0520627152172212 & 45.1378686300762 \tabularnewline
Median & 2.3 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.32580645161290 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.32580645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.32580645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.32580645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.32580645161290 &  &  \tabularnewline
Midmean - Closest Observation & 2.32580645161290 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.32580645161290 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.36060606060606 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49623&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]2.365[/C][C]0.198949572011075[/C][C]11.8874344694159[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.62823660038811[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.81575922266091[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.375[/C][C]0.194712956921773[/C][C]12.1974420066671[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.365[/C][C]0.191836574162595[/C][C]12.328201805749[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.375[/C][C]0.186123478241039[/C][C]12.7603461016577[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.38833333333333[/C][C]0.171748924398423[/C][C]13.9059580238936[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.43[/C][C]0.149505777149681[/C][C]16.2535525136742[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.4[/C][C]0.137080124204705[/C][C]17.5080086476725[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.42333333333333[/C][C]0.117130635136083[/C][C]20.6891504559664[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.37[/C][C]0.0995838799833707[/C][C]23.7990325381554[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.355[/C][C]0.0965045884568207[/C][C]24.4029847456808[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.305[/C][C]0.087088013147036[/C][C]26.4674771728726[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.305[/C][C]0.0804094395335628[/C][C]28.6657886607690[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.345[/C][C]0.0663165240036916[/C][C]35.3607194470787[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.32333333333333[/C][C]0.0628138073033889[/C][C]36.9876215608409[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.34666666666667[/C][C]0.0590157819870286[/C][C]39.7633749423578[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.32166666666667[/C][C]0.0551880025991621[/C][C]42.0683220505233[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.32166666666667[/C][C]0.0551880025991621[/C][C]42.0683220505233[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.35[/C][C]0.0507848013208454[/C][C]46.2736869866498[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.35[/C][C]0.0507848013208454[/C][C]46.2736869866498[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.35[/C][C]0.0507848013208454[/C][C]46.2736869866498[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.35[/C][C]0.0409284893801109[/C][C]57.4172180696699[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.37413793103448[/C][C]0.183310954111650[/C][C]12.9514242208813[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.37321428571429[/C][C]0.169001864883059[/C][C]14.0425331244506[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.37777777777778[/C][C]0.152790641730199[/C][C]15.5623260093148[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.37884615384615[/C][C]0.134823960370762[/C][C]17.6440904665936[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.376[/C][C]0.118064665781607[/C][C]20.1245646550601[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.3625[/C][C]0.105505579496842[/C][C]22.3921806909814[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.35434782608696[/C][C]0.0937519866064107[/C][C]25.1125113323835[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.34090909090909[/C][C]0.0854238395645076[/C][C]27.4034637502024[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.33571428571429[/C][C]0.0804185789152212[/C][C]29.0444610837583[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.3325[/C][C]0.0747120540852748[/C][C]31.2198617553432[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.33684210526316[/C][C]0.0699950265080944[/C][C]33.3858307060277[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.34166666666667[/C][C]0.0656318496047436[/C][C]35.6788157086681[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.34117647058824[/C][C]0.0639069130099421[/C][C]36.6341661695350[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.34375[/C][C]0.0623688139346332[/C][C]37.5788772006537[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.34333333333333[/C][C]0.0611542863852978[/C][C]38.3183824363405[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.34642857142857[/C][C]0.0603083221983454[/C][C]38.9072102472277[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.35[/C][C]0.0587694321381971[/C][C]39.9867739826709[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.35[/C][C]0.0577350269189626[/C][C]40.7031939778686[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.35[/C][C]0.0557320429022713[/C][C]42.1660480689867[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.35[/C][C]0.0520627152172212[/C][C]45.1378686300762[/C][/ROW]
[ROW][C]Median[/C][C]2.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.32580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.32580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.32580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.32580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.32580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.32580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.32580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.36060606060606[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49623&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49623&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.3650.19894957201107511.8874344694159
Geometric MeanNaN
Harmonic Mean3.62823660038811
Quadratic Mean2.81575922266091
Winsorized Mean ( 1 / 20 )2.3750.19471295692177312.1974420066671
Winsorized Mean ( 2 / 20 )2.3650.19183657416259512.328201805749
Winsorized Mean ( 3 / 20 )2.3750.18612347824103912.7603461016577
Winsorized Mean ( 4 / 20 )2.388333333333330.17174892439842313.9059580238936
Winsorized Mean ( 5 / 20 )2.430.14950577714968116.2535525136742
Winsorized Mean ( 6 / 20 )2.40.13708012420470517.5080086476725
Winsorized Mean ( 7 / 20 )2.423333333333330.11713063513608320.6891504559664
Winsorized Mean ( 8 / 20 )2.370.099583879983370723.7990325381554
Winsorized Mean ( 9 / 20 )2.3550.096504588456820724.4029847456808
Winsorized Mean ( 10 / 20 )2.3050.08708801314703626.4674771728726
Winsorized Mean ( 11 / 20 )2.3050.080409439533562828.6657886607690
Winsorized Mean ( 12 / 20 )2.3450.066316524003691635.3607194470787
Winsorized Mean ( 13 / 20 )2.323333333333330.062813807303388936.9876215608409
Winsorized Mean ( 14 / 20 )2.346666666666670.059015781987028639.7633749423578
Winsorized Mean ( 15 / 20 )2.321666666666670.055188002599162142.0683220505233
Winsorized Mean ( 16 / 20 )2.321666666666670.055188002599162142.0683220505233
Winsorized Mean ( 17 / 20 )2.350.050784801320845446.2736869866498
Winsorized Mean ( 18 / 20 )2.350.050784801320845446.2736869866498
Winsorized Mean ( 19 / 20 )2.350.050784801320845446.2736869866498
Winsorized Mean ( 20 / 20 )2.350.040928489380110957.4172180696699
Trimmed Mean ( 1 / 20 )2.374137931034480.18331095411165012.9514242208813
Trimmed Mean ( 2 / 20 )2.373214285714290.16900186488305914.0425331244506
Trimmed Mean ( 3 / 20 )2.377777777777780.15279064173019915.5623260093148
Trimmed Mean ( 4 / 20 )2.378846153846150.13482396037076217.6440904665936
Trimmed Mean ( 5 / 20 )2.3760.11806466578160720.1245646550601
Trimmed Mean ( 6 / 20 )2.36250.10550557949684222.3921806909814
Trimmed Mean ( 7 / 20 )2.354347826086960.093751986606410725.1125113323835
Trimmed Mean ( 8 / 20 )2.340909090909090.085423839564507627.4034637502024
Trimmed Mean ( 9 / 20 )2.335714285714290.080418578915221229.0444610837583
Trimmed Mean ( 10 / 20 )2.33250.074712054085274831.2198617553432
Trimmed Mean ( 11 / 20 )2.336842105263160.069995026508094433.3858307060277
Trimmed Mean ( 12 / 20 )2.341666666666670.065631849604743635.6788157086681
Trimmed Mean ( 13 / 20 )2.341176470588240.063906913009942136.6341661695350
Trimmed Mean ( 14 / 20 )2.343750.062368813934633237.5788772006537
Trimmed Mean ( 15 / 20 )2.343333333333330.061154286385297838.3183824363405
Trimmed Mean ( 16 / 20 )2.346428571428570.060308322198345438.9072102472277
Trimmed Mean ( 17 / 20 )2.350.058769432138197139.9867739826709
Trimmed Mean ( 18 / 20 )2.350.057735026918962640.7031939778686
Trimmed Mean ( 19 / 20 )2.350.055732042902271342.1660480689867
Trimmed Mean ( 20 / 20 )2.350.052062715217221245.1378686300762
Median2.3
Midrange2.1
Midmean - Weighted Average at Xnp2.32580645161290
Midmean - Weighted Average at X(n+1)p2.32580645161290
Midmean - Empirical Distribution Function2.32580645161290
Midmean - Empirical Distribution Function - Averaging2.32580645161290
Midmean - Empirical Distribution Function - Interpolation2.32580645161290
Midmean - Closest Observation2.32580645161290
Midmean - True Basic - Statistics Graphics Toolkit2.32580645161290
Midmean - MS Excel (old versions)2.36060606060606
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')