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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Jan 2015 09:23:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jan/21/t1421832239vksk8gb1k93viz2.htm/, Retrieved Tue, 14 May 2024 07:15:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=276087, Retrieved Tue, 14 May 2024 07:15:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency] [2015-01-21 09:23:43] [e719845b3f21bd57beb5defeff8ed9b5] [Current]
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Dataseries X:
67
72
74
62
56
66
65
59
61
69
74
69
66
68
58
64
66
57
68
62
59
73
61
61
57
58
57
67
81
79
76
78
74
67
84
85
79
82
87
90
87
93
92
82
80
79
77
72
65
73
76
77
76
76
76
75
78
73
80
77
83
84
85
81
84
83
83
88
92
92
89
82
73
81
91
80
81
82
84
87
85
74
81
82
86
85
82
86
88
86
83
81
81
81
82
86
85
87
89
90
90
92
86
86
82
80
79
77
79
76
78
78
77
72
75
79
81
86
88
97
94
96
94
91
92
93
93
87
84
80
78
75
73
81
76
77
71
71
78
67
76
68
82
64
71
81
69
63
70
77
75
76
68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276087&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276087&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276087&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean77.88235294117650.765221704254667101.777501223694
Geometric Mean77.2839385094042
Harmonic Mean76.6573324168489
Quadratic Mean78.4516836445635
Winsorized Mean ( 1 / 51 )77.88235294117650.762970696804404102.077777386964
Winsorized Mean ( 2 / 51 )77.85620915032680.759099047559208102.563966323847
Winsorized Mean ( 3 / 51 )77.85620915032680.759099047559208102.563966323847
Winsorized Mean ( 4 / 51 )77.85620915032680.750897771388692103.684165963552
Winsorized Mean ( 5 / 51 )77.85620915032680.750897771388692103.684165963552
Winsorized Mean ( 6 / 51 )77.89542483660130.744210737285219104.668504408783
Winsorized Mean ( 7 / 51 )77.84967320261440.738270930245567105.448650371104
Winsorized Mean ( 8 / 51 )77.95424836601310.721395221407549108.060389163533
Winsorized Mean ( 9 / 51 )77.95424836601310.721395221407549108.060389163533
Winsorized Mean ( 10 / 51 )77.95424836601310.721395221407549108.060389163533
Winsorized Mean ( 11 / 51 )78.02614379084970.710500854873698109.818507966074
Winsorized Mean ( 12 / 51 )77.94771241830070.700618359838797111.255594895109
Winsorized Mean ( 13 / 51 )78.03267973856210.688148374604435113.395137761413
Winsorized Mean ( 14 / 51 )78.03267973856210.664108760319155117.499850026164
Winsorized Mean ( 15 / 51 )78.03267973856210.664108760319155117.499850026164
Winsorized Mean ( 16 / 51 )78.13725490196080.649882820239225120.232836549208
Winsorized Mean ( 17 / 51 )78.02614379084970.636909929294488122.507343977633
Winsorized Mean ( 18 / 51 )78.14379084967320.621428100807433125.748724185693
Winsorized Mean ( 19 / 51 )78.01960784313730.60757675843641128.411113097742
Winsorized Mean ( 20 / 51 )78.01960784313730.60757675843641128.411113097742
Winsorized Mean ( 21 / 51 )78.1568627450980.590102814665719132.44617853479
Winsorized Mean ( 22 / 51 )78.01307189542480.574811475660614135.719405750845
Winsorized Mean ( 23 / 51 )78.01307189542480.574811475660614135.719405750845
Winsorized Mean ( 24 / 51 )78.01307189542480.574811475660614135.719405750845
Winsorized Mean ( 25 / 51 )78.17647058823530.554643720427633140.948987086631
Winsorized Mean ( 26 / 51 )78.17647058823530.554643720427633140.948987086631
Winsorized Mean ( 27 / 51 )780.536747329027764145.319772976393
Winsorized Mean ( 28 / 51 )780.536747329027764145.319772976393
Winsorized Mean ( 29 / 51 )78.18954248366010.513973274766946152.127642276953
Winsorized Mean ( 30 / 51 )78.18954248366010.513973274766946152.127642276953
Winsorized Mean ( 31 / 51 )78.18954248366010.513973274766946152.127642276953
Winsorized Mean ( 32 / 51 )78.39869281045750.489864582328318160.041561767601
Winsorized Mean ( 33 / 51 )78.61437908496730.466095421323819168.66584713852
Winsorized Mean ( 34 / 51 )78.39215686274510.443606425788479176.715557542722
Winsorized Mean ( 35 / 51 )78.39215686274510.443606425788479176.715557542722
Winsorized Mean ( 36 / 51 )78.62745098039220.418430976000926187.910206199022
Winsorized Mean ( 37 / 51 )78.62745098039220.418430976000926187.910206199022
Winsorized Mean ( 38 / 51 )78.62745098039220.418430976000926187.910206199022
Winsorized Mean ( 39 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 40 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 41 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 42 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 43 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 44 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 45 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 46 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 47 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 48 / 51 )78.62745098039220.252929576297389310.866969894987
Winsorized Mean ( 49 / 51 )78.62745098039220.252929576297389310.866969894987
Winsorized Mean ( 50 / 51 )78.62745098039220.252929576297389310.866969894987
Winsorized Mean ( 51 / 51 )78.62745098039220.252929576297389310.866969894987
Trimmed Mean ( 1 / 51 )77.90066225165560.75096729186819103.73376190308
Trimmed Mean ( 2 / 51 )77.91946308724830.737955267867774105.588328290394
Trimmed Mean ( 3 / 51 )77.95238095238090.726018019794922107.369760566549
Trimmed Mean ( 4 / 51 )77.98620689655170.71304123134322109.371244562733
Trimmed Mean ( 5 / 51 )78.0209790209790.701440633990331111.229625488241
Trimmed Mean ( 6 / 51 )78.05673758865250.688799746769322113.322831424898
Trimmed Mean ( 7 / 51 )78.05673758865250.67651073341913115.381373469344
Trimmed Mean ( 8 / 51 )78.12408759124090.664247141727777117.612982704046
Trimmed Mean ( 9 / 51 )78.14814814814820.653900870235632119.510696047839
Trimmed Mean ( 10 / 51 )78.17293233082710.642579608294266121.654860069926
Trimmed Mean ( 11 / 51 )78.19847328244270.630169272091976124.091219209796
Trimmed Mean ( 12 / 51 )78.21705426356590.618176045394492126.528769347009
Trimmed Mean ( 13 / 51 )78.2440944881890.606356832527753129.039684705141
Trimmed Mean ( 14 / 51 )78.2440944881890.595048818815896131.491891108849
Trimmed Mean ( 15 / 51 )78.28455284552850.585661031504491133.668707041042
Trimmed Mean ( 16 / 51 )78.30578512396690.575300014581757136.112955221973
Trimmed Mean ( 17 / 51 )78.31932773109240.56558631117579138.474581480367
Trimmed Mean ( 18 / 51 )78.34188034188030.556313387313812140.823287967522
Trimmed Mean ( 19 / 51 )78.35652173913040.547818822370198143.033642765527
Trimmed Mean ( 20 / 51 )78.38053097345130.539864457176465145.185573770475
Trimmed Mean ( 21 / 51 )78.40540540540540.531000998436386147.655853070488
Trimmed Mean ( 22 / 51 )78.42201834862390.523049030663498149.932441800234
Trimmed Mean ( 23 / 51 )78.44859813084110.515708736370435152.118032133726
Trimmed Mean ( 24 / 51 )78.47619047619050.507470787714666154.641788997547
Trimmed Mean ( 25 / 51 )78.5048543689320.498211877127877157.573229328658
Trimmed Mean ( 26 / 51 )78.52475247524750.490017995104189160.248711802005
Trimmed Mean ( 27 / 51 )78.54545454545450.480772913940624163.373293852313
Trimmed Mean ( 28 / 51 )78.54545454545450.472125743056368166.365540749759
Trimmed Mean ( 29 / 51 )78.61052631578950.462307067435374170.039637836119
Trimmed Mean ( 30 / 51 )78.63440860215050.453747820057319173.299804706978
Trimmed Mean ( 31 / 51 )78.65934065934070.443985661314572177.16639863198
Trimmed Mean ( 32 / 51 )78.6853932584270.432819669843182181.797174991922
Trimmed Mean ( 33 / 51 )78.70114942528740.422918331521969186.090655238479
Trimmed Mean ( 34 / 51 )78.70588235294120.414317815132379189.964996624134
Trimmed Mean ( 35 / 51 )78.72289156626510.40685907738267193.489333143777
Trimmed Mean ( 36 / 51 )78.74074074074070.398212742391574197.735361926999
Trimmed Mean ( 37 / 51 )78.7468354430380.391183406835349201.304130152389
Trimmed Mean ( 38 / 51 )78.75324675324680.382974938080139205.635510114679
Trimmed Mean ( 39 / 51 )78.760.373365506979155210.946106503612
Trimmed Mean ( 40 / 51 )78.76712328767120.368323647027126213.853017375966
Trimmed Mean ( 41 / 51 )78.77464788732390.362307151560479217.425042669008
Trimmed Mean ( 42 / 51 )78.78260869565220.355129003623436221.842226041301
Trimmed Mean ( 43 / 51 )78.79104477611940.34655199811302227.357063889799
Trimmed Mean ( 44 / 51 )78.80.336269122990683234.336115368473
Trimmed Mean ( 45 / 51 )78.80952380952380.331683430445856237.604645199148
Trimmed Mean ( 46 / 51 )78.81967213114750.326019373792645241.763767638173
Trimmed Mean ( 47 / 51 )78.83050847457630.319036156545695247.08957545157
Trimmed Mean ( 48 / 51 )78.84210526315790.310417975238241253.986919419366
Trimmed Mean ( 49 / 51 )78.84210526315790.308595364300021255.48700461523
Trimmed Mean ( 50 / 51 )78.86792452830190.30600868899824257.730997072294
Trimmed Mean ( 51 / 51 )78.88235294117650.302469650168999260.794274391175
Median79
Midrange76.5
Midmean - Weighted Average at Xnp78.5
Midmean - Weighted Average at X(n+1)p78.8915662650602
Midmean - Empirical Distribution Function78.8915662650602
Midmean - Empirical Distribution Function - Averaging78.8915662650602
Midmean - Empirical Distribution Function - Interpolation78.8915662650602
Midmean - Closest Observation78.8915662650602
Midmean - True Basic - Statistics Graphics Toolkit78.8915662650602
Midmean - MS Excel (old versions)78.8915662650602
Number of observations153

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 77.8823529411765 & 0.765221704254667 & 101.777501223694 \tabularnewline
Geometric Mean & 77.2839385094042 &  &  \tabularnewline
Harmonic Mean & 76.6573324168489 &  &  \tabularnewline
Quadratic Mean & 78.4516836445635 &  &  \tabularnewline
Winsorized Mean ( 1 / 51 ) & 77.8823529411765 & 0.762970696804404 & 102.077777386964 \tabularnewline
Winsorized Mean ( 2 / 51 ) & 77.8562091503268 & 0.759099047559208 & 102.563966323847 \tabularnewline
Winsorized Mean ( 3 / 51 ) & 77.8562091503268 & 0.759099047559208 & 102.563966323847 \tabularnewline
Winsorized Mean ( 4 / 51 ) & 77.8562091503268 & 0.750897771388692 & 103.684165963552 \tabularnewline
Winsorized Mean ( 5 / 51 ) & 77.8562091503268 & 0.750897771388692 & 103.684165963552 \tabularnewline
Winsorized Mean ( 6 / 51 ) & 77.8954248366013 & 0.744210737285219 & 104.668504408783 \tabularnewline
Winsorized Mean ( 7 / 51 ) & 77.8496732026144 & 0.738270930245567 & 105.448650371104 \tabularnewline
Winsorized Mean ( 8 / 51 ) & 77.9542483660131 & 0.721395221407549 & 108.060389163533 \tabularnewline
Winsorized Mean ( 9 / 51 ) & 77.9542483660131 & 0.721395221407549 & 108.060389163533 \tabularnewline
Winsorized Mean ( 10 / 51 ) & 77.9542483660131 & 0.721395221407549 & 108.060389163533 \tabularnewline
Winsorized Mean ( 11 / 51 ) & 78.0261437908497 & 0.710500854873698 & 109.818507966074 \tabularnewline
Winsorized Mean ( 12 / 51 ) & 77.9477124183007 & 0.700618359838797 & 111.255594895109 \tabularnewline
Winsorized Mean ( 13 / 51 ) & 78.0326797385621 & 0.688148374604435 & 113.395137761413 \tabularnewline
Winsorized Mean ( 14 / 51 ) & 78.0326797385621 & 0.664108760319155 & 117.499850026164 \tabularnewline
Winsorized Mean ( 15 / 51 ) & 78.0326797385621 & 0.664108760319155 & 117.499850026164 \tabularnewline
Winsorized Mean ( 16 / 51 ) & 78.1372549019608 & 0.649882820239225 & 120.232836549208 \tabularnewline
Winsorized Mean ( 17 / 51 ) & 78.0261437908497 & 0.636909929294488 & 122.507343977633 \tabularnewline
Winsorized Mean ( 18 / 51 ) & 78.1437908496732 & 0.621428100807433 & 125.748724185693 \tabularnewline
Winsorized Mean ( 19 / 51 ) & 78.0196078431373 & 0.60757675843641 & 128.411113097742 \tabularnewline
Winsorized Mean ( 20 / 51 ) & 78.0196078431373 & 0.60757675843641 & 128.411113097742 \tabularnewline
Winsorized Mean ( 21 / 51 ) & 78.156862745098 & 0.590102814665719 & 132.44617853479 \tabularnewline
Winsorized Mean ( 22 / 51 ) & 78.0130718954248 & 0.574811475660614 & 135.719405750845 \tabularnewline
Winsorized Mean ( 23 / 51 ) & 78.0130718954248 & 0.574811475660614 & 135.719405750845 \tabularnewline
Winsorized Mean ( 24 / 51 ) & 78.0130718954248 & 0.574811475660614 & 135.719405750845 \tabularnewline
Winsorized Mean ( 25 / 51 ) & 78.1764705882353 & 0.554643720427633 & 140.948987086631 \tabularnewline
Winsorized Mean ( 26 / 51 ) & 78.1764705882353 & 0.554643720427633 & 140.948987086631 \tabularnewline
Winsorized Mean ( 27 / 51 ) & 78 & 0.536747329027764 & 145.319772976393 \tabularnewline
Winsorized Mean ( 28 / 51 ) & 78 & 0.536747329027764 & 145.319772976393 \tabularnewline
Winsorized Mean ( 29 / 51 ) & 78.1895424836601 & 0.513973274766946 & 152.127642276953 \tabularnewline
Winsorized Mean ( 30 / 51 ) & 78.1895424836601 & 0.513973274766946 & 152.127642276953 \tabularnewline
Winsorized Mean ( 31 / 51 ) & 78.1895424836601 & 0.513973274766946 & 152.127642276953 \tabularnewline
Winsorized Mean ( 32 / 51 ) & 78.3986928104575 & 0.489864582328318 & 160.041561767601 \tabularnewline
Winsorized Mean ( 33 / 51 ) & 78.6143790849673 & 0.466095421323819 & 168.66584713852 \tabularnewline
Winsorized Mean ( 34 / 51 ) & 78.3921568627451 & 0.443606425788479 & 176.715557542722 \tabularnewline
Winsorized Mean ( 35 / 51 ) & 78.3921568627451 & 0.443606425788479 & 176.715557542722 \tabularnewline
Winsorized Mean ( 36 / 51 ) & 78.6274509803922 & 0.418430976000926 & 187.910206199022 \tabularnewline
Winsorized Mean ( 37 / 51 ) & 78.6274509803922 & 0.418430976000926 & 187.910206199022 \tabularnewline
Winsorized Mean ( 38 / 51 ) & 78.6274509803922 & 0.418430976000926 & 187.910206199022 \tabularnewline
Winsorized Mean ( 39 / 51 ) & 78.6274509803922 & 0.367201312168832 & 214.126279985189 \tabularnewline
Winsorized Mean ( 40 / 51 ) & 78.6274509803922 & 0.367201312168832 & 214.126279985189 \tabularnewline
Winsorized Mean ( 41 / 51 ) & 78.6274509803922 & 0.367201312168832 & 214.126279985189 \tabularnewline
Winsorized Mean ( 42 / 51 ) & 78.6274509803922 & 0.367201312168832 & 214.126279985189 \tabularnewline
Winsorized Mean ( 43 / 51 ) & 78.6274509803922 & 0.367201312168832 & 214.126279985189 \tabularnewline
Winsorized Mean ( 44 / 51 ) & 78.6274509803922 & 0.311443584580081 & 252.461295956394 \tabularnewline
Winsorized Mean ( 45 / 51 ) & 78.6274509803922 & 0.311443584580081 & 252.461295956394 \tabularnewline
Winsorized Mean ( 46 / 51 ) & 78.6274509803922 & 0.311443584580081 & 252.461295956394 \tabularnewline
Winsorized Mean ( 47 / 51 ) & 78.6274509803922 & 0.311443584580081 & 252.461295956394 \tabularnewline
Winsorized Mean ( 48 / 51 ) & 78.6274509803922 & 0.252929576297389 & 310.866969894987 \tabularnewline
Winsorized Mean ( 49 / 51 ) & 78.6274509803922 & 0.252929576297389 & 310.866969894987 \tabularnewline
Winsorized Mean ( 50 / 51 ) & 78.6274509803922 & 0.252929576297389 & 310.866969894987 \tabularnewline
Winsorized Mean ( 51 / 51 ) & 78.6274509803922 & 0.252929576297389 & 310.866969894987 \tabularnewline
Trimmed Mean ( 1 / 51 ) & 77.9006622516556 & 0.75096729186819 & 103.73376190308 \tabularnewline
Trimmed Mean ( 2 / 51 ) & 77.9194630872483 & 0.737955267867774 & 105.588328290394 \tabularnewline
Trimmed Mean ( 3 / 51 ) & 77.9523809523809 & 0.726018019794922 & 107.369760566549 \tabularnewline
Trimmed Mean ( 4 / 51 ) & 77.9862068965517 & 0.71304123134322 & 109.371244562733 \tabularnewline
Trimmed Mean ( 5 / 51 ) & 78.020979020979 & 0.701440633990331 & 111.229625488241 \tabularnewline
Trimmed Mean ( 6 / 51 ) & 78.0567375886525 & 0.688799746769322 & 113.322831424898 \tabularnewline
Trimmed Mean ( 7 / 51 ) & 78.0567375886525 & 0.67651073341913 & 115.381373469344 \tabularnewline
Trimmed Mean ( 8 / 51 ) & 78.1240875912409 & 0.664247141727777 & 117.612982704046 \tabularnewline
Trimmed Mean ( 9 / 51 ) & 78.1481481481482 & 0.653900870235632 & 119.510696047839 \tabularnewline
Trimmed Mean ( 10 / 51 ) & 78.1729323308271 & 0.642579608294266 & 121.654860069926 \tabularnewline
Trimmed Mean ( 11 / 51 ) & 78.1984732824427 & 0.630169272091976 & 124.091219209796 \tabularnewline
Trimmed Mean ( 12 / 51 ) & 78.2170542635659 & 0.618176045394492 & 126.528769347009 \tabularnewline
Trimmed Mean ( 13 / 51 ) & 78.244094488189 & 0.606356832527753 & 129.039684705141 \tabularnewline
Trimmed Mean ( 14 / 51 ) & 78.244094488189 & 0.595048818815896 & 131.491891108849 \tabularnewline
Trimmed Mean ( 15 / 51 ) & 78.2845528455285 & 0.585661031504491 & 133.668707041042 \tabularnewline
Trimmed Mean ( 16 / 51 ) & 78.3057851239669 & 0.575300014581757 & 136.112955221973 \tabularnewline
Trimmed Mean ( 17 / 51 ) & 78.3193277310924 & 0.56558631117579 & 138.474581480367 \tabularnewline
Trimmed Mean ( 18 / 51 ) & 78.3418803418803 & 0.556313387313812 & 140.823287967522 \tabularnewline
Trimmed Mean ( 19 / 51 ) & 78.3565217391304 & 0.547818822370198 & 143.033642765527 \tabularnewline
Trimmed Mean ( 20 / 51 ) & 78.3805309734513 & 0.539864457176465 & 145.185573770475 \tabularnewline
Trimmed Mean ( 21 / 51 ) & 78.4054054054054 & 0.531000998436386 & 147.655853070488 \tabularnewline
Trimmed Mean ( 22 / 51 ) & 78.4220183486239 & 0.523049030663498 & 149.932441800234 \tabularnewline
Trimmed Mean ( 23 / 51 ) & 78.4485981308411 & 0.515708736370435 & 152.118032133726 \tabularnewline
Trimmed Mean ( 24 / 51 ) & 78.4761904761905 & 0.507470787714666 & 154.641788997547 \tabularnewline
Trimmed Mean ( 25 / 51 ) & 78.504854368932 & 0.498211877127877 & 157.573229328658 \tabularnewline
Trimmed Mean ( 26 / 51 ) & 78.5247524752475 & 0.490017995104189 & 160.248711802005 \tabularnewline
Trimmed Mean ( 27 / 51 ) & 78.5454545454545 & 0.480772913940624 & 163.373293852313 \tabularnewline
Trimmed Mean ( 28 / 51 ) & 78.5454545454545 & 0.472125743056368 & 166.365540749759 \tabularnewline
Trimmed Mean ( 29 / 51 ) & 78.6105263157895 & 0.462307067435374 & 170.039637836119 \tabularnewline
Trimmed Mean ( 30 / 51 ) & 78.6344086021505 & 0.453747820057319 & 173.299804706978 \tabularnewline
Trimmed Mean ( 31 / 51 ) & 78.6593406593407 & 0.443985661314572 & 177.16639863198 \tabularnewline
Trimmed Mean ( 32 / 51 ) & 78.685393258427 & 0.432819669843182 & 181.797174991922 \tabularnewline
Trimmed Mean ( 33 / 51 ) & 78.7011494252874 & 0.422918331521969 & 186.090655238479 \tabularnewline
Trimmed Mean ( 34 / 51 ) & 78.7058823529412 & 0.414317815132379 & 189.964996624134 \tabularnewline
Trimmed Mean ( 35 / 51 ) & 78.7228915662651 & 0.40685907738267 & 193.489333143777 \tabularnewline
Trimmed Mean ( 36 / 51 ) & 78.7407407407407 & 0.398212742391574 & 197.735361926999 \tabularnewline
Trimmed Mean ( 37 / 51 ) & 78.746835443038 & 0.391183406835349 & 201.304130152389 \tabularnewline
Trimmed Mean ( 38 / 51 ) & 78.7532467532468 & 0.382974938080139 & 205.635510114679 \tabularnewline
Trimmed Mean ( 39 / 51 ) & 78.76 & 0.373365506979155 & 210.946106503612 \tabularnewline
Trimmed Mean ( 40 / 51 ) & 78.7671232876712 & 0.368323647027126 & 213.853017375966 \tabularnewline
Trimmed Mean ( 41 / 51 ) & 78.7746478873239 & 0.362307151560479 & 217.425042669008 \tabularnewline
Trimmed Mean ( 42 / 51 ) & 78.7826086956522 & 0.355129003623436 & 221.842226041301 \tabularnewline
Trimmed Mean ( 43 / 51 ) & 78.7910447761194 & 0.34655199811302 & 227.357063889799 \tabularnewline
Trimmed Mean ( 44 / 51 ) & 78.8 & 0.336269122990683 & 234.336115368473 \tabularnewline
Trimmed Mean ( 45 / 51 ) & 78.8095238095238 & 0.331683430445856 & 237.604645199148 \tabularnewline
Trimmed Mean ( 46 / 51 ) & 78.8196721311475 & 0.326019373792645 & 241.763767638173 \tabularnewline
Trimmed Mean ( 47 / 51 ) & 78.8305084745763 & 0.319036156545695 & 247.08957545157 \tabularnewline
Trimmed Mean ( 48 / 51 ) & 78.8421052631579 & 0.310417975238241 & 253.986919419366 \tabularnewline
Trimmed Mean ( 49 / 51 ) & 78.8421052631579 & 0.308595364300021 & 255.48700461523 \tabularnewline
Trimmed Mean ( 50 / 51 ) & 78.8679245283019 & 0.30600868899824 & 257.730997072294 \tabularnewline
Trimmed Mean ( 51 / 51 ) & 78.8823529411765 & 0.302469650168999 & 260.794274391175 \tabularnewline
Median & 79 &  &  \tabularnewline
Midrange & 76.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 78.5 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 78.8915662650602 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 78.8915662650602 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 78.8915662650602 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 78.8915662650602 &  &  \tabularnewline
Midmean - Closest Observation & 78.8915662650602 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 78.8915662650602 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 78.8915662650602 &  &  \tabularnewline
Number of observations & 153 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=276087&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]77.8823529411765[/C][C]0.765221704254667[/C][C]101.777501223694[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]77.2839385094042[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]76.6573324168489[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]78.4516836445635[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 51 )[/C][C]77.8823529411765[/C][C]0.762970696804404[/C][C]102.077777386964[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 51 )[/C][C]77.8562091503268[/C][C]0.759099047559208[/C][C]102.563966323847[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 51 )[/C][C]77.8562091503268[/C][C]0.759099047559208[/C][C]102.563966323847[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 51 )[/C][C]77.8562091503268[/C][C]0.750897771388692[/C][C]103.684165963552[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 51 )[/C][C]77.8562091503268[/C][C]0.750897771388692[/C][C]103.684165963552[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 51 )[/C][C]77.8954248366013[/C][C]0.744210737285219[/C][C]104.668504408783[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 51 )[/C][C]77.8496732026144[/C][C]0.738270930245567[/C][C]105.448650371104[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 51 )[/C][C]77.9542483660131[/C][C]0.721395221407549[/C][C]108.060389163533[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 51 )[/C][C]77.9542483660131[/C][C]0.721395221407549[/C][C]108.060389163533[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 51 )[/C][C]77.9542483660131[/C][C]0.721395221407549[/C][C]108.060389163533[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 51 )[/C][C]78.0261437908497[/C][C]0.710500854873698[/C][C]109.818507966074[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 51 )[/C][C]77.9477124183007[/C][C]0.700618359838797[/C][C]111.255594895109[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 51 )[/C][C]78.0326797385621[/C][C]0.688148374604435[/C][C]113.395137761413[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 51 )[/C][C]78.0326797385621[/C][C]0.664108760319155[/C][C]117.499850026164[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 51 )[/C][C]78.0326797385621[/C][C]0.664108760319155[/C][C]117.499850026164[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 51 )[/C][C]78.1372549019608[/C][C]0.649882820239225[/C][C]120.232836549208[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 51 )[/C][C]78.0261437908497[/C][C]0.636909929294488[/C][C]122.507343977633[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 51 )[/C][C]78.1437908496732[/C][C]0.621428100807433[/C][C]125.748724185693[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 51 )[/C][C]78.0196078431373[/C][C]0.60757675843641[/C][C]128.411113097742[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 51 )[/C][C]78.0196078431373[/C][C]0.60757675843641[/C][C]128.411113097742[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 51 )[/C][C]78.156862745098[/C][C]0.590102814665719[/C][C]132.44617853479[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 51 )[/C][C]78.0130718954248[/C][C]0.574811475660614[/C][C]135.719405750845[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 51 )[/C][C]78.0130718954248[/C][C]0.574811475660614[/C][C]135.719405750845[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 51 )[/C][C]78.0130718954248[/C][C]0.574811475660614[/C][C]135.719405750845[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 51 )[/C][C]78.1764705882353[/C][C]0.554643720427633[/C][C]140.948987086631[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 51 )[/C][C]78.1764705882353[/C][C]0.554643720427633[/C][C]140.948987086631[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 51 )[/C][C]78[/C][C]0.536747329027764[/C][C]145.319772976393[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 51 )[/C][C]78[/C][C]0.536747329027764[/C][C]145.319772976393[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 51 )[/C][C]78.1895424836601[/C][C]0.513973274766946[/C][C]152.127642276953[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 51 )[/C][C]78.1895424836601[/C][C]0.513973274766946[/C][C]152.127642276953[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 51 )[/C][C]78.1895424836601[/C][C]0.513973274766946[/C][C]152.127642276953[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 51 )[/C][C]78.3986928104575[/C][C]0.489864582328318[/C][C]160.041561767601[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 51 )[/C][C]78.6143790849673[/C][C]0.466095421323819[/C][C]168.66584713852[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 51 )[/C][C]78.3921568627451[/C][C]0.443606425788479[/C][C]176.715557542722[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 51 )[/C][C]78.3921568627451[/C][C]0.443606425788479[/C][C]176.715557542722[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 51 )[/C][C]78.6274509803922[/C][C]0.418430976000926[/C][C]187.910206199022[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 51 )[/C][C]78.6274509803922[/C][C]0.418430976000926[/C][C]187.910206199022[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 51 )[/C][C]78.6274509803922[/C][C]0.418430976000926[/C][C]187.910206199022[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 51 )[/C][C]78.6274509803922[/C][C]0.367201312168832[/C][C]214.126279985189[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 51 )[/C][C]78.6274509803922[/C][C]0.367201312168832[/C][C]214.126279985189[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 51 )[/C][C]78.6274509803922[/C][C]0.367201312168832[/C][C]214.126279985189[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 51 )[/C][C]78.6274509803922[/C][C]0.367201312168832[/C][C]214.126279985189[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 51 )[/C][C]78.6274509803922[/C][C]0.367201312168832[/C][C]214.126279985189[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 51 )[/C][C]78.6274509803922[/C][C]0.311443584580081[/C][C]252.461295956394[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 51 )[/C][C]78.6274509803922[/C][C]0.311443584580081[/C][C]252.461295956394[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 51 )[/C][C]78.6274509803922[/C][C]0.311443584580081[/C][C]252.461295956394[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 51 )[/C][C]78.6274509803922[/C][C]0.311443584580081[/C][C]252.461295956394[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 51 )[/C][C]78.6274509803922[/C][C]0.252929576297389[/C][C]310.866969894987[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 51 )[/C][C]78.6274509803922[/C][C]0.252929576297389[/C][C]310.866969894987[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 51 )[/C][C]78.6274509803922[/C][C]0.252929576297389[/C][C]310.866969894987[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 51 )[/C][C]78.6274509803922[/C][C]0.252929576297389[/C][C]310.866969894987[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 51 )[/C][C]77.9006622516556[/C][C]0.75096729186819[/C][C]103.73376190308[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 51 )[/C][C]77.9194630872483[/C][C]0.737955267867774[/C][C]105.588328290394[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 51 )[/C][C]77.9523809523809[/C][C]0.726018019794922[/C][C]107.369760566549[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 51 )[/C][C]77.9862068965517[/C][C]0.71304123134322[/C][C]109.371244562733[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 51 )[/C][C]78.020979020979[/C][C]0.701440633990331[/C][C]111.229625488241[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 51 )[/C][C]78.0567375886525[/C][C]0.688799746769322[/C][C]113.322831424898[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 51 )[/C][C]78.0567375886525[/C][C]0.67651073341913[/C][C]115.381373469344[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 51 )[/C][C]78.1240875912409[/C][C]0.664247141727777[/C][C]117.612982704046[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 51 )[/C][C]78.1481481481482[/C][C]0.653900870235632[/C][C]119.510696047839[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 51 )[/C][C]78.1729323308271[/C][C]0.642579608294266[/C][C]121.654860069926[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 51 )[/C][C]78.1984732824427[/C][C]0.630169272091976[/C][C]124.091219209796[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 51 )[/C][C]78.2170542635659[/C][C]0.618176045394492[/C][C]126.528769347009[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 51 )[/C][C]78.244094488189[/C][C]0.606356832527753[/C][C]129.039684705141[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 51 )[/C][C]78.244094488189[/C][C]0.595048818815896[/C][C]131.491891108849[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 51 )[/C][C]78.2845528455285[/C][C]0.585661031504491[/C][C]133.668707041042[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 51 )[/C][C]78.3057851239669[/C][C]0.575300014581757[/C][C]136.112955221973[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 51 )[/C][C]78.3193277310924[/C][C]0.56558631117579[/C][C]138.474581480367[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 51 )[/C][C]78.3418803418803[/C][C]0.556313387313812[/C][C]140.823287967522[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 51 )[/C][C]78.3565217391304[/C][C]0.547818822370198[/C][C]143.033642765527[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 51 )[/C][C]78.3805309734513[/C][C]0.539864457176465[/C][C]145.185573770475[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 51 )[/C][C]78.4054054054054[/C][C]0.531000998436386[/C][C]147.655853070488[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 51 )[/C][C]78.4220183486239[/C][C]0.523049030663498[/C][C]149.932441800234[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 51 )[/C][C]78.4485981308411[/C][C]0.515708736370435[/C][C]152.118032133726[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 51 )[/C][C]78.4761904761905[/C][C]0.507470787714666[/C][C]154.641788997547[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 51 )[/C][C]78.504854368932[/C][C]0.498211877127877[/C][C]157.573229328658[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 51 )[/C][C]78.5247524752475[/C][C]0.490017995104189[/C][C]160.248711802005[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 51 )[/C][C]78.5454545454545[/C][C]0.480772913940624[/C][C]163.373293852313[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 51 )[/C][C]78.5454545454545[/C][C]0.472125743056368[/C][C]166.365540749759[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 51 )[/C][C]78.6105263157895[/C][C]0.462307067435374[/C][C]170.039637836119[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 51 )[/C][C]78.6344086021505[/C][C]0.453747820057319[/C][C]173.299804706978[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 51 )[/C][C]78.6593406593407[/C][C]0.443985661314572[/C][C]177.16639863198[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 51 )[/C][C]78.685393258427[/C][C]0.432819669843182[/C][C]181.797174991922[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 51 )[/C][C]78.7011494252874[/C][C]0.422918331521969[/C][C]186.090655238479[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 51 )[/C][C]78.7058823529412[/C][C]0.414317815132379[/C][C]189.964996624134[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 51 )[/C][C]78.7228915662651[/C][C]0.40685907738267[/C][C]193.489333143777[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 51 )[/C][C]78.7407407407407[/C][C]0.398212742391574[/C][C]197.735361926999[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 51 )[/C][C]78.746835443038[/C][C]0.391183406835349[/C][C]201.304130152389[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 51 )[/C][C]78.7532467532468[/C][C]0.382974938080139[/C][C]205.635510114679[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 51 )[/C][C]78.76[/C][C]0.373365506979155[/C][C]210.946106503612[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 51 )[/C][C]78.7671232876712[/C][C]0.368323647027126[/C][C]213.853017375966[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 51 )[/C][C]78.7746478873239[/C][C]0.362307151560479[/C][C]217.425042669008[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 51 )[/C][C]78.7826086956522[/C][C]0.355129003623436[/C][C]221.842226041301[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 51 )[/C][C]78.7910447761194[/C][C]0.34655199811302[/C][C]227.357063889799[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 51 )[/C][C]78.8[/C][C]0.336269122990683[/C][C]234.336115368473[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 51 )[/C][C]78.8095238095238[/C][C]0.331683430445856[/C][C]237.604645199148[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 51 )[/C][C]78.8196721311475[/C][C]0.326019373792645[/C][C]241.763767638173[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 51 )[/C][C]78.8305084745763[/C][C]0.319036156545695[/C][C]247.08957545157[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 51 )[/C][C]78.8421052631579[/C][C]0.310417975238241[/C][C]253.986919419366[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 51 )[/C][C]78.8421052631579[/C][C]0.308595364300021[/C][C]255.48700461523[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 51 )[/C][C]78.8679245283019[/C][C]0.30600868899824[/C][C]257.730997072294[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 51 )[/C][C]78.8823529411765[/C][C]0.302469650168999[/C][C]260.794274391175[/C][/ROW]
[ROW][C]Median[/C][C]79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]76.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]78.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]78.8915662650602[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]78.8915662650602[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]78.8915662650602[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]78.8915662650602[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]78.8915662650602[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]78.8915662650602[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]78.8915662650602[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]153[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=276087&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=276087&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 Mean77.88235294117650.765221704254667101.777501223694
Geometric Mean77.2839385094042
Harmonic Mean76.6573324168489
Quadratic Mean78.4516836445635
Winsorized Mean ( 1 / 51 )77.88235294117650.762970696804404102.077777386964
Winsorized Mean ( 2 / 51 )77.85620915032680.759099047559208102.563966323847
Winsorized Mean ( 3 / 51 )77.85620915032680.759099047559208102.563966323847
Winsorized Mean ( 4 / 51 )77.85620915032680.750897771388692103.684165963552
Winsorized Mean ( 5 / 51 )77.85620915032680.750897771388692103.684165963552
Winsorized Mean ( 6 / 51 )77.89542483660130.744210737285219104.668504408783
Winsorized Mean ( 7 / 51 )77.84967320261440.738270930245567105.448650371104
Winsorized Mean ( 8 / 51 )77.95424836601310.721395221407549108.060389163533
Winsorized Mean ( 9 / 51 )77.95424836601310.721395221407549108.060389163533
Winsorized Mean ( 10 / 51 )77.95424836601310.721395221407549108.060389163533
Winsorized Mean ( 11 / 51 )78.02614379084970.710500854873698109.818507966074
Winsorized Mean ( 12 / 51 )77.94771241830070.700618359838797111.255594895109
Winsorized Mean ( 13 / 51 )78.03267973856210.688148374604435113.395137761413
Winsorized Mean ( 14 / 51 )78.03267973856210.664108760319155117.499850026164
Winsorized Mean ( 15 / 51 )78.03267973856210.664108760319155117.499850026164
Winsorized Mean ( 16 / 51 )78.13725490196080.649882820239225120.232836549208
Winsorized Mean ( 17 / 51 )78.02614379084970.636909929294488122.507343977633
Winsorized Mean ( 18 / 51 )78.14379084967320.621428100807433125.748724185693
Winsorized Mean ( 19 / 51 )78.01960784313730.60757675843641128.411113097742
Winsorized Mean ( 20 / 51 )78.01960784313730.60757675843641128.411113097742
Winsorized Mean ( 21 / 51 )78.1568627450980.590102814665719132.44617853479
Winsorized Mean ( 22 / 51 )78.01307189542480.574811475660614135.719405750845
Winsorized Mean ( 23 / 51 )78.01307189542480.574811475660614135.719405750845
Winsorized Mean ( 24 / 51 )78.01307189542480.574811475660614135.719405750845
Winsorized Mean ( 25 / 51 )78.17647058823530.554643720427633140.948987086631
Winsorized Mean ( 26 / 51 )78.17647058823530.554643720427633140.948987086631
Winsorized Mean ( 27 / 51 )780.536747329027764145.319772976393
Winsorized Mean ( 28 / 51 )780.536747329027764145.319772976393
Winsorized Mean ( 29 / 51 )78.18954248366010.513973274766946152.127642276953
Winsorized Mean ( 30 / 51 )78.18954248366010.513973274766946152.127642276953
Winsorized Mean ( 31 / 51 )78.18954248366010.513973274766946152.127642276953
Winsorized Mean ( 32 / 51 )78.39869281045750.489864582328318160.041561767601
Winsorized Mean ( 33 / 51 )78.61437908496730.466095421323819168.66584713852
Winsorized Mean ( 34 / 51 )78.39215686274510.443606425788479176.715557542722
Winsorized Mean ( 35 / 51 )78.39215686274510.443606425788479176.715557542722
Winsorized Mean ( 36 / 51 )78.62745098039220.418430976000926187.910206199022
Winsorized Mean ( 37 / 51 )78.62745098039220.418430976000926187.910206199022
Winsorized Mean ( 38 / 51 )78.62745098039220.418430976000926187.910206199022
Winsorized Mean ( 39 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 40 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 41 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 42 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 43 / 51 )78.62745098039220.367201312168832214.126279985189
Winsorized Mean ( 44 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 45 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 46 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 47 / 51 )78.62745098039220.311443584580081252.461295956394
Winsorized Mean ( 48 / 51 )78.62745098039220.252929576297389310.866969894987
Winsorized Mean ( 49 / 51 )78.62745098039220.252929576297389310.866969894987
Winsorized Mean ( 50 / 51 )78.62745098039220.252929576297389310.866969894987
Winsorized Mean ( 51 / 51 )78.62745098039220.252929576297389310.866969894987
Trimmed Mean ( 1 / 51 )77.90066225165560.75096729186819103.73376190308
Trimmed Mean ( 2 / 51 )77.91946308724830.737955267867774105.588328290394
Trimmed Mean ( 3 / 51 )77.95238095238090.726018019794922107.369760566549
Trimmed Mean ( 4 / 51 )77.98620689655170.71304123134322109.371244562733
Trimmed Mean ( 5 / 51 )78.0209790209790.701440633990331111.229625488241
Trimmed Mean ( 6 / 51 )78.05673758865250.688799746769322113.322831424898
Trimmed Mean ( 7 / 51 )78.05673758865250.67651073341913115.381373469344
Trimmed Mean ( 8 / 51 )78.12408759124090.664247141727777117.612982704046
Trimmed Mean ( 9 / 51 )78.14814814814820.653900870235632119.510696047839
Trimmed Mean ( 10 / 51 )78.17293233082710.642579608294266121.654860069926
Trimmed Mean ( 11 / 51 )78.19847328244270.630169272091976124.091219209796
Trimmed Mean ( 12 / 51 )78.21705426356590.618176045394492126.528769347009
Trimmed Mean ( 13 / 51 )78.2440944881890.606356832527753129.039684705141
Trimmed Mean ( 14 / 51 )78.2440944881890.595048818815896131.491891108849
Trimmed Mean ( 15 / 51 )78.28455284552850.585661031504491133.668707041042
Trimmed Mean ( 16 / 51 )78.30578512396690.575300014581757136.112955221973
Trimmed Mean ( 17 / 51 )78.31932773109240.56558631117579138.474581480367
Trimmed Mean ( 18 / 51 )78.34188034188030.556313387313812140.823287967522
Trimmed Mean ( 19 / 51 )78.35652173913040.547818822370198143.033642765527
Trimmed Mean ( 20 / 51 )78.38053097345130.539864457176465145.185573770475
Trimmed Mean ( 21 / 51 )78.40540540540540.531000998436386147.655853070488
Trimmed Mean ( 22 / 51 )78.42201834862390.523049030663498149.932441800234
Trimmed Mean ( 23 / 51 )78.44859813084110.515708736370435152.118032133726
Trimmed Mean ( 24 / 51 )78.47619047619050.507470787714666154.641788997547
Trimmed Mean ( 25 / 51 )78.5048543689320.498211877127877157.573229328658
Trimmed Mean ( 26 / 51 )78.52475247524750.490017995104189160.248711802005
Trimmed Mean ( 27 / 51 )78.54545454545450.480772913940624163.373293852313
Trimmed Mean ( 28 / 51 )78.54545454545450.472125743056368166.365540749759
Trimmed Mean ( 29 / 51 )78.61052631578950.462307067435374170.039637836119
Trimmed Mean ( 30 / 51 )78.63440860215050.453747820057319173.299804706978
Trimmed Mean ( 31 / 51 )78.65934065934070.443985661314572177.16639863198
Trimmed Mean ( 32 / 51 )78.6853932584270.432819669843182181.797174991922
Trimmed Mean ( 33 / 51 )78.70114942528740.422918331521969186.090655238479
Trimmed Mean ( 34 / 51 )78.70588235294120.414317815132379189.964996624134
Trimmed Mean ( 35 / 51 )78.72289156626510.40685907738267193.489333143777
Trimmed Mean ( 36 / 51 )78.74074074074070.398212742391574197.735361926999
Trimmed Mean ( 37 / 51 )78.7468354430380.391183406835349201.304130152389
Trimmed Mean ( 38 / 51 )78.75324675324680.382974938080139205.635510114679
Trimmed Mean ( 39 / 51 )78.760.373365506979155210.946106503612
Trimmed Mean ( 40 / 51 )78.76712328767120.368323647027126213.853017375966
Trimmed Mean ( 41 / 51 )78.77464788732390.362307151560479217.425042669008
Trimmed Mean ( 42 / 51 )78.78260869565220.355129003623436221.842226041301
Trimmed Mean ( 43 / 51 )78.79104477611940.34655199811302227.357063889799
Trimmed Mean ( 44 / 51 )78.80.336269122990683234.336115368473
Trimmed Mean ( 45 / 51 )78.80952380952380.331683430445856237.604645199148
Trimmed Mean ( 46 / 51 )78.81967213114750.326019373792645241.763767638173
Trimmed Mean ( 47 / 51 )78.83050847457630.319036156545695247.08957545157
Trimmed Mean ( 48 / 51 )78.84210526315790.310417975238241253.986919419366
Trimmed Mean ( 49 / 51 )78.84210526315790.308595364300021255.48700461523
Trimmed Mean ( 50 / 51 )78.86792452830190.30600868899824257.730997072294
Trimmed Mean ( 51 / 51 )78.88235294117650.302469650168999260.794274391175
Median79
Midrange76.5
Midmean - Weighted Average at Xnp78.5
Midmean - Weighted Average at X(n+1)p78.8915662650602
Midmean - Empirical Distribution Function78.8915662650602
Midmean - Empirical Distribution Function - Averaging78.8915662650602
Midmean - Empirical Distribution Function - Interpolation78.8915662650602
Midmean - Closest Observation78.8915662650602
Midmean - True Basic - Statistics Graphics Toolkit78.8915662650602
Midmean - MS Excel (old versions)78.8915662650602
Number of observations153



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')