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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 computationTue, 05 Mar 2013 13:18:29 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/05/t1362507555z4ur0y8lq2qnoyo.htm/, Retrieved Sat, 04 May 2024 13:19:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207443, Retrieved Sat, 04 May 2024 13:19:58 +0000
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Original text written by user:Robuustheid Apple interesse
IsPrivate?No (this computation is public)
User-defined keywordsRobuustheid Apple interesse
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid Apple...] [2013-03-05 18:18:29] [c6583091fa4b3042e72e3a6292788221] [Current]
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Dataseries X:
38
35
33
35
33
32
33
38
45
42
40
44
50
37
37
35
33
40
38
39
52
48
49
50
48
45
42
39
38
44
47
45
51
51
47
49
44
40
40
38
36
45
39
43
50
49
47
49
58
43
39
44
45
57
54
52
61
59
60
58
52
49
60
51
52
56
56
57
58
100
70
70




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207443&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207443&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean46.98611111111111.2721423921349436.9346320047223
Geometric Mean45.9370087336917
Harmonic Mean45.0034297864486
Quadratic Mean48.1933317194632
Winsorized Mean ( 1 / 24 )46.58333333333331.078990935897843.1730534367952
Winsorized Mean ( 2 / 24 )46.58333333333331.078990935897843.1730534367952
Winsorized Mean ( 3 / 24 )46.20833333333330.98102847169937947.101928910676
Winsorized Mean ( 4 / 24 )46.15277777777780.96953995072373547.6027601991295
Winsorized Mean ( 5 / 24 )46.29166666666670.94455806874268949.0088097265275
Winsorized Mean ( 6 / 24 )46.20833333333330.92794755177323549.7962770040536
Winsorized Mean ( 7 / 24 )46.11111111111110.90955533417676350.6963231135862
Winsorized Mean ( 8 / 24 )46.22222222222220.89101369672703351.8759951637227
Winsorized Mean ( 9 / 24 )46.34722222222220.87146552455838953.1830817354576
Winsorized Mean ( 10 / 24 )46.20833333333330.84589996615359654.6262385414766
Winsorized Mean ( 11 / 24 )46.36111111111110.82325016105807256.3147306907612
Winsorized Mean ( 12 / 24 )46.19444444444440.79356737209684158.2111186380874
Winsorized Mean ( 13 / 24 )46.19444444444440.79356737209684158.2111186380874
Winsorized Mean ( 14 / 24 )45.80555555555560.72880561520950962.8501682748257
Winsorized Mean ( 15 / 24 )45.38888888888890.66653624180644168.0966555785119
Winsorized Mean ( 16 / 24 )45.61111111111110.63281284380753272.0767783989283
Winsorized Mean ( 17 / 24 )45.61111111111110.63281284380753272.0767783989283
Winsorized Mean ( 18 / 24 )45.61111111111110.63281284380753272.0767783989283
Winsorized Mean ( 19 / 24 )45.34722222222220.59640279337812276.034557057267
Winsorized Mean ( 20 / 24 )45.6250.55574869490947482.0964590972757
Winsorized Mean ( 21 / 24 )45.6250.55574869490947482.0964590972757
Winsorized Mean ( 22 / 24 )45.31944444444440.5153460287023287.9398344420393
Winsorized Mean ( 23 / 24 )45.31944444444440.5153460287023287.9398344420393
Winsorized Mean ( 24 / 24 )45.98611111111110.422143838989015108.9346968115
Trimmed Mean ( 1 / 24 )46.44285714285711.0393172855264644.685927762023
Trimmed Mean ( 2 / 24 )46.29411764705880.99163729410477746.6845266129809
Trimmed Mean ( 3 / 24 )46.13636363636360.93367119183852249.4139307709763
Trimmed Mean ( 4 / 24 )46.1093750.91099903393546450.6140767249885
Trimmed Mean ( 5 / 24 )46.09677419354840.88787283970847551.9182163615725
Trimmed Mean ( 6 / 24 )46.050.86763038551891853.0755962084686
Trimmed Mean ( 7 / 24 )46.01724137931030.84757630300725554.2927418051192
Trimmed Mean ( 8 / 24 )460.82768649564006755.5765984371018
Trimmed Mean ( 9 / 24 )45.9629629629630.80744394996130556.9240291727564
Trimmed Mean ( 10 / 24 )45.90384615384620.78650937375915858.3640166098042
Trimmed Mean ( 11 / 24 )45.860.76612462352773359.8597128869595
Trimmed Mean ( 12 / 24 )45.79166666666670.74493462832171661.4707182693762
Trimmed Mean ( 13 / 24 )45.73913043478260.72460869507244163.1225249514981
Trimmed Mean ( 14 / 24 )45.68181818181820.69790741832918565.4554128270796
Trimmed Mean ( 15 / 24 )45.66666666666670.67875224275583167.2803178981089
Trimmed Mean ( 16 / 24 )45.70.66717929009240568.4973299960653
Trimmed Mean ( 17 / 24 )45.71052631578950.65857717094891969.4080030893372
Trimmed Mean ( 18 / 24 )45.72222222222220.6456338230837270.8175758262488
Trimmed Mean ( 19 / 24 )45.73529411764710.62666366602812372.9822017726405
Trimmed Mean ( 20 / 24 )45.781250.6086314218484775.2199908788115
Trimmed Mean ( 21 / 24 )45.80.59383809086393277.1253995064023
Trimmed Mean ( 22 / 24 )45.82142857142860.57055985553913180.3095908809272
Trimmed Mean ( 23 / 24 )45.88461538461540.54723619728715183.8479172468527
Trimmed Mean ( 24 / 24 )45.95833333333330.50890322058590490.3085920352816
Median45
Midrange66
Midmean - Weighted Average at Xnp45.8536585365854
Midmean - Weighted Average at X(n+1)p45.8536585365854
Midmean - Empirical Distribution Function45.8536585365854
Midmean - Empirical Distribution Function - Averaging45.8536585365854
Midmean - Empirical Distribution Function - Interpolation45.8536585365854
Midmean - Closest Observation45.8536585365854
Midmean - True Basic - Statistics Graphics Toolkit45.8536585365854
Midmean - MS Excel (old versions)45.8536585365854
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 46.9861111111111 & 1.27214239213494 & 36.9346320047223 \tabularnewline
Geometric Mean & 45.9370087336917 &  &  \tabularnewline
Harmonic Mean & 45.0034297864486 &  &  \tabularnewline
Quadratic Mean & 48.1933317194632 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 46.5833333333333 & 1.0789909358978 & 43.1730534367952 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 46.5833333333333 & 1.0789909358978 & 43.1730534367952 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 46.2083333333333 & 0.981028471699379 & 47.101928910676 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 46.1527777777778 & 0.969539950723735 & 47.6027601991295 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 46.2916666666667 & 0.944558068742689 & 49.0088097265275 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 46.2083333333333 & 0.927947551773235 & 49.7962770040536 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 46.1111111111111 & 0.909555334176763 & 50.6963231135862 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 46.2222222222222 & 0.891013696727033 & 51.8759951637227 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 46.3472222222222 & 0.871465524558389 & 53.1830817354576 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 46.2083333333333 & 0.845899966153596 & 54.6262385414766 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 46.3611111111111 & 0.823250161058072 & 56.3147306907612 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 46.1944444444444 & 0.793567372096841 & 58.2111186380874 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 46.1944444444444 & 0.793567372096841 & 58.2111186380874 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 45.8055555555556 & 0.728805615209509 & 62.8501682748257 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 45.3888888888889 & 0.666536241806441 & 68.0966555785119 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 45.6111111111111 & 0.632812843807532 & 72.0767783989283 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 45.6111111111111 & 0.632812843807532 & 72.0767783989283 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 45.6111111111111 & 0.632812843807532 & 72.0767783989283 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 45.3472222222222 & 0.596402793378122 & 76.034557057267 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 45.625 & 0.555748694909474 & 82.0964590972757 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 45.625 & 0.555748694909474 & 82.0964590972757 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 45.3194444444444 & 0.51534602870232 & 87.9398344420393 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 45.3194444444444 & 0.51534602870232 & 87.9398344420393 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 45.9861111111111 & 0.422143838989015 & 108.9346968115 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 46.4428571428571 & 1.03931728552646 & 44.685927762023 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 46.2941176470588 & 0.991637294104777 & 46.6845266129809 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 46.1363636363636 & 0.933671191838522 & 49.4139307709763 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 46.109375 & 0.910999033935464 & 50.6140767249885 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 46.0967741935484 & 0.887872839708475 & 51.9182163615725 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 46.05 & 0.867630385518918 & 53.0755962084686 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 46.0172413793103 & 0.847576303007255 & 54.2927418051192 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 46 & 0.827686495640067 & 55.5765984371018 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 45.962962962963 & 0.807443949961305 & 56.9240291727564 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 45.9038461538462 & 0.786509373759158 & 58.3640166098042 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 45.86 & 0.766124623527733 & 59.8597128869595 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 45.7916666666667 & 0.744934628321716 & 61.4707182693762 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 45.7391304347826 & 0.724608695072441 & 63.1225249514981 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 45.6818181818182 & 0.697907418329185 & 65.4554128270796 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 45.6666666666667 & 0.678752242755831 & 67.2803178981089 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 45.7 & 0.667179290092405 & 68.4973299960653 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 45.7105263157895 & 0.658577170948919 & 69.4080030893372 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 45.7222222222222 & 0.64563382308372 & 70.8175758262488 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 45.7352941176471 & 0.626663666028123 & 72.9822017726405 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 45.78125 & 0.60863142184847 & 75.2199908788115 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 45.8 & 0.593838090863932 & 77.1253995064023 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 45.8214285714286 & 0.570559855539131 & 80.3095908809272 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 45.8846153846154 & 0.547236197287151 & 83.8479172468527 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 45.9583333333333 & 0.508903220585904 & 90.3085920352816 \tabularnewline
Median & 45 &  &  \tabularnewline
Midrange & 66 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 45.8536585365854 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 45.8536585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 45.8536585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 45.8536585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 45.8536585365854 &  &  \tabularnewline
Midmean - Closest Observation & 45.8536585365854 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 45.8536585365854 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 45.8536585365854 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207443&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]46.9861111111111[/C][C]1.27214239213494[/C][C]36.9346320047223[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]45.9370087336917[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]45.0034297864486[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]48.1933317194632[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]46.5833333333333[/C][C]1.0789909358978[/C][C]43.1730534367952[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]46.5833333333333[/C][C]1.0789909358978[/C][C]43.1730534367952[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]46.2083333333333[/C][C]0.981028471699379[/C][C]47.101928910676[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]46.1527777777778[/C][C]0.969539950723735[/C][C]47.6027601991295[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]46.2916666666667[/C][C]0.944558068742689[/C][C]49.0088097265275[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]46.2083333333333[/C][C]0.927947551773235[/C][C]49.7962770040536[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]46.1111111111111[/C][C]0.909555334176763[/C][C]50.6963231135862[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]46.2222222222222[/C][C]0.891013696727033[/C][C]51.8759951637227[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]46.3472222222222[/C][C]0.871465524558389[/C][C]53.1830817354576[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]46.2083333333333[/C][C]0.845899966153596[/C][C]54.6262385414766[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]46.3611111111111[/C][C]0.823250161058072[/C][C]56.3147306907612[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]46.1944444444444[/C][C]0.793567372096841[/C][C]58.2111186380874[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]46.1944444444444[/C][C]0.793567372096841[/C][C]58.2111186380874[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]45.8055555555556[/C][C]0.728805615209509[/C][C]62.8501682748257[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]45.3888888888889[/C][C]0.666536241806441[/C][C]68.0966555785119[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]45.6111111111111[/C][C]0.632812843807532[/C][C]72.0767783989283[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]45.6111111111111[/C][C]0.632812843807532[/C][C]72.0767783989283[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]45.6111111111111[/C][C]0.632812843807532[/C][C]72.0767783989283[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]45.3472222222222[/C][C]0.596402793378122[/C][C]76.034557057267[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]45.625[/C][C]0.555748694909474[/C][C]82.0964590972757[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]45.625[/C][C]0.555748694909474[/C][C]82.0964590972757[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]45.3194444444444[/C][C]0.51534602870232[/C][C]87.9398344420393[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]45.3194444444444[/C][C]0.51534602870232[/C][C]87.9398344420393[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]45.9861111111111[/C][C]0.422143838989015[/C][C]108.9346968115[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]46.4428571428571[/C][C]1.03931728552646[/C][C]44.685927762023[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]46.2941176470588[/C][C]0.991637294104777[/C][C]46.6845266129809[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]46.1363636363636[/C][C]0.933671191838522[/C][C]49.4139307709763[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]46.109375[/C][C]0.910999033935464[/C][C]50.6140767249885[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]46.0967741935484[/C][C]0.887872839708475[/C][C]51.9182163615725[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]46.05[/C][C]0.867630385518918[/C][C]53.0755962084686[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]46.0172413793103[/C][C]0.847576303007255[/C][C]54.2927418051192[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]46[/C][C]0.827686495640067[/C][C]55.5765984371018[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]45.962962962963[/C][C]0.807443949961305[/C][C]56.9240291727564[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]45.9038461538462[/C][C]0.786509373759158[/C][C]58.3640166098042[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]45.86[/C][C]0.766124623527733[/C][C]59.8597128869595[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]45.7916666666667[/C][C]0.744934628321716[/C][C]61.4707182693762[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]45.7391304347826[/C][C]0.724608695072441[/C][C]63.1225249514981[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]45.6818181818182[/C][C]0.697907418329185[/C][C]65.4554128270796[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]45.6666666666667[/C][C]0.678752242755831[/C][C]67.2803178981089[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]45.7[/C][C]0.667179290092405[/C][C]68.4973299960653[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]45.7105263157895[/C][C]0.658577170948919[/C][C]69.4080030893372[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]45.7222222222222[/C][C]0.64563382308372[/C][C]70.8175758262488[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]45.7352941176471[/C][C]0.626663666028123[/C][C]72.9822017726405[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]45.78125[/C][C]0.60863142184847[/C][C]75.2199908788115[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]45.8[/C][C]0.593838090863932[/C][C]77.1253995064023[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]45.8214285714286[/C][C]0.570559855539131[/C][C]80.3095908809272[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]45.8846153846154[/C][C]0.547236197287151[/C][C]83.8479172468527[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]45.9583333333333[/C][C]0.508903220585904[/C][C]90.3085920352816[/C][/ROW]
[ROW][C]Median[/C][C]45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]66[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]45.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207443&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 Mean46.98611111111111.2721423921349436.9346320047223
Geometric Mean45.9370087336917
Harmonic Mean45.0034297864486
Quadratic Mean48.1933317194632
Winsorized Mean ( 1 / 24 )46.58333333333331.078990935897843.1730534367952
Winsorized Mean ( 2 / 24 )46.58333333333331.078990935897843.1730534367952
Winsorized Mean ( 3 / 24 )46.20833333333330.98102847169937947.101928910676
Winsorized Mean ( 4 / 24 )46.15277777777780.96953995072373547.6027601991295
Winsorized Mean ( 5 / 24 )46.29166666666670.94455806874268949.0088097265275
Winsorized Mean ( 6 / 24 )46.20833333333330.92794755177323549.7962770040536
Winsorized Mean ( 7 / 24 )46.11111111111110.90955533417676350.6963231135862
Winsorized Mean ( 8 / 24 )46.22222222222220.89101369672703351.8759951637227
Winsorized Mean ( 9 / 24 )46.34722222222220.87146552455838953.1830817354576
Winsorized Mean ( 10 / 24 )46.20833333333330.84589996615359654.6262385414766
Winsorized Mean ( 11 / 24 )46.36111111111110.82325016105807256.3147306907612
Winsorized Mean ( 12 / 24 )46.19444444444440.79356737209684158.2111186380874
Winsorized Mean ( 13 / 24 )46.19444444444440.79356737209684158.2111186380874
Winsorized Mean ( 14 / 24 )45.80555555555560.72880561520950962.8501682748257
Winsorized Mean ( 15 / 24 )45.38888888888890.66653624180644168.0966555785119
Winsorized Mean ( 16 / 24 )45.61111111111110.63281284380753272.0767783989283
Winsorized Mean ( 17 / 24 )45.61111111111110.63281284380753272.0767783989283
Winsorized Mean ( 18 / 24 )45.61111111111110.63281284380753272.0767783989283
Winsorized Mean ( 19 / 24 )45.34722222222220.59640279337812276.034557057267
Winsorized Mean ( 20 / 24 )45.6250.55574869490947482.0964590972757
Winsorized Mean ( 21 / 24 )45.6250.55574869490947482.0964590972757
Winsorized Mean ( 22 / 24 )45.31944444444440.5153460287023287.9398344420393
Winsorized Mean ( 23 / 24 )45.31944444444440.5153460287023287.9398344420393
Winsorized Mean ( 24 / 24 )45.98611111111110.422143838989015108.9346968115
Trimmed Mean ( 1 / 24 )46.44285714285711.0393172855264644.685927762023
Trimmed Mean ( 2 / 24 )46.29411764705880.99163729410477746.6845266129809
Trimmed Mean ( 3 / 24 )46.13636363636360.93367119183852249.4139307709763
Trimmed Mean ( 4 / 24 )46.1093750.91099903393546450.6140767249885
Trimmed Mean ( 5 / 24 )46.09677419354840.88787283970847551.9182163615725
Trimmed Mean ( 6 / 24 )46.050.86763038551891853.0755962084686
Trimmed Mean ( 7 / 24 )46.01724137931030.84757630300725554.2927418051192
Trimmed Mean ( 8 / 24 )460.82768649564006755.5765984371018
Trimmed Mean ( 9 / 24 )45.9629629629630.80744394996130556.9240291727564
Trimmed Mean ( 10 / 24 )45.90384615384620.78650937375915858.3640166098042
Trimmed Mean ( 11 / 24 )45.860.76612462352773359.8597128869595
Trimmed Mean ( 12 / 24 )45.79166666666670.74493462832171661.4707182693762
Trimmed Mean ( 13 / 24 )45.73913043478260.72460869507244163.1225249514981
Trimmed Mean ( 14 / 24 )45.68181818181820.69790741832918565.4554128270796
Trimmed Mean ( 15 / 24 )45.66666666666670.67875224275583167.2803178981089
Trimmed Mean ( 16 / 24 )45.70.66717929009240568.4973299960653
Trimmed Mean ( 17 / 24 )45.71052631578950.65857717094891969.4080030893372
Trimmed Mean ( 18 / 24 )45.72222222222220.6456338230837270.8175758262488
Trimmed Mean ( 19 / 24 )45.73529411764710.62666366602812372.9822017726405
Trimmed Mean ( 20 / 24 )45.781250.6086314218484775.2199908788115
Trimmed Mean ( 21 / 24 )45.80.59383809086393277.1253995064023
Trimmed Mean ( 22 / 24 )45.82142857142860.57055985553913180.3095908809272
Trimmed Mean ( 23 / 24 )45.88461538461540.54723619728715183.8479172468527
Trimmed Mean ( 24 / 24 )45.95833333333330.50890322058590490.3085920352816
Median45
Midrange66
Midmean - Weighted Average at Xnp45.8536585365854
Midmean - Weighted Average at X(n+1)p45.8536585365854
Midmean - Empirical Distribution Function45.8536585365854
Midmean - Empirical Distribution Function - Averaging45.8536585365854
Midmean - Empirical Distribution Function - Interpolation45.8536585365854
Midmean - Closest Observation45.8536585365854
Midmean - True Basic - Statistics Graphics Toolkit45.8536585365854
Midmean - MS Excel (old versions)45.8536585365854
Number of observations72



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')