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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Dec 2008 08:45:07 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/15/t1229356237b31pso5223i5mf2.htm/, Retrieved Wed, 15 May 2024 00:09:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33717, Retrieved Wed, 15 May 2024 00:09:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-15 15:45:07] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
132,69
124,05
109,65
102,79
94,09
92,23
90,6
92,6
81,71
76,36
71,44
75,26
70,3
67,68
67,65
61,92
58,34
55,04
62,5
59,44
60,03
64,24
74,33
74,41
69,75
72,03
68,18
63,01
61,71
63,52
57,42
56,12
59,15
63,77
63,96
57,81
55,3
51,8
53,26
53,38
45,85
44,23
40,22
44,61
49,14
42,94
41,84
37,75
35,54
37,13
33,19
32,67
30,52
30,7
29,59
28,76
29,08
26,95
29,58
28,24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33717&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33717&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33717&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean60.13416666666673.0416842577465219.7700226489708
Geometric Mean55.8238340458235
Harmonic Mean51.7212294952947
Quadratic Mean64.5133842314911
Winsorized Mean ( 1 / 20 )60.01166666666672.9824135201035520.1218463711173
Winsorized Mean ( 2 / 20 )59.5492.8191877932410521.1227503690133
Winsorized Mean ( 3 / 20 )59.2222.7178568513457021.7899629153306
Winsorized Mean ( 4 / 20 )58.67533333333332.5645347863566122.8795232747427
Winsorized Mean ( 5 / 20 )58.5522.5357115561603623.0909544335796
Winsorized Mean ( 6 / 20 )58.6082.5094759823944723.3546765982904
Winsorized Mean ( 7 / 20 )58.43883333333332.4628376345627123.7282525300168
Winsorized Mean ( 8 / 20 )57.51616666666672.1677794503343526.532296289549
Winsorized Mean ( 9 / 20 )56.79166666666672.0099697578559028.2549856507534
Winsorized Mean ( 10 / 20 )571.9034953575649229.9449114879473
Winsorized Mean ( 11 / 20 )57.13566666666671.8233406877633931.3357054170454
Winsorized Mean ( 12 / 20 )57.24366666666671.7978424760635331.840201479723
Winsorized Mean ( 13 / 20 )57.28051.6222739224244935.3087719701457
Winsorized Mean ( 14 / 20 )57.52083333333331.5346376169468837.4817042786749
Winsorized Mean ( 15 / 20 )57.51083333333331.4439855448606439.8278456027645
Winsorized Mean ( 16 / 20 )57.70816666666671.3637549420266442.3156425603183
Winsorized Mean ( 17 / 20 )57.3711.2804920201076344.803871558042
Winsorized Mean ( 18 / 20 )57.5931.1966764780927048.1274605579226
Winsorized Mean ( 19 / 20 )58.62533333333331.0266953312456057.1010031400537
Winsorized Mean ( 20 / 20 )58.37533333333330.72518177992553780.4975179317487
Trimmed Mean ( 1 / 20 )59.45534482758622.8236781028946821.0559924541809
Trimmed Mean ( 2 / 20 )58.85928571428572.6231052018198722.4387819723929
Trimmed Mean ( 3 / 20 )58.47611111111112.4867858377234823.5147354565292
Trimmed Mean ( 4 / 20 )58.18923076923082.3676723403319524.5765555385390
Trimmed Mean ( 5 / 20 )58.04342.2819931068239125.4353967268486
Trimmed Mean ( 6 / 20 )57.916252.1832926737795426.5270207222103
Trimmed Mean ( 7 / 20 )57.76586956521742.0647487495227527.9771907252975
Trimmed Mean ( 8 / 20 )57.63477272727271.9253236593627429.9351085449961
Trimmed Mean ( 9 / 20 )57.65595238095241.8369236850777231.3872333670263
Trimmed Mean ( 10 / 20 )57.81.7652759644795632.7427558993818
Trimmed Mean ( 11 / 20 )57.92631578947371.6993650567687934.0870347773397
Trimmed Mean ( 12 / 20 )58.04611111111111.6319211717354435.5691880934315
Trimmed Mean ( 13 / 20 )58.16411764705881.5449357852952237.6482428594561
Trimmed Mean ( 14 / 20 )58.29156251.4767163407654439.4737708866858
Trimmed Mean ( 15 / 20 )58.40166666666671.4057953190017441.543506282364
Trimmed Mean ( 16 / 20 )58.52892857142861.3304828994928143.9907409510791
Trimmed Mean ( 17 / 20 )58.64730769230771.2450044865773147.1061014836478
Trimmed Mean ( 18 / 20 )58.8351.1410964406905051.5600591694054
Trimmed Mean ( 19 / 20 )59.02318181818181.0098395540048658.4480787904427
Trimmed Mean ( 20 / 20 )59.0860.88697932094805666.6148562932058
Median59.295
Midrange79.82
Midmean - Weighted Average at Xnp57.8674193548387
Midmean - Weighted Average at X(n+1)p58.4016666666667
Midmean - Empirical Distribution Function57.8674193548387
Midmean - Empirical Distribution Function - Averaging58.4016666666667
Midmean - Empirical Distribution Function - Interpolation58.4016666666667
Midmean - Closest Observation57.8674193548387
Midmean - True Basic - Statistics Graphics Toolkit58.4016666666667
Midmean - MS Excel (old versions)58.2915625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 60.1341666666667 & 3.04168425774652 & 19.7700226489708 \tabularnewline
Geometric Mean & 55.8238340458235 &  &  \tabularnewline
Harmonic Mean & 51.7212294952947 &  &  \tabularnewline
Quadratic Mean & 64.5133842314911 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 60.0116666666667 & 2.98241352010355 & 20.1218463711173 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 59.549 & 2.81918779324105 & 21.1227503690133 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 59.222 & 2.71785685134570 & 21.7899629153306 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 58.6753333333333 & 2.56453478635661 & 22.8795232747427 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 58.552 & 2.53571155616036 & 23.0909544335796 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 58.608 & 2.50947598239447 & 23.3546765982904 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 58.4388333333333 & 2.46283763456271 & 23.7282525300168 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 57.5161666666667 & 2.16777945033435 & 26.532296289549 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 56.7916666666667 & 2.00996975785590 & 28.2549856507534 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 57 & 1.90349535756492 & 29.9449114879473 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 57.1356666666667 & 1.82334068776339 & 31.3357054170454 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 57.2436666666667 & 1.79784247606353 & 31.840201479723 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 57.2805 & 1.62227392242449 & 35.3087719701457 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 57.5208333333333 & 1.53463761694688 & 37.4817042786749 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 57.5108333333333 & 1.44398554486064 & 39.8278456027645 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 57.7081666666667 & 1.36375494202664 & 42.3156425603183 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 57.371 & 1.28049202010763 & 44.803871558042 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 57.593 & 1.19667647809270 & 48.1274605579226 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 58.6253333333333 & 1.02669533124560 & 57.1010031400537 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 58.3753333333333 & 0.725181779925537 & 80.4975179317487 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 59.4553448275862 & 2.82367810289468 & 21.0559924541809 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 58.8592857142857 & 2.62310520181987 & 22.4387819723929 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 58.4761111111111 & 2.48678583772348 & 23.5147354565292 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 58.1892307692308 & 2.36767234033195 & 24.5765555385390 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 58.0434 & 2.28199310682391 & 25.4353967268486 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 57.91625 & 2.18329267377954 & 26.5270207222103 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 57.7658695652174 & 2.06474874952275 & 27.9771907252975 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 57.6347727272727 & 1.92532365936274 & 29.9351085449961 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 57.6559523809524 & 1.83692368507772 & 31.3872333670263 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 57.8 & 1.76527596447956 & 32.7427558993818 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 57.9263157894737 & 1.69936505676879 & 34.0870347773397 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 58.0461111111111 & 1.63192117173544 & 35.5691880934315 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 58.1641176470588 & 1.54493578529522 & 37.6482428594561 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 58.2915625 & 1.47671634076544 & 39.4737708866858 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 58.4016666666667 & 1.40579531900174 & 41.543506282364 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 58.5289285714286 & 1.33048289949281 & 43.9907409510791 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 58.6473076923077 & 1.24500448657731 & 47.1061014836478 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 58.835 & 1.14109644069050 & 51.5600591694054 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 59.0231818181818 & 1.00983955400486 & 58.4480787904427 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 59.086 & 0.886979320948056 & 66.6148562932058 \tabularnewline
Median & 59.295 &  &  \tabularnewline
Midrange & 79.82 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 57.8674193548387 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 58.4016666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 57.8674193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 58.4016666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 58.4016666666667 &  &  \tabularnewline
Midmean - Closest Observation & 57.8674193548387 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 58.4016666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 58.2915625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33717&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]60.1341666666667[/C][C]3.04168425774652[/C][C]19.7700226489708[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]55.8238340458235[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]51.7212294952947[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]64.5133842314911[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]60.0116666666667[/C][C]2.98241352010355[/C][C]20.1218463711173[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]59.549[/C][C]2.81918779324105[/C][C]21.1227503690133[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]59.222[/C][C]2.71785685134570[/C][C]21.7899629153306[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]58.6753333333333[/C][C]2.56453478635661[/C][C]22.8795232747427[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]58.552[/C][C]2.53571155616036[/C][C]23.0909544335796[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]58.608[/C][C]2.50947598239447[/C][C]23.3546765982904[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]58.4388333333333[/C][C]2.46283763456271[/C][C]23.7282525300168[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]57.5161666666667[/C][C]2.16777945033435[/C][C]26.532296289549[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]56.7916666666667[/C][C]2.00996975785590[/C][C]28.2549856507534[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]57[/C][C]1.90349535756492[/C][C]29.9449114879473[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]57.1356666666667[/C][C]1.82334068776339[/C][C]31.3357054170454[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]57.2436666666667[/C][C]1.79784247606353[/C][C]31.840201479723[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]57.2805[/C][C]1.62227392242449[/C][C]35.3087719701457[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]57.5208333333333[/C][C]1.53463761694688[/C][C]37.4817042786749[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]57.5108333333333[/C][C]1.44398554486064[/C][C]39.8278456027645[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]57.7081666666667[/C][C]1.36375494202664[/C][C]42.3156425603183[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]57.371[/C][C]1.28049202010763[/C][C]44.803871558042[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]57.593[/C][C]1.19667647809270[/C][C]48.1274605579226[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]58.6253333333333[/C][C]1.02669533124560[/C][C]57.1010031400537[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]58.3753333333333[/C][C]0.725181779925537[/C][C]80.4975179317487[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]59.4553448275862[/C][C]2.82367810289468[/C][C]21.0559924541809[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]58.8592857142857[/C][C]2.62310520181987[/C][C]22.4387819723929[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]58.4761111111111[/C][C]2.48678583772348[/C][C]23.5147354565292[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]58.1892307692308[/C][C]2.36767234033195[/C][C]24.5765555385390[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]58.0434[/C][C]2.28199310682391[/C][C]25.4353967268486[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]57.91625[/C][C]2.18329267377954[/C][C]26.5270207222103[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]57.7658695652174[/C][C]2.06474874952275[/C][C]27.9771907252975[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]57.6347727272727[/C][C]1.92532365936274[/C][C]29.9351085449961[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]57.6559523809524[/C][C]1.83692368507772[/C][C]31.3872333670263[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]57.8[/C][C]1.76527596447956[/C][C]32.7427558993818[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]57.9263157894737[/C][C]1.69936505676879[/C][C]34.0870347773397[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]58.0461111111111[/C][C]1.63192117173544[/C][C]35.5691880934315[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]58.1641176470588[/C][C]1.54493578529522[/C][C]37.6482428594561[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]58.2915625[/C][C]1.47671634076544[/C][C]39.4737708866858[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]58.4016666666667[/C][C]1.40579531900174[/C][C]41.543506282364[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]58.5289285714286[/C][C]1.33048289949281[/C][C]43.9907409510791[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]58.6473076923077[/C][C]1.24500448657731[/C][C]47.1061014836478[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]58.835[/C][C]1.14109644069050[/C][C]51.5600591694054[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]59.0231818181818[/C][C]1.00983955400486[/C][C]58.4480787904427[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]59.086[/C][C]0.886979320948056[/C][C]66.6148562932058[/C][/ROW]
[ROW][C]Median[/C][C]59.295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]79.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]57.8674193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]58.4016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]57.8674193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]58.4016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]58.4016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]57.8674193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]58.4016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]58.2915625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33717&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33717&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 Mean60.13416666666673.0416842577465219.7700226489708
Geometric Mean55.8238340458235
Harmonic Mean51.7212294952947
Quadratic Mean64.5133842314911
Winsorized Mean ( 1 / 20 )60.01166666666672.9824135201035520.1218463711173
Winsorized Mean ( 2 / 20 )59.5492.8191877932410521.1227503690133
Winsorized Mean ( 3 / 20 )59.2222.7178568513457021.7899629153306
Winsorized Mean ( 4 / 20 )58.67533333333332.5645347863566122.8795232747427
Winsorized Mean ( 5 / 20 )58.5522.5357115561603623.0909544335796
Winsorized Mean ( 6 / 20 )58.6082.5094759823944723.3546765982904
Winsorized Mean ( 7 / 20 )58.43883333333332.4628376345627123.7282525300168
Winsorized Mean ( 8 / 20 )57.51616666666672.1677794503343526.532296289549
Winsorized Mean ( 9 / 20 )56.79166666666672.0099697578559028.2549856507534
Winsorized Mean ( 10 / 20 )571.9034953575649229.9449114879473
Winsorized Mean ( 11 / 20 )57.13566666666671.8233406877633931.3357054170454
Winsorized Mean ( 12 / 20 )57.24366666666671.7978424760635331.840201479723
Winsorized Mean ( 13 / 20 )57.28051.6222739224244935.3087719701457
Winsorized Mean ( 14 / 20 )57.52083333333331.5346376169468837.4817042786749
Winsorized Mean ( 15 / 20 )57.51083333333331.4439855448606439.8278456027645
Winsorized Mean ( 16 / 20 )57.70816666666671.3637549420266442.3156425603183
Winsorized Mean ( 17 / 20 )57.3711.2804920201076344.803871558042
Winsorized Mean ( 18 / 20 )57.5931.1966764780927048.1274605579226
Winsorized Mean ( 19 / 20 )58.62533333333331.0266953312456057.1010031400537
Winsorized Mean ( 20 / 20 )58.37533333333330.72518177992553780.4975179317487
Trimmed Mean ( 1 / 20 )59.45534482758622.8236781028946821.0559924541809
Trimmed Mean ( 2 / 20 )58.85928571428572.6231052018198722.4387819723929
Trimmed Mean ( 3 / 20 )58.47611111111112.4867858377234823.5147354565292
Trimmed Mean ( 4 / 20 )58.18923076923082.3676723403319524.5765555385390
Trimmed Mean ( 5 / 20 )58.04342.2819931068239125.4353967268486
Trimmed Mean ( 6 / 20 )57.916252.1832926737795426.5270207222103
Trimmed Mean ( 7 / 20 )57.76586956521742.0647487495227527.9771907252975
Trimmed Mean ( 8 / 20 )57.63477272727271.9253236593627429.9351085449961
Trimmed Mean ( 9 / 20 )57.65595238095241.8369236850777231.3872333670263
Trimmed Mean ( 10 / 20 )57.81.7652759644795632.7427558993818
Trimmed Mean ( 11 / 20 )57.92631578947371.6993650567687934.0870347773397
Trimmed Mean ( 12 / 20 )58.04611111111111.6319211717354435.5691880934315
Trimmed Mean ( 13 / 20 )58.16411764705881.5449357852952237.6482428594561
Trimmed Mean ( 14 / 20 )58.29156251.4767163407654439.4737708866858
Trimmed Mean ( 15 / 20 )58.40166666666671.4057953190017441.543506282364
Trimmed Mean ( 16 / 20 )58.52892857142861.3304828994928143.9907409510791
Trimmed Mean ( 17 / 20 )58.64730769230771.2450044865773147.1061014836478
Trimmed Mean ( 18 / 20 )58.8351.1410964406905051.5600591694054
Trimmed Mean ( 19 / 20 )59.02318181818181.0098395540048658.4480787904427
Trimmed Mean ( 20 / 20 )59.0860.88697932094805666.6148562932058
Median59.295
Midrange79.82
Midmean - Weighted Average at Xnp57.8674193548387
Midmean - Weighted Average at X(n+1)p58.4016666666667
Midmean - Empirical Distribution Function57.8674193548387
Midmean - Empirical Distribution Function - Averaging58.4016666666667
Midmean - Empirical Distribution Function - Interpolation58.4016666666667
Midmean - Closest Observation57.8674193548387
Midmean - True Basic - Statistics Graphics Toolkit58.4016666666667
Midmean - MS Excel (old versions)58.2915625
Number of observations60



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')