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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Oct 2012 13:23:46 -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/2012/Oct/11/t134997626990ff91ou7www1xt.htm/, Retrieved Sun, 28 Apr 2024 18:29:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175177, Retrieved Sun, 28 Apr 2024 18:29:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-11 17:23:46] [4fb632b17dd9b46a28f1faaf764882b5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
33,7
34,59
35,1
35,87
37,15
37,61
37,97
38,94
39,18
39,49
39,86
40,02
40,2
40,85
41,45
41,7
41,92
41,97
42,31
42,61
42,82
43,07
43,51
43,57
43,86
44,49
45,99
48,22
49,46
50,39
50,4
50,59
51,32
51,86
52,47
52,73
52,73
53,59
54,11
54,8
55,72
56,06
56,66
57,05
57,31
57,89
58,32
58,72
59,02
59,54
61,49
62,26
63,49
64,36
65,93
66,82
68,85
71,27
72,27
73,4
73,58
74,84
75,74
77,81
78,74
79,06
79,48
81,19
85,11
86,64
88,48
89,2

Tables (Output of Computation)





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=175177&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=175177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175177&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean55.26069444444441.781964102130831.0111154194218
Geometric Mean53.328348101866
Harmonic Mean51.5335347931428
Quadratic Mean57.2642774409433
Winsorized Mean ( 1 / 24 )55.26305555555561.7772407073995131.0948625729024
Winsorized Mean ( 2 / 24 )55.22611111111111.7617938996205131.3465219302932
Winsorized Mean ( 3 / 24 )55.19444444444441.7409836238283631.7030233306123
Winsorized Mean ( 4 / 24 )55.04777777777781.6798207928282432.7700300012934
Winsorized Mean ( 5 / 24 )54.96097222222221.6496078298081733.3175990251051
Winsorized Mean ( 6 / 24 )54.95597222222221.6379036333666633.5526285568229
Winsorized Mean ( 7 / 24 )55.01916666666671.6179782172037634.0048871373266
Winsorized Mean ( 8 / 24 )54.94251.593138281296834.4869623968091
Winsorized Mean ( 9 / 24 )54.72251.5366327757661235.6119567817477
Winsorized Mean ( 10 / 24 )54.64888888888891.5056429921656136.2960470531502
Winsorized Mean ( 11 / 24 )54.48083333333331.4664119597174937.1524747682971
Winsorized Mean ( 12 / 24 )54.48083333333331.4567620206808937.3985816213611
Winsorized Mean ( 13 / 24 )54.39416666666671.4037187608442738.7500460804209
Winsorized Mean ( 14 / 24 )54.31638888888891.3533820342302840.1338184748261
Winsorized Mean ( 15 / 24 )53.86430555555561.259556331742342.7645069919557
Winsorized Mean ( 16 / 24 )53.46208333333331.1790132896400645.3447673602174
Winsorized Mean ( 17 / 24 )53.263751.1442252854287746.5500550270051
Winsorized Mean ( 18 / 24 )52.956251.0723442910103349.3836265497403
Winsorized Mean ( 19 / 24 )52.80583333333331.0272585283733651.4046190660008
Winsorized Mean ( 20 / 24 )52.52250.96986515022677954.1544357869946
Winsorized Mean ( 21 / 24 )52.37083333333330.9281571496489456.424532583886
Winsorized Mean ( 22 / 24 )51.90944444444440.82909272888285562.6099381119755
Winsorized Mean ( 23 / 24 )51.76250.80503646798684464.2983294029432
Winsorized Mean ( 24 / 24 )51.75916666666670.77855574704189166.4810026299655
Trimmed Mean ( 1 / 24 )55.08385714285711.7394280287494131.667798973241
Trimmed Mean ( 2 / 24 )54.89411764705881.6941221428032732.4026917895219
Trimmed Mean ( 3 / 24 )54.71303030303031.6496220231010833.1670101010029
Trimmed Mean ( 4 / 24 )54.53251.6055037099609633.9659757007512
Trimmed Mean ( 5 / 24 )54.38290322580651.5747622920363934.5340395187401
Trimmed Mean ( 6 / 24 )54.24416666666671.5465053239621635.0753184138368
Trimmed Mean ( 7 / 24 )54.09689655172411.5146602247050335.7155325460925
Trimmed Mean ( 8 / 24 )53.92751.4799514788904836.4386946256031
Trimmed Mean ( 9 / 24 )53.75833333333331.4426591632176837.2633638658155
Trimmed Mean ( 10 / 24 )53.611.4094941221024438.0349227139975
Trimmed Mean ( 11 / 24 )53.46041.3743665245026438.8982116829034
Trimmed Mean ( 12 / 24 )53.321251.3384308792494239.8386280731226
Trimmed Mean ( 13 / 24 )53.171.2938009762647341.0959652801503
Trimmed Mean ( 14 / 24 )53.01590909090911.2481231710552242.47650417874
Trimmed Mean ( 15 / 24 )52.85666666666671.1999158248964844.050312171878
Trimmed Mean ( 16 / 24 )52.735751.1598213217549745.4688571513789
Trimmed Mean ( 17 / 24 )52.64973684210531.1260720188269246.7552127766684
Trimmed Mean ( 18 / 24 )52.57751.0882677640132948.3130179342132
Trimmed Mean ( 19 / 24 )52.53294117647061.0546287524997849.8117854761232
Trimmed Mean ( 20 / 24 )52.5006251.0186665003876951.5385800750483
Trimmed Mean ( 21 / 24 )52.4980.98285291985574653.4138922919466
Trimmed Mean ( 22 / 24 )52.51357142857140.94187548103170655.7542610314576
Trimmed Mean ( 23 / 24 )52.58961538461540.91153673807042557.693358027389
Trimmed Mean ( 24 / 24 )52.69750.86926365015354360.6231492490129
Median52.73
Midrange61.45
Midmean - Weighted Average at Xnp52.2908108108108
Midmean - Weighted Average at X(n+1)p52.5775
Midmean - Empirical Distribution Function52.2908108108108
Midmean - Empirical Distribution Function - Averaging52.5775
Midmean - Empirical Distribution Function - Interpolation52.5775
Midmean - Closest Observation52.2908108108108
Midmean - True Basic - Statistics Graphics Toolkit52.5775
Midmean - MS Excel (old versions)52.6497368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 55.2606944444444 & 1.7819641021308 & 31.0111154194218 \tabularnewline
Geometric Mean & 53.328348101866 &  &  \tabularnewline
Harmonic Mean & 51.5335347931428 &  &  \tabularnewline
Quadratic Mean & 57.2642774409433 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 55.2630555555556 & 1.77724070739951 & 31.0948625729024 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 55.2261111111111 & 1.76179389962051 & 31.3465219302932 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 55.1944444444444 & 1.74098362382836 & 31.7030233306123 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 55.0477777777778 & 1.67982079282824 & 32.7700300012934 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 54.9609722222222 & 1.64960782980817 & 33.3175990251051 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 54.9559722222222 & 1.63790363336666 & 33.5526285568229 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 55.0191666666667 & 1.61797821720376 & 34.0048871373266 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 54.9425 & 1.5931382812968 & 34.4869623968091 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 54.7225 & 1.53663277576612 & 35.6119567817477 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 54.6488888888889 & 1.50564299216561 & 36.2960470531502 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 54.4808333333333 & 1.46641195971749 & 37.1524747682971 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 54.4808333333333 & 1.45676202068089 & 37.3985816213611 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 54.3941666666667 & 1.40371876084427 & 38.7500460804209 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 54.3163888888889 & 1.35338203423028 & 40.1338184748261 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 53.8643055555556 & 1.2595563317423 & 42.7645069919557 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 53.4620833333333 & 1.17901328964006 & 45.3447673602174 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 53.26375 & 1.14422528542877 & 46.5500550270051 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 52.95625 & 1.07234429101033 & 49.3836265497403 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 52.8058333333333 & 1.02725852837336 & 51.4046190660008 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 52.5225 & 0.969865150226779 & 54.1544357869946 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 52.3708333333333 & 0.92815714964894 & 56.424532583886 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 51.9094444444444 & 0.829092728882855 & 62.6099381119755 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 51.7625 & 0.805036467986844 & 64.2983294029432 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 51.7591666666667 & 0.778555747041891 & 66.4810026299655 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 55.0838571428571 & 1.73942802874941 & 31.667798973241 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 54.8941176470588 & 1.69412214280327 & 32.4026917895219 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 54.7130303030303 & 1.64962202310108 & 33.1670101010029 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 54.5325 & 1.60550370996096 & 33.9659757007512 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 54.3829032258065 & 1.57476229203639 & 34.5340395187401 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 54.2441666666667 & 1.54650532396216 & 35.0753184138368 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 54.0968965517241 & 1.51466022470503 & 35.7155325460925 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 53.9275 & 1.47995147889048 & 36.4386946256031 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 53.7583333333333 & 1.44265916321768 & 37.2633638658155 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 53.61 & 1.40949412210244 & 38.0349227139975 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 53.4604 & 1.37436652450264 & 38.8982116829034 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 53.32125 & 1.33843087924942 & 39.8386280731226 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 53.17 & 1.29380097626473 & 41.0959652801503 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 53.0159090909091 & 1.24812317105522 & 42.47650417874 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 52.8566666666667 & 1.19991582489648 & 44.050312171878 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 52.73575 & 1.15982132175497 & 45.4688571513789 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 52.6497368421053 & 1.12607201882692 & 46.7552127766684 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 52.5775 & 1.08826776401329 & 48.3130179342132 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 52.5329411764706 & 1.05462875249978 & 49.8117854761232 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 52.500625 & 1.01866650038769 & 51.5385800750483 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 52.498 & 0.982852919855746 & 53.4138922919466 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 52.5135714285714 & 0.941875481031706 & 55.7542610314576 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 52.5896153846154 & 0.911536738070425 & 57.693358027389 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 52.6975 & 0.869263650153543 & 60.6231492490129 \tabularnewline
Median & 52.73 &  &  \tabularnewline
Midrange & 61.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.2908108108108 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.5775 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.2908108108108 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.5775 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.5775 &  &  \tabularnewline
Midmean - Closest Observation & 52.2908108108108 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.5775 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.6497368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175177&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]55.2606944444444[/C][C]1.7819641021308[/C][C]31.0111154194218[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]53.328348101866[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]51.5335347931428[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]57.2642774409433[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]55.2630555555556[/C][C]1.77724070739951[/C][C]31.0948625729024[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]55.2261111111111[/C][C]1.76179389962051[/C][C]31.3465219302932[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]55.1944444444444[/C][C]1.74098362382836[/C][C]31.7030233306123[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]55.0477777777778[/C][C]1.67982079282824[/C][C]32.7700300012934[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]54.9609722222222[/C][C]1.64960782980817[/C][C]33.3175990251051[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]54.9559722222222[/C][C]1.63790363336666[/C][C]33.5526285568229[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]55.0191666666667[/C][C]1.61797821720376[/C][C]34.0048871373266[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]54.9425[/C][C]1.5931382812968[/C][C]34.4869623968091[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]54.7225[/C][C]1.53663277576612[/C][C]35.6119567817477[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]54.6488888888889[/C][C]1.50564299216561[/C][C]36.2960470531502[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]54.4808333333333[/C][C]1.46641195971749[/C][C]37.1524747682971[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]54.4808333333333[/C][C]1.45676202068089[/C][C]37.3985816213611[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]54.3941666666667[/C][C]1.40371876084427[/C][C]38.7500460804209[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]54.3163888888889[/C][C]1.35338203423028[/C][C]40.1338184748261[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]53.8643055555556[/C][C]1.2595563317423[/C][C]42.7645069919557[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]53.4620833333333[/C][C]1.17901328964006[/C][C]45.3447673602174[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]53.26375[/C][C]1.14422528542877[/C][C]46.5500550270051[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]52.95625[/C][C]1.07234429101033[/C][C]49.3836265497403[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]52.8058333333333[/C][C]1.02725852837336[/C][C]51.4046190660008[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]52.5225[/C][C]0.969865150226779[/C][C]54.1544357869946[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]52.3708333333333[/C][C]0.92815714964894[/C][C]56.424532583886[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]51.9094444444444[/C][C]0.829092728882855[/C][C]62.6099381119755[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]51.7625[/C][C]0.805036467986844[/C][C]64.2983294029432[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]51.7591666666667[/C][C]0.778555747041891[/C][C]66.4810026299655[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]55.0838571428571[/C][C]1.73942802874941[/C][C]31.667798973241[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]54.8941176470588[/C][C]1.69412214280327[/C][C]32.4026917895219[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]54.7130303030303[/C][C]1.64962202310108[/C][C]33.1670101010029[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]54.5325[/C][C]1.60550370996096[/C][C]33.9659757007512[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]54.3829032258065[/C][C]1.57476229203639[/C][C]34.5340395187401[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]54.2441666666667[/C][C]1.54650532396216[/C][C]35.0753184138368[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]54.0968965517241[/C][C]1.51466022470503[/C][C]35.7155325460925[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]53.9275[/C][C]1.47995147889048[/C][C]36.4386946256031[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]53.7583333333333[/C][C]1.44265916321768[/C][C]37.2633638658155[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]53.61[/C][C]1.40949412210244[/C][C]38.0349227139975[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]53.4604[/C][C]1.37436652450264[/C][C]38.8982116829034[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]53.32125[/C][C]1.33843087924942[/C][C]39.8386280731226[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]53.17[/C][C]1.29380097626473[/C][C]41.0959652801503[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]53.0159090909091[/C][C]1.24812317105522[/C][C]42.47650417874[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]52.8566666666667[/C][C]1.19991582489648[/C][C]44.050312171878[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]52.73575[/C][C]1.15982132175497[/C][C]45.4688571513789[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]52.6497368421053[/C][C]1.12607201882692[/C][C]46.7552127766684[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]52.5775[/C][C]1.08826776401329[/C][C]48.3130179342132[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]52.5329411764706[/C][C]1.05462875249978[/C][C]49.8117854761232[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]52.500625[/C][C]1.01866650038769[/C][C]51.5385800750483[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]52.498[/C][C]0.982852919855746[/C][C]53.4138922919466[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]52.5135714285714[/C][C]0.941875481031706[/C][C]55.7542610314576[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]52.5896153846154[/C][C]0.911536738070425[/C][C]57.693358027389[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]52.6975[/C][C]0.869263650153543[/C][C]60.6231492490129[/C][/ROW]
[ROW][C]Median[/C][C]52.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]61.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.2908108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.5775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.2908108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.5775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.5775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.2908108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.5775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.6497368421053[/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=175177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175177&T=1

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


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean55.26069444444441.781964102130831.0111154194218
Geometric Mean53.328348101866
Harmonic Mean51.5335347931428
Quadratic Mean57.2642774409433
Winsorized Mean ( 1 / 24 )55.26305555555561.7772407073995131.0948625729024
Winsorized Mean ( 2 / 24 )55.22611111111111.7617938996205131.3465219302932
Winsorized Mean ( 3 / 24 )55.19444444444441.7409836238283631.7030233306123
Winsorized Mean ( 4 / 24 )55.04777777777781.6798207928282432.7700300012934
Winsorized Mean ( 5 / 24 )54.96097222222221.6496078298081733.3175990251051
Winsorized Mean ( 6 / 24 )54.95597222222221.6379036333666633.5526285568229
Winsorized Mean ( 7 / 24 )55.01916666666671.6179782172037634.0048871373266
Winsorized Mean ( 8 / 24 )54.94251.593138281296834.4869623968091
Winsorized Mean ( 9 / 24 )54.72251.5366327757661235.6119567817477
Winsorized Mean ( 10 / 24 )54.64888888888891.5056429921656136.2960470531502
Winsorized Mean ( 11 / 24 )54.48083333333331.4664119597174937.1524747682971
Winsorized Mean ( 12 / 24 )54.48083333333331.4567620206808937.3985816213611
Winsorized Mean ( 13 / 24 )54.39416666666671.4037187608442738.7500460804209
Winsorized Mean ( 14 / 24 )54.31638888888891.3533820342302840.1338184748261
Winsorized Mean ( 15 / 24 )53.86430555555561.259556331742342.7645069919557
Winsorized Mean ( 16 / 24 )53.46208333333331.1790132896400645.3447673602174
Winsorized Mean ( 17 / 24 )53.263751.1442252854287746.5500550270051
Winsorized Mean ( 18 / 24 )52.956251.0723442910103349.3836265497403
Winsorized Mean ( 19 / 24 )52.80583333333331.0272585283733651.4046190660008
Winsorized Mean ( 20 / 24 )52.52250.96986515022677954.1544357869946
Winsorized Mean ( 21 / 24 )52.37083333333330.9281571496489456.424532583886
Winsorized Mean ( 22 / 24 )51.90944444444440.82909272888285562.6099381119755
Winsorized Mean ( 23 / 24 )51.76250.80503646798684464.2983294029432
Winsorized Mean ( 24 / 24 )51.75916666666670.77855574704189166.4810026299655
Trimmed Mean ( 1 / 24 )55.08385714285711.7394280287494131.667798973241
Trimmed Mean ( 2 / 24 )54.89411764705881.6941221428032732.4026917895219
Trimmed Mean ( 3 / 24 )54.71303030303031.6496220231010833.1670101010029
Trimmed Mean ( 4 / 24 )54.53251.6055037099609633.9659757007512
Trimmed Mean ( 5 / 24 )54.38290322580651.5747622920363934.5340395187401
Trimmed Mean ( 6 / 24 )54.24416666666671.5465053239621635.0753184138368
Trimmed Mean ( 7 / 24 )54.09689655172411.5146602247050335.7155325460925
Trimmed Mean ( 8 / 24 )53.92751.4799514788904836.4386946256031
Trimmed Mean ( 9 / 24 )53.75833333333331.4426591632176837.2633638658155
Trimmed Mean ( 10 / 24 )53.611.4094941221024438.0349227139975
Trimmed Mean ( 11 / 24 )53.46041.3743665245026438.8982116829034
Trimmed Mean ( 12 / 24 )53.321251.3384308792494239.8386280731226
Trimmed Mean ( 13 / 24 )53.171.2938009762647341.0959652801503
Trimmed Mean ( 14 / 24 )53.01590909090911.2481231710552242.47650417874
Trimmed Mean ( 15 / 24 )52.85666666666671.1999158248964844.050312171878
Trimmed Mean ( 16 / 24 )52.735751.1598213217549745.4688571513789
Trimmed Mean ( 17 / 24 )52.64973684210531.1260720188269246.7552127766684
Trimmed Mean ( 18 / 24 )52.57751.0882677640132948.3130179342132
Trimmed Mean ( 19 / 24 )52.53294117647061.0546287524997849.8117854761232
Trimmed Mean ( 20 / 24 )52.5006251.0186665003876951.5385800750483
Trimmed Mean ( 21 / 24 )52.4980.98285291985574653.4138922919466
Trimmed Mean ( 22 / 24 )52.51357142857140.94187548103170655.7542610314576
Trimmed Mean ( 23 / 24 )52.58961538461540.91153673807042557.693358027389
Trimmed Mean ( 24 / 24 )52.69750.86926365015354360.6231492490129
Median52.73
Midrange61.45
Midmean - Weighted Average at Xnp52.2908108108108
Midmean - Weighted Average at X(n+1)p52.5775
Midmean - Empirical Distribution Function52.2908108108108
Midmean - Empirical Distribution Function - Averaging52.5775
Midmean - Empirical Distribution Function - Interpolation52.5775
Midmean - Closest Observation52.2908108108108
Midmean - True Basic - Statistics Graphics Toolkit52.5775
Midmean - MS Excel (old versions)52.6497368421053
Number of observations72


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')