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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 computationThu, 01 May 2014 10:55:38 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/01/t13989561523bohl2xzjryv36h.htm/, Retrieved Wed, 15 May 2024 23:28:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234760, Retrieved Wed, 15 May 2024 23:28:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Notched Boxplots] [] [2014-02-13 13:26:53] [db363657be53a1294332fdf107f4512c]
- RM D    [Central Tendency] [] [2014-05-01 14:55:38] [a3f6f3ab25c27d7686091f6989fa462a] [Current]
- RMP       [Central Tendency] [] [2014-05-22 23:26:04] [db363657be53a1294332fdf107f4512c]
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Dataseries X:
0.978
0.973
0.96
0.978
0.985
1.035
1.015
1.05
1.022
1.042
1.058
1.056
1.098
1.097
1.139
1.182
1.189
1.191
1.168
1.168
1.177
1.184
1.2
1.251
1.288
1.313
1.363
1.377
1.342
1.334
1.348
1.327
1.349
1.361
1.393
1.38
1.421
1.432
1.457
1.453
1.428
1.383
1.408
1.458
1.474
1.491
1.476
1.446
1.451
1.472
1.449
1.415
1.39
1.394
1.418
1.426
1.437
1.406
1.387
1.404




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234760&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234760&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234760&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.279116666666670.021785369211378658.7144819192955
Geometric Mean1.26748645230654
Harmonic Mean1.25523339584169
Quadratic Mean1.29001588491512
Winsorized Mean ( 1 / 20 )1.279083333333330.021692721730637358.963709082519
Winsorized Mean ( 2 / 20 )1.279183333333330.021642922561124259.1040017687376
Winsorized Mean ( 3 / 20 )1.279083333333330.021627735014225959.1408824128832
Winsorized Mean ( 4 / 20 )1.278616666666670.02138143092761259.8003319326707
Winsorized Mean ( 5 / 20 )1.281033333333330.020807443348036161.5661093920143
Winsorized Mean ( 6 / 20 )1.281333333333330.020599992686448562.2006693320937
Winsorized Mean ( 7 / 20 )1.282616666666670.020248039476367563.3452274806
Winsorized Mean ( 8 / 20 )1.283283333333330.020018467344927464.1049742331304
Winsorized Mean ( 9 / 20 )1.284033333333330.019712237253842865.138894017878
Winsorized Mean ( 10 / 20 )1.283533333333330.019306207348533266.4829352633494
Winsorized Mean ( 11 / 20 )1.282983333333330.019110672199116267.1343906674653
Winsorized Mean ( 12 / 20 )1.289983333333330.017494833646864273.7351014231882
Winsorized Mean ( 13 / 20 )1.289766666666670.017396609297961374.1389683803392
Winsorized Mean ( 14 / 20 )1.298166666666670.015511817377172583.6888828111835
Winsorized Mean ( 15 / 20 )1.304666666666670.01418668243701691.9641834839779
Winsorized Mean ( 16 / 20 )1.303866666666670.014079003613520792.6107203647923
Winsorized Mean ( 17 / 20 )1.304433333333330.013402280071357797.3292101335107
Winsorized Mean ( 18 / 20 )1.305333333333330.013083147107242899.7721207774776
Winsorized Mean ( 19 / 20 )1.305333333333330.0128997145912163101.190869309788
Winsorized Mean ( 20 / 20 )1.303666666666670.0122089313113998106.77975274129
Trimmed Mean ( 1 / 20 )1.280965517241380.021534900632728559.4832332448557
Trimmed Mean ( 2 / 20 )1.282982142857140.021320490282602360.1760149908029
Trimmed Mean ( 3 / 20 )1.285092592592590.021067862605017660.9977678650008
Trimmed Mean ( 4 / 20 )1.287403846153850.020740391651648962.0723016120813
Trimmed Mean ( 5 / 20 )1.290040.020403040189628463.2278321274774
Trimmed Mean ( 6 / 20 )1.292291666666670.02015157452829164.1285704425927
Trimmed Mean ( 7 / 20 )1.294673913043480.019866512360742765.1686561553614
Trimmed Mean ( 8 / 20 )1.297022727272730.019573585574909766.263931169326
Trimmed Mean ( 9 / 20 )1.299476190476190.019225516523428267.5912238244756
Trimmed Mean ( 10 / 20 )1.302050.018819553047909469.186021404724
Trimmed Mean ( 11 / 20 )1.304973684210530.018350099586247171.1153461634928
Trimmed Mean ( 12 / 20 )1.308305555555560.017725992906322473.8071803633025
Trimmed Mean ( 13 / 20 )1.3110.017322617694187275.6814023806531
Trimmed Mean ( 14 / 20 )1.31406250.016734040151690478.5263145115173
Trimmed Mean ( 15 / 20 )1.316333333333330.016454418638174679.9987749357133
Trimmed Mean ( 16 / 20 )1.3180.016391942142277380.4053594479618
Trimmed Mean ( 17 / 20 )1.320038461538460.016225192260966481.3573386562653
Trimmed Mean ( 18 / 20 )1.322333333333330.016083643084799882.216033168694
Trimmed Mean ( 19 / 20 )1.324909090909090.015842420599038483.6304706485012
Trimmed Mean ( 20 / 20 )1.3280.015359893091733286.4589351025326
Median1.3485
Midrange1.2255
Midmean - Weighted Average at Xnp1.31061290322581
Midmean - Weighted Average at X(n+1)p1.31633333333333
Midmean - Empirical Distribution Function1.31061290322581
Midmean - Empirical Distribution Function - Averaging1.31633333333333
Midmean - Empirical Distribution Function - Interpolation1.31633333333333
Midmean - Closest Observation1.31061290322581
Midmean - True Basic - Statistics Graphics Toolkit1.31633333333333
Midmean - MS Excel (old versions)1.3140625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.27911666666667 & 0.0217853692113786 & 58.7144819192955 \tabularnewline
Geometric Mean & 1.26748645230654 &  &  \tabularnewline
Harmonic Mean & 1.25523339584169 &  &  \tabularnewline
Quadratic Mean & 1.29001588491512 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.27908333333333 & 0.0216927217306373 & 58.963709082519 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.27918333333333 & 0.0216429225611242 & 59.1040017687376 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.27908333333333 & 0.0216277350142259 & 59.1408824128832 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.27861666666667 & 0.021381430927612 & 59.8003319326707 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.28103333333333 & 0.0208074433480361 & 61.5661093920143 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.28133333333333 & 0.0205999926864485 & 62.2006693320937 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.28261666666667 & 0.0202480394763675 & 63.3452274806 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.28328333333333 & 0.0200184673449274 & 64.1049742331304 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.28403333333333 & 0.0197122372538428 & 65.138894017878 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.28353333333333 & 0.0193062073485332 & 66.4829352633494 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.28298333333333 & 0.0191106721991162 & 67.1343906674653 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.28998333333333 & 0.0174948336468642 & 73.7351014231882 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.28976666666667 & 0.0173966092979613 & 74.1389683803392 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.29816666666667 & 0.0155118173771725 & 83.6888828111835 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.30466666666667 & 0.014186682437016 & 91.9641834839779 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.30386666666667 & 0.0140790036135207 & 92.6107203647923 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.30443333333333 & 0.0134022800713577 & 97.3292101335107 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.30533333333333 & 0.0130831471072428 & 99.7721207774776 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.30533333333333 & 0.0128997145912163 & 101.190869309788 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.30366666666667 & 0.0122089313113998 & 106.77975274129 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.28096551724138 & 0.0215349006327285 & 59.4832332448557 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.28298214285714 & 0.0213204902826023 & 60.1760149908029 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.28509259259259 & 0.0210678626050176 & 60.9977678650008 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.28740384615385 & 0.0207403916516489 & 62.0723016120813 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.29004 & 0.0204030401896284 & 63.2278321274774 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.29229166666667 & 0.020151574528291 & 64.1285704425927 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.29467391304348 & 0.0198665123607427 & 65.1686561553614 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.29702272727273 & 0.0195735855749097 & 66.263931169326 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.29947619047619 & 0.0192255165234282 & 67.5912238244756 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.30205 & 0.0188195530479094 & 69.186021404724 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.30497368421053 & 0.0183500995862471 & 71.1153461634928 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.30830555555556 & 0.0177259929063224 & 73.8071803633025 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.311 & 0.0173226176941872 & 75.6814023806531 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.3140625 & 0.0167340401516904 & 78.5263145115173 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.31633333333333 & 0.0164544186381746 & 79.9987749357133 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.318 & 0.0163919421422773 & 80.4053594479618 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.32003846153846 & 0.0162251922609664 & 81.3573386562653 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.32233333333333 & 0.0160836430847998 & 82.216033168694 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.32490909090909 & 0.0158424205990384 & 83.6304706485012 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.328 & 0.0153598930917332 & 86.4589351025326 \tabularnewline
Median & 1.3485 &  &  \tabularnewline
Midrange & 1.2255 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.31061290322581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.31633333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.31061290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.31633333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.31633333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.31061290322581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.31633333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.3140625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234760&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]1.27911666666667[/C][C]0.0217853692113786[/C][C]58.7144819192955[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.26748645230654[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.25523339584169[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.29001588491512[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.27908333333333[/C][C]0.0216927217306373[/C][C]58.963709082519[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.27918333333333[/C][C]0.0216429225611242[/C][C]59.1040017687376[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.27908333333333[/C][C]0.0216277350142259[/C][C]59.1408824128832[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.27861666666667[/C][C]0.021381430927612[/C][C]59.8003319326707[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.28103333333333[/C][C]0.0208074433480361[/C][C]61.5661093920143[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.28133333333333[/C][C]0.0205999926864485[/C][C]62.2006693320937[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.28261666666667[/C][C]0.0202480394763675[/C][C]63.3452274806[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.28328333333333[/C][C]0.0200184673449274[/C][C]64.1049742331304[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.28403333333333[/C][C]0.0197122372538428[/C][C]65.138894017878[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.28353333333333[/C][C]0.0193062073485332[/C][C]66.4829352633494[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.28298333333333[/C][C]0.0191106721991162[/C][C]67.1343906674653[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.28998333333333[/C][C]0.0174948336468642[/C][C]73.7351014231882[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.28976666666667[/C][C]0.0173966092979613[/C][C]74.1389683803392[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.29816666666667[/C][C]0.0155118173771725[/C][C]83.6888828111835[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.30466666666667[/C][C]0.014186682437016[/C][C]91.9641834839779[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.30386666666667[/C][C]0.0140790036135207[/C][C]92.6107203647923[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.30443333333333[/C][C]0.0134022800713577[/C][C]97.3292101335107[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.30533333333333[/C][C]0.0130831471072428[/C][C]99.7721207774776[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.30533333333333[/C][C]0.0128997145912163[/C][C]101.190869309788[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.30366666666667[/C][C]0.0122089313113998[/C][C]106.77975274129[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.28096551724138[/C][C]0.0215349006327285[/C][C]59.4832332448557[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.28298214285714[/C][C]0.0213204902826023[/C][C]60.1760149908029[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.28509259259259[/C][C]0.0210678626050176[/C][C]60.9977678650008[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.28740384615385[/C][C]0.0207403916516489[/C][C]62.0723016120813[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.29004[/C][C]0.0204030401896284[/C][C]63.2278321274774[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.29229166666667[/C][C]0.020151574528291[/C][C]64.1285704425927[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.29467391304348[/C][C]0.0198665123607427[/C][C]65.1686561553614[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.29702272727273[/C][C]0.0195735855749097[/C][C]66.263931169326[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.29947619047619[/C][C]0.0192255165234282[/C][C]67.5912238244756[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.30205[/C][C]0.0188195530479094[/C][C]69.186021404724[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.30497368421053[/C][C]0.0183500995862471[/C][C]71.1153461634928[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.30830555555556[/C][C]0.0177259929063224[/C][C]73.8071803633025[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.311[/C][C]0.0173226176941872[/C][C]75.6814023806531[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.3140625[/C][C]0.0167340401516904[/C][C]78.5263145115173[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.31633333333333[/C][C]0.0164544186381746[/C][C]79.9987749357133[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.318[/C][C]0.0163919421422773[/C][C]80.4053594479618[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.32003846153846[/C][C]0.0162251922609664[/C][C]81.3573386562653[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.32233333333333[/C][C]0.0160836430847998[/C][C]82.216033168694[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.32490909090909[/C][C]0.0158424205990384[/C][C]83.6304706485012[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.328[/C][C]0.0153598930917332[/C][C]86.4589351025326[/C][/ROW]
[ROW][C]Median[/C][C]1.3485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.31061290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.31633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.31061290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.31633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.31633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.31061290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.31633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.3140625[/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=234760&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234760&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 Mean1.279116666666670.021785369211378658.7144819192955
Geometric Mean1.26748645230654
Harmonic Mean1.25523339584169
Quadratic Mean1.29001588491512
Winsorized Mean ( 1 / 20 )1.279083333333330.021692721730637358.963709082519
Winsorized Mean ( 2 / 20 )1.279183333333330.021642922561124259.1040017687376
Winsorized Mean ( 3 / 20 )1.279083333333330.021627735014225959.1408824128832
Winsorized Mean ( 4 / 20 )1.278616666666670.02138143092761259.8003319326707
Winsorized Mean ( 5 / 20 )1.281033333333330.020807443348036161.5661093920143
Winsorized Mean ( 6 / 20 )1.281333333333330.020599992686448562.2006693320937
Winsorized Mean ( 7 / 20 )1.282616666666670.020248039476367563.3452274806
Winsorized Mean ( 8 / 20 )1.283283333333330.020018467344927464.1049742331304
Winsorized Mean ( 9 / 20 )1.284033333333330.019712237253842865.138894017878
Winsorized Mean ( 10 / 20 )1.283533333333330.019306207348533266.4829352633494
Winsorized Mean ( 11 / 20 )1.282983333333330.019110672199116267.1343906674653
Winsorized Mean ( 12 / 20 )1.289983333333330.017494833646864273.7351014231882
Winsorized Mean ( 13 / 20 )1.289766666666670.017396609297961374.1389683803392
Winsorized Mean ( 14 / 20 )1.298166666666670.015511817377172583.6888828111835
Winsorized Mean ( 15 / 20 )1.304666666666670.01418668243701691.9641834839779
Winsorized Mean ( 16 / 20 )1.303866666666670.014079003613520792.6107203647923
Winsorized Mean ( 17 / 20 )1.304433333333330.013402280071357797.3292101335107
Winsorized Mean ( 18 / 20 )1.305333333333330.013083147107242899.7721207774776
Winsorized Mean ( 19 / 20 )1.305333333333330.0128997145912163101.190869309788
Winsorized Mean ( 20 / 20 )1.303666666666670.0122089313113998106.77975274129
Trimmed Mean ( 1 / 20 )1.280965517241380.021534900632728559.4832332448557
Trimmed Mean ( 2 / 20 )1.282982142857140.021320490282602360.1760149908029
Trimmed Mean ( 3 / 20 )1.285092592592590.021067862605017660.9977678650008
Trimmed Mean ( 4 / 20 )1.287403846153850.020740391651648962.0723016120813
Trimmed Mean ( 5 / 20 )1.290040.020403040189628463.2278321274774
Trimmed Mean ( 6 / 20 )1.292291666666670.02015157452829164.1285704425927
Trimmed Mean ( 7 / 20 )1.294673913043480.019866512360742765.1686561553614
Trimmed Mean ( 8 / 20 )1.297022727272730.019573585574909766.263931169326
Trimmed Mean ( 9 / 20 )1.299476190476190.019225516523428267.5912238244756
Trimmed Mean ( 10 / 20 )1.302050.018819553047909469.186021404724
Trimmed Mean ( 11 / 20 )1.304973684210530.018350099586247171.1153461634928
Trimmed Mean ( 12 / 20 )1.308305555555560.017725992906322473.8071803633025
Trimmed Mean ( 13 / 20 )1.3110.017322617694187275.6814023806531
Trimmed Mean ( 14 / 20 )1.31406250.016734040151690478.5263145115173
Trimmed Mean ( 15 / 20 )1.316333333333330.016454418638174679.9987749357133
Trimmed Mean ( 16 / 20 )1.3180.016391942142277380.4053594479618
Trimmed Mean ( 17 / 20 )1.320038461538460.016225192260966481.3573386562653
Trimmed Mean ( 18 / 20 )1.322333333333330.016083643084799882.216033168694
Trimmed Mean ( 19 / 20 )1.324909090909090.015842420599038483.6304706485012
Trimmed Mean ( 20 / 20 )1.3280.015359893091733286.4589351025326
Median1.3485
Midrange1.2255
Midmean - Weighted Average at Xnp1.31061290322581
Midmean - Weighted Average at X(n+1)p1.31633333333333
Midmean - Empirical Distribution Function1.31061290322581
Midmean - Empirical Distribution Function - Averaging1.31633333333333
Midmean - Empirical Distribution Function - Interpolation1.31633333333333
Midmean - Closest Observation1.31061290322581
Midmean - True Basic - Statistics Graphics Toolkit1.31633333333333
Midmean - MS Excel (old versions)1.3140625
Number of observations60



Parameters (Session):
par1 = grey ;
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')