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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 computationMon, 04 Mar 2013 07:34:28 -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/04/t1362400552p2lo27lsfzh0iy8.htm/, Retrieved Sat, 27 Apr 2024 13:54:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207315, Retrieved Sat, 27 Apr 2024 13:54:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5 oef 2] [2013-03-04 12:34:28] [480fcaba71e70207c3e0ad7177944aa6] [Current]
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Dataseries X:
79,57
77,45
75,79
74,88
74,5
74,59
74,59
73,57
73,3
73,23
73
72,31
72,31
71,24
70,82
70,66
69,94
69,87
69,87
68,88
68,09
68,38
66,78
67,2
67,2
66,67
65,86
66,05
66,31
66,39
66,39
65,72
65,52
64,93
65,27
65,04
65,02
64,72
64,68
64,41
64,79
64,71
64,71
64,83
64,77
64,19
64,27
64,23
64,23
63,03
62,85
62,15
61,69
62,1
62,1
61,81
61,28
61,05
61,08
60,98
60,98
61,11
60,58
60,37
59,44
59,29
59,29
59,33
59,06
58,75
58,92
58,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207315&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207315&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean66.07916666666670.603060878940858109.572961825546
Geometric Mean65.8886068455619
Harmonic Mean65.7029053012969
Quadratic Mean66.2742613647594
Winsorized Mean ( 1 / 24 )66.050.594392649082452111.121831842907
Winsorized Mean ( 2 / 24 )66.00861111111110.581884293655765113.439410258701
Winsorized Mean ( 3 / 24 )65.97652777777780.572241432124719115.294915876343
Winsorized Mean ( 4 / 24 )65.97319444444440.566601343459033116.436706700492
Winsorized Mean ( 5 / 24 )65.97319444444440.566601343459033116.436706700492
Winsorized Mean ( 6 / 24 )65.96902777777780.564446845141947116.873764723032
Winsorized Mean ( 7 / 24 )65.88930555555560.544043802548928121.110295249857
Winsorized Mean ( 8 / 24 )65.96263888888890.521643716704656126.451516191147
Winsorized Mean ( 9 / 24 )65.98013888888890.515994394260516127.869875376159
Winsorized Mean ( 10 / 24 )66.003750.501681345124737131.565087363551
Winsorized Mean ( 11 / 24 )65.89833333333330.481432111449031136.87980457928
Winsorized Mean ( 12 / 24 )65.910.479760471012531137.381055719112
Winsorized Mean ( 13 / 24 )65.72222222222220.443865208422704148.067974184706
Winsorized Mean ( 14 / 24 )65.64638888888890.428910952376695153.053654902322
Winsorized Mean ( 15 / 24 )65.64847222222220.418020179992726157.046179501106
Winsorized Mean ( 16 / 24 )65.57958333333330.378184881088652173.406147661309
Winsorized Mean ( 17 / 24 )65.59138888888890.371418331399609176.597069513834
Winsorized Mean ( 18 / 24 )65.66388888888890.36118017276286181.803692009422
Winsorized Mean ( 19 / 24 )65.40263888888890.319654791856449204.603968265428
Winsorized Mean ( 20 / 24 )65.27763888888890.296732498699832219.98816838368
Winsorized Mean ( 21 / 24 )65.39722222222220.254613013162953256.849488601621
Winsorized Mean ( 22 / 24 )65.18027777777780.207699408512986313.820237835211
Winsorized Mean ( 23 / 24 )65.55083333333330.157525335170751416.128829450063
Winsorized Mean ( 24 / 24 )65.42416666666670.135680016588326482.194565653494
Trimmed Mean ( 1 / 24 )65.99142857142860.579603787196993113.856103133087
Trimmed Mean ( 2 / 24 )65.92941176470590.561923624607988117.328065376678
Trimmed Mean ( 3 / 24 )65.88621212121210.5488084046751120.053212669397
Trimmed Mean ( 4 / 24 )65.852343750.537425970455111122.5328647483
Trimmed Mean ( 5 / 24 )65.81725806451610.52566641591657125.207272276953
Trimmed Mean ( 6 / 24 )65.77983333333330.511288308092868128.655070519206
Trimmed Mean ( 7 / 24 )65.74068965517240.494274897861827133.004305781173
Trimmed Mean ( 8 / 24 )65.71339285714280.478987926317057137.192169669941
Trimmed Mean ( 9 / 24 )65.67185185185190.465602640985195141.046991728597
Trimmed Mean ( 10 / 24 )65.62442307692310.450101162875789145.799274673354
Trimmed Mean ( 11 / 24 )65.56980.433849639146738151.134849688841
Trimmed Mean ( 12 / 24 )65.5250.418202629972974156.682419726137
Trimmed Mean ( 13 / 24 )65.47478260869560.398294521076864164.387856583295
Trimmed Mean ( 14 / 24 )65.44363636363640.38179171608669171.411881416454
Trimmed Mean ( 15 / 24 )65.41880952380950.363934207143311179.754494740443
Trimmed Mean ( 16 / 24 )65.391250.342918691772068190.690246898132
Trimmed Mean ( 17 / 24 )65.3689473684210.325576584386326200.779019448324
Trimmed Mean ( 18 / 24 )65.34277777777780.303532015285622215.274746936631
Trimmed Mean ( 19 / 24 )65.3050.275283114677202237.228498655201
Trimmed Mean ( 20 / 24 )65.29343750.249937737962603261.23881104249
Trimmed Mean ( 21 / 24 )65.29533333333330.221180081274265295.213443078387
Trimmed Mean ( 22 / 24 )65.28285714285710.195067385686147334.668232278941
Trimmed Mean ( 23 / 24 )65.29576923076920.175462617607041372.134931766508
Trimmed Mean ( 24 / 24 )65.26250.165592097497505394.116029606928
Median64.975
Midrange69.15
Midmean - Weighted Average at Xnp65.368947368421
Midmean - Weighted Average at X(n+1)p65.4651351351351
Midmean - Empirical Distribution Function65.368947368421
Midmean - Empirical Distribution Function - Averaging65.4651351351351
Midmean - Empirical Distribution Function - Interpolation65.4651351351351
Midmean - Closest Observation65.368947368421
Midmean - True Basic - Statistics Graphics Toolkit65.4651351351351
Midmean - MS Excel (old versions)65.368947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 66.0791666666667 & 0.603060878940858 & 109.572961825546 \tabularnewline
Geometric Mean & 65.8886068455619 &  &  \tabularnewline
Harmonic Mean & 65.7029053012969 &  &  \tabularnewline
Quadratic Mean & 66.2742613647594 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 66.05 & 0.594392649082452 & 111.121831842907 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 66.0086111111111 & 0.581884293655765 & 113.439410258701 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 65.9765277777778 & 0.572241432124719 & 115.294915876343 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 65.9731944444444 & 0.566601343459033 & 116.436706700492 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 65.9731944444444 & 0.566601343459033 & 116.436706700492 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 65.9690277777778 & 0.564446845141947 & 116.873764723032 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 65.8893055555556 & 0.544043802548928 & 121.110295249857 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 65.9626388888889 & 0.521643716704656 & 126.451516191147 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 65.9801388888889 & 0.515994394260516 & 127.869875376159 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 66.00375 & 0.501681345124737 & 131.565087363551 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 65.8983333333333 & 0.481432111449031 & 136.87980457928 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 65.91 & 0.479760471012531 & 137.381055719112 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 65.7222222222222 & 0.443865208422704 & 148.067974184706 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 65.6463888888889 & 0.428910952376695 & 153.053654902322 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 65.6484722222222 & 0.418020179992726 & 157.046179501106 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 65.5795833333333 & 0.378184881088652 & 173.406147661309 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 65.5913888888889 & 0.371418331399609 & 176.597069513834 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 65.6638888888889 & 0.36118017276286 & 181.803692009422 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 65.4026388888889 & 0.319654791856449 & 204.603968265428 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 65.2776388888889 & 0.296732498699832 & 219.98816838368 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 65.3972222222222 & 0.254613013162953 & 256.849488601621 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 65.1802777777778 & 0.207699408512986 & 313.820237835211 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 65.5508333333333 & 0.157525335170751 & 416.128829450063 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 65.4241666666667 & 0.135680016588326 & 482.194565653494 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 65.9914285714286 & 0.579603787196993 & 113.856103133087 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 65.9294117647059 & 0.561923624607988 & 117.328065376678 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 65.8862121212121 & 0.5488084046751 & 120.053212669397 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 65.85234375 & 0.537425970455111 & 122.5328647483 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 65.8172580645161 & 0.52566641591657 & 125.207272276953 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 65.7798333333333 & 0.511288308092868 & 128.655070519206 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 65.7406896551724 & 0.494274897861827 & 133.004305781173 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 65.7133928571428 & 0.478987926317057 & 137.192169669941 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 65.6718518518519 & 0.465602640985195 & 141.046991728597 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 65.6244230769231 & 0.450101162875789 & 145.799274673354 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 65.5698 & 0.433849639146738 & 151.134849688841 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 65.525 & 0.418202629972974 & 156.682419726137 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 65.4747826086956 & 0.398294521076864 & 164.387856583295 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 65.4436363636364 & 0.38179171608669 & 171.411881416454 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 65.4188095238095 & 0.363934207143311 & 179.754494740443 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 65.39125 & 0.342918691772068 & 190.690246898132 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 65.368947368421 & 0.325576584386326 & 200.779019448324 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 65.3427777777778 & 0.303532015285622 & 215.274746936631 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 65.305 & 0.275283114677202 & 237.228498655201 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 65.2934375 & 0.249937737962603 & 261.23881104249 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 65.2953333333333 & 0.221180081274265 & 295.213443078387 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 65.2828571428571 & 0.195067385686147 & 334.668232278941 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 65.2957692307692 & 0.175462617607041 & 372.134931766508 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 65.2625 & 0.165592097497505 & 394.116029606928 \tabularnewline
Median & 64.975 &  &  \tabularnewline
Midrange & 69.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 65.368947368421 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 65.4651351351351 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 65.368947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 65.4651351351351 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 65.4651351351351 &  &  \tabularnewline
Midmean - Closest Observation & 65.368947368421 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 65.4651351351351 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 65.368947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207315&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]66.0791666666667[/C][C]0.603060878940858[/C][C]109.572961825546[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]65.8886068455619[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]65.7029053012969[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]66.2742613647594[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]66.05[/C][C]0.594392649082452[/C][C]111.121831842907[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]66.0086111111111[/C][C]0.581884293655765[/C][C]113.439410258701[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]65.9765277777778[/C][C]0.572241432124719[/C][C]115.294915876343[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]65.9731944444444[/C][C]0.566601343459033[/C][C]116.436706700492[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]65.9731944444444[/C][C]0.566601343459033[/C][C]116.436706700492[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]65.9690277777778[/C][C]0.564446845141947[/C][C]116.873764723032[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]65.8893055555556[/C][C]0.544043802548928[/C][C]121.110295249857[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]65.9626388888889[/C][C]0.521643716704656[/C][C]126.451516191147[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]65.9801388888889[/C][C]0.515994394260516[/C][C]127.869875376159[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]66.00375[/C][C]0.501681345124737[/C][C]131.565087363551[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]65.8983333333333[/C][C]0.481432111449031[/C][C]136.87980457928[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]65.91[/C][C]0.479760471012531[/C][C]137.381055719112[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]65.7222222222222[/C][C]0.443865208422704[/C][C]148.067974184706[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]65.6463888888889[/C][C]0.428910952376695[/C][C]153.053654902322[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]65.6484722222222[/C][C]0.418020179992726[/C][C]157.046179501106[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]65.5795833333333[/C][C]0.378184881088652[/C][C]173.406147661309[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]65.5913888888889[/C][C]0.371418331399609[/C][C]176.597069513834[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]65.6638888888889[/C][C]0.36118017276286[/C][C]181.803692009422[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]65.4026388888889[/C][C]0.319654791856449[/C][C]204.603968265428[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]65.2776388888889[/C][C]0.296732498699832[/C][C]219.98816838368[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]65.3972222222222[/C][C]0.254613013162953[/C][C]256.849488601621[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]65.1802777777778[/C][C]0.207699408512986[/C][C]313.820237835211[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]65.5508333333333[/C][C]0.157525335170751[/C][C]416.128829450063[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]65.4241666666667[/C][C]0.135680016588326[/C][C]482.194565653494[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]65.9914285714286[/C][C]0.579603787196993[/C][C]113.856103133087[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]65.9294117647059[/C][C]0.561923624607988[/C][C]117.328065376678[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]65.8862121212121[/C][C]0.5488084046751[/C][C]120.053212669397[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]65.85234375[/C][C]0.537425970455111[/C][C]122.5328647483[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]65.8172580645161[/C][C]0.52566641591657[/C][C]125.207272276953[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]65.7798333333333[/C][C]0.511288308092868[/C][C]128.655070519206[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]65.7406896551724[/C][C]0.494274897861827[/C][C]133.004305781173[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]65.7133928571428[/C][C]0.478987926317057[/C][C]137.192169669941[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]65.6718518518519[/C][C]0.465602640985195[/C][C]141.046991728597[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]65.6244230769231[/C][C]0.450101162875789[/C][C]145.799274673354[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]65.5698[/C][C]0.433849639146738[/C][C]151.134849688841[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]65.525[/C][C]0.418202629972974[/C][C]156.682419726137[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]65.4747826086956[/C][C]0.398294521076864[/C][C]164.387856583295[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]65.4436363636364[/C][C]0.38179171608669[/C][C]171.411881416454[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]65.4188095238095[/C][C]0.363934207143311[/C][C]179.754494740443[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]65.39125[/C][C]0.342918691772068[/C][C]190.690246898132[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]65.368947368421[/C][C]0.325576584386326[/C][C]200.779019448324[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]65.3427777777778[/C][C]0.303532015285622[/C][C]215.274746936631[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]65.305[/C][C]0.275283114677202[/C][C]237.228498655201[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]65.2934375[/C][C]0.249937737962603[/C][C]261.23881104249[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]65.2953333333333[/C][C]0.221180081274265[/C][C]295.213443078387[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]65.2828571428571[/C][C]0.195067385686147[/C][C]334.668232278941[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]65.2957692307692[/C][C]0.175462617607041[/C][C]372.134931766508[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]65.2625[/C][C]0.165592097497505[/C][C]394.116029606928[/C][/ROW]
[ROW][C]Median[/C][C]64.975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]69.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]65.368947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]65.4651351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]65.368947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]65.4651351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]65.4651351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]65.368947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]65.4651351351351[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]65.368947368421[/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=207315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207315&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 Mean66.07916666666670.603060878940858109.572961825546
Geometric Mean65.8886068455619
Harmonic Mean65.7029053012969
Quadratic Mean66.2742613647594
Winsorized Mean ( 1 / 24 )66.050.594392649082452111.121831842907
Winsorized Mean ( 2 / 24 )66.00861111111110.581884293655765113.439410258701
Winsorized Mean ( 3 / 24 )65.97652777777780.572241432124719115.294915876343
Winsorized Mean ( 4 / 24 )65.97319444444440.566601343459033116.436706700492
Winsorized Mean ( 5 / 24 )65.97319444444440.566601343459033116.436706700492
Winsorized Mean ( 6 / 24 )65.96902777777780.564446845141947116.873764723032
Winsorized Mean ( 7 / 24 )65.88930555555560.544043802548928121.110295249857
Winsorized Mean ( 8 / 24 )65.96263888888890.521643716704656126.451516191147
Winsorized Mean ( 9 / 24 )65.98013888888890.515994394260516127.869875376159
Winsorized Mean ( 10 / 24 )66.003750.501681345124737131.565087363551
Winsorized Mean ( 11 / 24 )65.89833333333330.481432111449031136.87980457928
Winsorized Mean ( 12 / 24 )65.910.479760471012531137.381055719112
Winsorized Mean ( 13 / 24 )65.72222222222220.443865208422704148.067974184706
Winsorized Mean ( 14 / 24 )65.64638888888890.428910952376695153.053654902322
Winsorized Mean ( 15 / 24 )65.64847222222220.418020179992726157.046179501106
Winsorized Mean ( 16 / 24 )65.57958333333330.378184881088652173.406147661309
Winsorized Mean ( 17 / 24 )65.59138888888890.371418331399609176.597069513834
Winsorized Mean ( 18 / 24 )65.66388888888890.36118017276286181.803692009422
Winsorized Mean ( 19 / 24 )65.40263888888890.319654791856449204.603968265428
Winsorized Mean ( 20 / 24 )65.27763888888890.296732498699832219.98816838368
Winsorized Mean ( 21 / 24 )65.39722222222220.254613013162953256.849488601621
Winsorized Mean ( 22 / 24 )65.18027777777780.207699408512986313.820237835211
Winsorized Mean ( 23 / 24 )65.55083333333330.157525335170751416.128829450063
Winsorized Mean ( 24 / 24 )65.42416666666670.135680016588326482.194565653494
Trimmed Mean ( 1 / 24 )65.99142857142860.579603787196993113.856103133087
Trimmed Mean ( 2 / 24 )65.92941176470590.561923624607988117.328065376678
Trimmed Mean ( 3 / 24 )65.88621212121210.5488084046751120.053212669397
Trimmed Mean ( 4 / 24 )65.852343750.537425970455111122.5328647483
Trimmed Mean ( 5 / 24 )65.81725806451610.52566641591657125.207272276953
Trimmed Mean ( 6 / 24 )65.77983333333330.511288308092868128.655070519206
Trimmed Mean ( 7 / 24 )65.74068965517240.494274897861827133.004305781173
Trimmed Mean ( 8 / 24 )65.71339285714280.478987926317057137.192169669941
Trimmed Mean ( 9 / 24 )65.67185185185190.465602640985195141.046991728597
Trimmed Mean ( 10 / 24 )65.62442307692310.450101162875789145.799274673354
Trimmed Mean ( 11 / 24 )65.56980.433849639146738151.134849688841
Trimmed Mean ( 12 / 24 )65.5250.418202629972974156.682419726137
Trimmed Mean ( 13 / 24 )65.47478260869560.398294521076864164.387856583295
Trimmed Mean ( 14 / 24 )65.44363636363640.38179171608669171.411881416454
Trimmed Mean ( 15 / 24 )65.41880952380950.363934207143311179.754494740443
Trimmed Mean ( 16 / 24 )65.391250.342918691772068190.690246898132
Trimmed Mean ( 17 / 24 )65.3689473684210.325576584386326200.779019448324
Trimmed Mean ( 18 / 24 )65.34277777777780.303532015285622215.274746936631
Trimmed Mean ( 19 / 24 )65.3050.275283114677202237.228498655201
Trimmed Mean ( 20 / 24 )65.29343750.249937737962603261.23881104249
Trimmed Mean ( 21 / 24 )65.29533333333330.221180081274265295.213443078387
Trimmed Mean ( 22 / 24 )65.28285714285710.195067385686147334.668232278941
Trimmed Mean ( 23 / 24 )65.29576923076920.175462617607041372.134931766508
Trimmed Mean ( 24 / 24 )65.26250.165592097497505394.116029606928
Median64.975
Midrange69.15
Midmean - Weighted Average at Xnp65.368947368421
Midmean - Weighted Average at X(n+1)p65.4651351351351
Midmean - Empirical Distribution Function65.368947368421
Midmean - Empirical Distribution Function - Averaging65.4651351351351
Midmean - Empirical Distribution Function - Interpolation65.4651351351351
Midmean - Closest Observation65.368947368421
Midmean - True Basic - Statistics Graphics Toolkit65.4651351351351
Midmean - MS Excel (old versions)65.368947368421
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')