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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 03 Mar 2016 13:47:41 +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/2016/Mar/03/t1457013310kwixt87vw157y8c.htm/, Retrieved Fri, 03 May 2024 09:33:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293300, Retrieved Fri, 03 May 2024 09:33:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-03 13:47:41] [d0e43a2339caadb8d5bf1f89f27a021a] [Current]
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Dataseries X:
86,88
90,65
90,68
89,64
102,62
101,84
92,51
94,29
94,68
96,94
94,03
89,65
84,9
89,07
89,8
93,22
92,23
98,41
96,63
89,8
90
92,13
93,27
90,81
85,42
88,28
88,73
90,18
92,74
96,13
94,85
94,25
96,94
101,22
98,71
95,51
93,91
98,17
97,59
99,64
107,88
108,49
100,25
99,27
101,73
101,25
97,09
94,74
94,53
93,48
96,05
106,22
98,33
99,86
93,78
88,96
83,77
89,46
86,78
88,4
87,19
92,23
95,99
104,75
105,63
108,71
96,4
93,31
93,77
98,7
95,04
95,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293300&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]1 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=293300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293300&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean94.9250.669018007154302141.887062806826
Geometric Mean94.7600016378231
Harmonic Mean94.5973072538885
Quadratic Mean95.0922403073283
Winsorized Mean ( 1 / 24 )94.93763888888890.664623203082563142.844304033567
Winsorized Mean ( 2 / 24 )94.93513888888890.656827569984935144.535861810835
Winsorized Mean ( 3 / 24 )94.92263888888890.627465652660139151.27941822228
Winsorized Mean ( 4 / 24 )94.89541666666670.618286001551384153.481425147194
Winsorized Mean ( 5 / 24 )94.85583333333330.599806070315632158.144170303942
Winsorized Mean ( 6 / 24 )94.76916666666670.54524831567218173.809187378847
Winsorized Mean ( 7 / 24 )94.7050.5283818715578179.235899446713
Winsorized Mean ( 8 / 24 )94.72944444444450.519999657250131182.172128622919
Winsorized Mean ( 9 / 24 )94.69819444444450.5041765830084187.827435140649
Winsorized Mean ( 10 / 24 )94.70930555555550.500978281087744189.048725525424
Winsorized Mean ( 11 / 24 )94.62069444444450.465378013109383203.320079116425
Winsorized Mean ( 12 / 24 )94.58569444444440.449804636186744210.281724186532
Winsorized Mean ( 13 / 24 )94.54777777777780.443028382808895213.41246169901
Winsorized Mean ( 14 / 24 )94.5050.427014053123484221.315901218528
Winsorized Mean ( 15 / 24 )94.38833333333330.409157499204071230.68948636392
Winsorized Mean ( 16 / 24 )94.43055555555560.40186482794701234.980891554927
Winsorized Mean ( 17 / 24 )94.40458333333330.385141781176726245.11644269001
Winsorized Mean ( 18 / 24 )94.50208333333330.364364246714791259.361570695781
Winsorized Mean ( 19 / 24 )94.46777777777780.356975384262795264.63387096807
Winsorized Mean ( 20 / 24 )94.34277777777780.328540199733982287.157485915473
Winsorized Mean ( 21 / 24 )94.58194444444440.252319260751534374.850275649713
Winsorized Mean ( 22 / 24 )94.56666666666670.241770659185916391.142030985435
Winsorized Mean ( 23 / 24 )94.56666666666670.241770659185916391.142030985435
Winsorized Mean ( 24 / 24 )94.55666666666670.214986624761381439.825811357415
Trimmed Mean ( 1 / 24 )94.88742857142860.639211460577738148.444504555138
Trimmed Mean ( 2 / 24 )94.83426470588230.608782133050367155.777017026937
Trimmed Mean ( 3 / 24 )94.77924242424240.577250468218569164.190845469103
Trimmed Mean ( 4 / 24 )94.725468750.553318314559136171.195252818396
Trimmed Mean ( 5 / 24 )94.67612903225810.527867172912806179.35597038518
Trimmed Mean ( 6 / 24 )94.6330.503152227304827188.080256559548
Trimmed Mean ( 7 / 24 )94.60482758620690.489451724901479193.287351485481
Trimmed Mean ( 8 / 24 )94.58642857142860.477115482533809198.246403719934
Trimmed Mean ( 9 / 24 )94.56259259259260.463846539086867203.866116536623
Trimmed Mean ( 10 / 24 )94.54173076923080.451090744546509209.58472749042
Trimmed Mean ( 11 / 24 )94.51760.435687733148785216.938859666547
Trimmed Mean ( 12 / 24 )94.50354166666670.424545594539025222.599275277557
Trimmed Mean ( 13 / 24 )94.49282608695650.413695570939343228.411500448022
Trimmed Mean ( 14 / 24 )94.48590909090910.401055467709762235.593120399214
Trimmed Mean ( 15 / 24 )94.48357142857140.388177615007741243.402936634271
Trimmed Mean ( 16 / 24 )94.4950.375252393695708251.817181149352
Trimmed Mean ( 17 / 24 )94.50263157894740.359568590134698262.822265825682
Trimmed Mean ( 18 / 24 )94.51416666666670.342520622713621275.937156477989
Trimmed Mean ( 19 / 24 )94.51558823529410.324753078056291291.038313789011
Trimmed Mean ( 20 / 24 )94.521250.301648277747018313.349211558475
Trimmed Mean ( 21 / 24 )94.54266666666670.277632409472079340.53180911566
Trimmed Mean ( 22 / 24 )94.53785714285710.269108049120209351.300741289339
Trimmed Mean ( 23 / 24 )94.53423076923080.259146630947348364.790506531562
Trimmed Mean ( 24 / 24 )94.530.242848434870066389.25513376513
Median94.41
Midrange96.24
Midmean - Weighted Average at Xnp94.3970270270271
Midmean - Weighted Average at X(n+1)p94.5141666666667
Midmean - Empirical Distribution Function94.3970270270271
Midmean - Empirical Distribution Function - Averaging94.5141666666667
Midmean - Empirical Distribution Function - Interpolation94.5141666666667
Midmean - Closest Observation94.3970270270271
Midmean - True Basic - Statistics Graphics Toolkit94.5141666666667
Midmean - MS Excel (old versions)94.5026315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 94.925 & 0.669018007154302 & 141.887062806826 \tabularnewline
Geometric Mean & 94.7600016378231 &  &  \tabularnewline
Harmonic Mean & 94.5973072538885 &  &  \tabularnewline
Quadratic Mean & 95.0922403073283 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 94.9376388888889 & 0.664623203082563 & 142.844304033567 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 94.9351388888889 & 0.656827569984935 & 144.535861810835 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 94.9226388888889 & 0.627465652660139 & 151.27941822228 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 94.8954166666667 & 0.618286001551384 & 153.481425147194 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 94.8558333333333 & 0.599806070315632 & 158.144170303942 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 94.7691666666667 & 0.54524831567218 & 173.809187378847 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 94.705 & 0.5283818715578 & 179.235899446713 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 94.7294444444445 & 0.519999657250131 & 182.172128622919 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 94.6981944444445 & 0.5041765830084 & 187.827435140649 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 94.7093055555555 & 0.500978281087744 & 189.048725525424 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 94.6206944444445 & 0.465378013109383 & 203.320079116425 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 94.5856944444444 & 0.449804636186744 & 210.281724186532 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 94.5477777777778 & 0.443028382808895 & 213.41246169901 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 94.505 & 0.427014053123484 & 221.315901218528 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 94.3883333333333 & 0.409157499204071 & 230.68948636392 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 94.4305555555556 & 0.40186482794701 & 234.980891554927 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 94.4045833333333 & 0.385141781176726 & 245.11644269001 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 94.5020833333333 & 0.364364246714791 & 259.361570695781 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 94.4677777777778 & 0.356975384262795 & 264.63387096807 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 94.3427777777778 & 0.328540199733982 & 287.157485915473 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 94.5819444444444 & 0.252319260751534 & 374.850275649713 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 94.5666666666667 & 0.241770659185916 & 391.142030985435 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 94.5666666666667 & 0.241770659185916 & 391.142030985435 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 94.5566666666667 & 0.214986624761381 & 439.825811357415 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 94.8874285714286 & 0.639211460577738 & 148.444504555138 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 94.8342647058823 & 0.608782133050367 & 155.777017026937 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 94.7792424242424 & 0.577250468218569 & 164.190845469103 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 94.72546875 & 0.553318314559136 & 171.195252818396 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 94.6761290322581 & 0.527867172912806 & 179.35597038518 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 94.633 & 0.503152227304827 & 188.080256559548 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 94.6048275862069 & 0.489451724901479 & 193.287351485481 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 94.5864285714286 & 0.477115482533809 & 198.246403719934 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 94.5625925925926 & 0.463846539086867 & 203.866116536623 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 94.5417307692308 & 0.451090744546509 & 209.58472749042 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 94.5176 & 0.435687733148785 & 216.938859666547 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 94.5035416666667 & 0.424545594539025 & 222.599275277557 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 94.4928260869565 & 0.413695570939343 & 228.411500448022 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 94.4859090909091 & 0.401055467709762 & 235.593120399214 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 94.4835714285714 & 0.388177615007741 & 243.402936634271 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 94.495 & 0.375252393695708 & 251.817181149352 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 94.5026315789474 & 0.359568590134698 & 262.822265825682 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 94.5141666666667 & 0.342520622713621 & 275.937156477989 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 94.5155882352941 & 0.324753078056291 & 291.038313789011 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 94.52125 & 0.301648277747018 & 313.349211558475 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 94.5426666666667 & 0.277632409472079 & 340.53180911566 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 94.5378571428571 & 0.269108049120209 & 351.300741289339 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 94.5342307692308 & 0.259146630947348 & 364.790506531562 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 94.53 & 0.242848434870066 & 389.25513376513 \tabularnewline
Median & 94.41 &  &  \tabularnewline
Midrange & 96.24 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 94.3970270270271 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 94.5141666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 94.3970270270271 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 94.5141666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 94.5141666666667 &  &  \tabularnewline
Midmean - Closest Observation & 94.3970270270271 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 94.5141666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 94.5026315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293300&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]94.925[/C][C]0.669018007154302[/C][C]141.887062806826[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]94.7600016378231[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]94.5973072538885[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]95.0922403073283[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]94.9376388888889[/C][C]0.664623203082563[/C][C]142.844304033567[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]94.9351388888889[/C][C]0.656827569984935[/C][C]144.535861810835[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]94.9226388888889[/C][C]0.627465652660139[/C][C]151.27941822228[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]94.8954166666667[/C][C]0.618286001551384[/C][C]153.481425147194[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]94.8558333333333[/C][C]0.599806070315632[/C][C]158.144170303942[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]94.7691666666667[/C][C]0.54524831567218[/C][C]173.809187378847[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]94.705[/C][C]0.5283818715578[/C][C]179.235899446713[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]94.7294444444445[/C][C]0.519999657250131[/C][C]182.172128622919[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]94.6981944444445[/C][C]0.5041765830084[/C][C]187.827435140649[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]94.7093055555555[/C][C]0.500978281087744[/C][C]189.048725525424[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]94.6206944444445[/C][C]0.465378013109383[/C][C]203.320079116425[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]94.5856944444444[/C][C]0.449804636186744[/C][C]210.281724186532[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]94.5477777777778[/C][C]0.443028382808895[/C][C]213.41246169901[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]94.505[/C][C]0.427014053123484[/C][C]221.315901218528[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]94.3883333333333[/C][C]0.409157499204071[/C][C]230.68948636392[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]94.4305555555556[/C][C]0.40186482794701[/C][C]234.980891554927[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]94.4045833333333[/C][C]0.385141781176726[/C][C]245.11644269001[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]94.5020833333333[/C][C]0.364364246714791[/C][C]259.361570695781[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]94.4677777777778[/C][C]0.356975384262795[/C][C]264.63387096807[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]94.3427777777778[/C][C]0.328540199733982[/C][C]287.157485915473[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]94.5819444444444[/C][C]0.252319260751534[/C][C]374.850275649713[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]94.5666666666667[/C][C]0.241770659185916[/C][C]391.142030985435[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]94.5666666666667[/C][C]0.241770659185916[/C][C]391.142030985435[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]94.5566666666667[/C][C]0.214986624761381[/C][C]439.825811357415[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]94.8874285714286[/C][C]0.639211460577738[/C][C]148.444504555138[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]94.8342647058823[/C][C]0.608782133050367[/C][C]155.777017026937[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]94.7792424242424[/C][C]0.577250468218569[/C][C]164.190845469103[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]94.72546875[/C][C]0.553318314559136[/C][C]171.195252818396[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]94.6761290322581[/C][C]0.527867172912806[/C][C]179.35597038518[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]94.633[/C][C]0.503152227304827[/C][C]188.080256559548[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]94.6048275862069[/C][C]0.489451724901479[/C][C]193.287351485481[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]94.5864285714286[/C][C]0.477115482533809[/C][C]198.246403719934[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]94.5625925925926[/C][C]0.463846539086867[/C][C]203.866116536623[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]94.5417307692308[/C][C]0.451090744546509[/C][C]209.58472749042[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]94.5176[/C][C]0.435687733148785[/C][C]216.938859666547[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]94.5035416666667[/C][C]0.424545594539025[/C][C]222.599275277557[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]94.4928260869565[/C][C]0.413695570939343[/C][C]228.411500448022[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]94.4859090909091[/C][C]0.401055467709762[/C][C]235.593120399214[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]94.4835714285714[/C][C]0.388177615007741[/C][C]243.402936634271[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]94.495[/C][C]0.375252393695708[/C][C]251.817181149352[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]94.5026315789474[/C][C]0.359568590134698[/C][C]262.822265825682[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]94.5141666666667[/C][C]0.342520622713621[/C][C]275.937156477989[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]94.5155882352941[/C][C]0.324753078056291[/C][C]291.038313789011[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]94.52125[/C][C]0.301648277747018[/C][C]313.349211558475[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]94.5426666666667[/C][C]0.277632409472079[/C][C]340.53180911566[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]94.5378571428571[/C][C]0.269108049120209[/C][C]351.300741289339[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]94.5342307692308[/C][C]0.259146630947348[/C][C]364.790506531562[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]94.53[/C][C]0.242848434870066[/C][C]389.25513376513[/C][/ROW]
[ROW][C]Median[/C][C]94.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]94.3970270270271[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]94.5141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]94.3970270270271[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]94.5141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]94.5141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]94.3970270270271[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]94.5141666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]94.5026315789474[/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=293300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293300&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 Mean94.9250.669018007154302141.887062806826
Geometric Mean94.7600016378231
Harmonic Mean94.5973072538885
Quadratic Mean95.0922403073283
Winsorized Mean ( 1 / 24 )94.93763888888890.664623203082563142.844304033567
Winsorized Mean ( 2 / 24 )94.93513888888890.656827569984935144.535861810835
Winsorized Mean ( 3 / 24 )94.92263888888890.627465652660139151.27941822228
Winsorized Mean ( 4 / 24 )94.89541666666670.618286001551384153.481425147194
Winsorized Mean ( 5 / 24 )94.85583333333330.599806070315632158.144170303942
Winsorized Mean ( 6 / 24 )94.76916666666670.54524831567218173.809187378847
Winsorized Mean ( 7 / 24 )94.7050.5283818715578179.235899446713
Winsorized Mean ( 8 / 24 )94.72944444444450.519999657250131182.172128622919
Winsorized Mean ( 9 / 24 )94.69819444444450.5041765830084187.827435140649
Winsorized Mean ( 10 / 24 )94.70930555555550.500978281087744189.048725525424
Winsorized Mean ( 11 / 24 )94.62069444444450.465378013109383203.320079116425
Winsorized Mean ( 12 / 24 )94.58569444444440.449804636186744210.281724186532
Winsorized Mean ( 13 / 24 )94.54777777777780.443028382808895213.41246169901
Winsorized Mean ( 14 / 24 )94.5050.427014053123484221.315901218528
Winsorized Mean ( 15 / 24 )94.38833333333330.409157499204071230.68948636392
Winsorized Mean ( 16 / 24 )94.43055555555560.40186482794701234.980891554927
Winsorized Mean ( 17 / 24 )94.40458333333330.385141781176726245.11644269001
Winsorized Mean ( 18 / 24 )94.50208333333330.364364246714791259.361570695781
Winsorized Mean ( 19 / 24 )94.46777777777780.356975384262795264.63387096807
Winsorized Mean ( 20 / 24 )94.34277777777780.328540199733982287.157485915473
Winsorized Mean ( 21 / 24 )94.58194444444440.252319260751534374.850275649713
Winsorized Mean ( 22 / 24 )94.56666666666670.241770659185916391.142030985435
Winsorized Mean ( 23 / 24 )94.56666666666670.241770659185916391.142030985435
Winsorized Mean ( 24 / 24 )94.55666666666670.214986624761381439.825811357415
Trimmed Mean ( 1 / 24 )94.88742857142860.639211460577738148.444504555138
Trimmed Mean ( 2 / 24 )94.83426470588230.608782133050367155.777017026937
Trimmed Mean ( 3 / 24 )94.77924242424240.577250468218569164.190845469103
Trimmed Mean ( 4 / 24 )94.725468750.553318314559136171.195252818396
Trimmed Mean ( 5 / 24 )94.67612903225810.527867172912806179.35597038518
Trimmed Mean ( 6 / 24 )94.6330.503152227304827188.080256559548
Trimmed Mean ( 7 / 24 )94.60482758620690.489451724901479193.287351485481
Trimmed Mean ( 8 / 24 )94.58642857142860.477115482533809198.246403719934
Trimmed Mean ( 9 / 24 )94.56259259259260.463846539086867203.866116536623
Trimmed Mean ( 10 / 24 )94.54173076923080.451090744546509209.58472749042
Trimmed Mean ( 11 / 24 )94.51760.435687733148785216.938859666547
Trimmed Mean ( 12 / 24 )94.50354166666670.424545594539025222.599275277557
Trimmed Mean ( 13 / 24 )94.49282608695650.413695570939343228.411500448022
Trimmed Mean ( 14 / 24 )94.48590909090910.401055467709762235.593120399214
Trimmed Mean ( 15 / 24 )94.48357142857140.388177615007741243.402936634271
Trimmed Mean ( 16 / 24 )94.4950.375252393695708251.817181149352
Trimmed Mean ( 17 / 24 )94.50263157894740.359568590134698262.822265825682
Trimmed Mean ( 18 / 24 )94.51416666666670.342520622713621275.937156477989
Trimmed Mean ( 19 / 24 )94.51558823529410.324753078056291291.038313789011
Trimmed Mean ( 20 / 24 )94.521250.301648277747018313.349211558475
Trimmed Mean ( 21 / 24 )94.54266666666670.277632409472079340.53180911566
Trimmed Mean ( 22 / 24 )94.53785714285710.269108049120209351.300741289339
Trimmed Mean ( 23 / 24 )94.53423076923080.259146630947348364.790506531562
Trimmed Mean ( 24 / 24 )94.530.242848434870066389.25513376513
Median94.41
Midrange96.24
Midmean - Weighted Average at Xnp94.3970270270271
Midmean - Weighted Average at X(n+1)p94.5141666666667
Midmean - Empirical Distribution Function94.3970270270271
Midmean - Empirical Distribution Function - Averaging94.5141666666667
Midmean - Empirical Distribution Function - Interpolation94.5141666666667
Midmean - Closest Observation94.3970270270271
Midmean - True Basic - Statistics Graphics Toolkit94.5141666666667
Midmean - MS Excel (old versions)94.5026315789474
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')