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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 10:55:56 -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/2012/Mar/07/t133113579928pmzi52vv2hvj4.htm/, Retrieved Mon, 29 Apr 2024 05:13:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163640, Retrieved Mon, 29 Apr 2024 05:13:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Prij...] [2012-03-07 15:55:56] [1f07dfe249cf12c76d4857e2b59f088a] [Current]
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Dataseries X:
92,8
90,61
88,49
88,33
87,7
87,33
87,33
87,33
85,47
86,1
86,1
86,13
83,31
83,31
83,55
84,11
84,11
77,59
77,59
76,44
72,71
72,9
72,39
72,46
72,48
72,48
72,48
72,3
72,3
72,3
71,14
71,14
68,99
68,42
68,42
69,28
65,22
70,21
70,21
71,2
68,94
68,94
68,93
68,93
68,93
68,93
59,94
61,04
60,2
60,2
60,12
60,25
58,03
62,37
62,16
62,16
62,16
62,16
62,29
64,39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163640&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163640&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163640&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean73.23051.2496313450724558.6016830393723
Geometric Mean72.6132675530843
Harmonic Mean72.0107736925263
Quadratic Mean73.8568836444286
Winsorized Mean ( 1 / 20 )73.22583333333331.2342396797623359.3286980916333
Winsorized Mean ( 2 / 20 )73.16116666666671.2171641601483160.1078877131515
Winsorized Mean ( 3 / 20 )73.15716666666671.2147387269163860.2246104825985
Winsorized Mean ( 4 / 20 )73.11516666666671.2059878734637560.6267842948293
Winsorized Mean ( 5 / 20 )73.08851.1989676308989860.9595272769782
Winsorized Mean ( 6 / 20 )73.16751.1849448633147661.7475987830533
Winsorized Mean ( 7 / 20 )73.29816666666671.162999616024863.0250996274653
Winsorized Mean ( 8 / 20 )73.13816666666671.1310541928218264.6637156122445
Winsorized Mean ( 9 / 20 )73.13366666666671.1301786261163964.7098299124402
Winsorized Mean ( 10 / 20 )73.13366666666671.1301786261163964.7098299124402
Winsorized Mean ( 11 / 20 )73.0421.1039995036026166.161261632498
Winsorized Mean ( 12 / 20 )72.7861.0505111534942569.2862705530507
Winsorized Mean ( 13 / 20 )73.22366666666670.98019290637607774.7033223668041
Winsorized Mean ( 14 / 20 )73.28666666666670.92653283185877579.0977547116617
Winsorized Mean ( 15 / 20 )74.02666666666670.8081979908828391.5947175095104
Winsorized Mean ( 16 / 20 )74.02666666666670.8081979908828391.5947175095104
Winsorized Mean ( 17 / 20 )72.55050.486982953390214148.979547425485
Winsorized Mean ( 18 / 20 )72.55050.486982953390214148.979547425485
Winsorized Mean ( 19 / 20 )72.18633333333330.424018905256671170.243195382142
Winsorized Mean ( 20 / 20 )71.00633333333330.238422661146962297.817048898575
Trimmed Mean ( 1 / 20 )73.15517241379311.2191304122081960.0060269854873
Trimmed Mean ( 2 / 20 )73.07946428571431.1998383933291560.9077561545127
Trimmed Mean ( 3 / 20 )73.03407407407411.1864100468798461.5588803096768
Trimmed Mean ( 4 / 20 )72.98673076923081.1698942443970962.3874603356517
Trimmed Mean ( 5 / 20 )72.94821.1516822722984563.3405599396912
Trimmed Mean ( 6 / 20 )72.9131251.1301540783460964.5160924488311
Trimmed Mean ( 7 / 20 )72.85782608695651.1060907316193665.8696651225798
Trimmed Mean ( 8 / 20 )72.77204545454541.0803606485938767.3590301065304
Trimmed Mean ( 9 / 20 )72.70666666666671.0551221597381968.9082927466027
Trimmed Mean ( 10 / 20 )72.63551.0210153286224771.140459857736
Trimmed Mean ( 11 / 20 )72.55684210526320.97442138101321474.461463509573
Trimmed Mean ( 12 / 20 )72.48333333333330.91834936465135978.9278417597107
Trimmed Mean ( 13 / 20 )72.43882352941180.85755235204007384.4716049779159
Trimmed Mean ( 14 / 20 )72.3256250.79292765218066591.213397339712
Trimmed Mean ( 15 / 20 )72.18833333333330.716522907260021100.748116496905
Trimmed Mean ( 16 / 20 )71.92571428571430.637081105983302112.89883440304
Trimmed Mean ( 17 / 20 )71.62269230769230.500092470739103143.218897500774
Trimmed Mean ( 18 / 20 )71.486250.464800803718842153.7997555685
Trimmed Mean ( 19 / 20 )71.3250.40262060923201177.151885334561
Trimmed Mean ( 20 / 20 )71.1890.334909964334486212.561606345344
Median71.75
Midrange75.415
Midmean - Weighted Average at Xnp71.9635483870968
Midmean - Weighted Average at X(n+1)p72.1883333333333
Midmean - Empirical Distribution Function71.9635483870968
Midmean - Empirical Distribution Function - Averaging72.1883333333333
Midmean - Empirical Distribution Function - Interpolation72.1883333333333
Midmean - Closest Observation71.9635483870968
Midmean - True Basic - Statistics Graphics Toolkit72.1883333333333
Midmean - MS Excel (old versions)72.325625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 73.2305 & 1.24963134507245 & 58.6016830393723 \tabularnewline
Geometric Mean & 72.6132675530843 &  &  \tabularnewline
Harmonic Mean & 72.0107736925263 &  &  \tabularnewline
Quadratic Mean & 73.8568836444286 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 73.2258333333333 & 1.23423967976233 & 59.3286980916333 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 73.1611666666667 & 1.21716416014831 & 60.1078877131515 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 73.1571666666667 & 1.21473872691638 & 60.2246104825985 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 73.1151666666667 & 1.20598787346375 & 60.6267842948293 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 73.0885 & 1.19896763089898 & 60.9595272769782 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 73.1675 & 1.18494486331476 & 61.7475987830533 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 73.2981666666667 & 1.1629996160248 & 63.0250996274653 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 73.1381666666667 & 1.13105419282182 & 64.6637156122445 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 73.1336666666667 & 1.13017862611639 & 64.7098299124402 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 73.1336666666667 & 1.13017862611639 & 64.7098299124402 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 73.042 & 1.10399950360261 & 66.161261632498 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 72.786 & 1.05051115349425 & 69.2862705530507 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 73.2236666666667 & 0.980192906376077 & 74.7033223668041 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 73.2866666666667 & 0.926532831858775 & 79.0977547116617 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 74.0266666666667 & 0.80819799088283 & 91.5947175095104 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 74.0266666666667 & 0.80819799088283 & 91.5947175095104 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 72.5505 & 0.486982953390214 & 148.979547425485 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 72.5505 & 0.486982953390214 & 148.979547425485 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 72.1863333333333 & 0.424018905256671 & 170.243195382142 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 71.0063333333333 & 0.238422661146962 & 297.817048898575 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 73.1551724137931 & 1.21913041220819 & 60.0060269854873 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 73.0794642857143 & 1.19983839332915 & 60.9077561545127 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 73.0340740740741 & 1.18641004687984 & 61.5588803096768 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 72.9867307692308 & 1.16989424439709 & 62.3874603356517 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 72.9482 & 1.15168227229845 & 63.3405599396912 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 72.913125 & 1.13015407834609 & 64.5160924488311 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 72.8578260869565 & 1.10609073161936 & 65.8696651225798 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 72.7720454545454 & 1.08036064859387 & 67.3590301065304 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 72.7066666666667 & 1.05512215973819 & 68.9082927466027 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 72.6355 & 1.02101532862247 & 71.140459857736 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 72.5568421052632 & 0.974421381013214 & 74.461463509573 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 72.4833333333333 & 0.918349364651359 & 78.9278417597107 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 72.4388235294118 & 0.857552352040073 & 84.4716049779159 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 72.325625 & 0.792927652180665 & 91.213397339712 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 72.1883333333333 & 0.716522907260021 & 100.748116496905 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 71.9257142857143 & 0.637081105983302 & 112.89883440304 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 71.6226923076923 & 0.500092470739103 & 143.218897500774 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 71.48625 & 0.464800803718842 & 153.7997555685 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 71.325 & 0.40262060923201 & 177.151885334561 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 71.189 & 0.334909964334486 & 212.561606345344 \tabularnewline
Median & 71.75 &  &  \tabularnewline
Midrange & 75.415 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 71.9635483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 72.1883333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 71.9635483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 72.1883333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 72.1883333333333 &  &  \tabularnewline
Midmean - Closest Observation & 71.9635483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 72.1883333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 72.325625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163640&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]73.2305[/C][C]1.24963134507245[/C][C]58.6016830393723[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]72.6132675530843[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]72.0107736925263[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]73.8568836444286[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]73.2258333333333[/C][C]1.23423967976233[/C][C]59.3286980916333[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]73.1611666666667[/C][C]1.21716416014831[/C][C]60.1078877131515[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]73.1571666666667[/C][C]1.21473872691638[/C][C]60.2246104825985[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]73.1151666666667[/C][C]1.20598787346375[/C][C]60.6267842948293[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]73.0885[/C][C]1.19896763089898[/C][C]60.9595272769782[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]73.1675[/C][C]1.18494486331476[/C][C]61.7475987830533[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]73.2981666666667[/C][C]1.1629996160248[/C][C]63.0250996274653[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]73.1381666666667[/C][C]1.13105419282182[/C][C]64.6637156122445[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]73.1336666666667[/C][C]1.13017862611639[/C][C]64.7098299124402[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]73.1336666666667[/C][C]1.13017862611639[/C][C]64.7098299124402[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]73.042[/C][C]1.10399950360261[/C][C]66.161261632498[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]72.786[/C][C]1.05051115349425[/C][C]69.2862705530507[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]73.2236666666667[/C][C]0.980192906376077[/C][C]74.7033223668041[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]73.2866666666667[/C][C]0.926532831858775[/C][C]79.0977547116617[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]74.0266666666667[/C][C]0.80819799088283[/C][C]91.5947175095104[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]74.0266666666667[/C][C]0.80819799088283[/C][C]91.5947175095104[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]72.5505[/C][C]0.486982953390214[/C][C]148.979547425485[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]72.5505[/C][C]0.486982953390214[/C][C]148.979547425485[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]72.1863333333333[/C][C]0.424018905256671[/C][C]170.243195382142[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]71.0063333333333[/C][C]0.238422661146962[/C][C]297.817048898575[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]73.1551724137931[/C][C]1.21913041220819[/C][C]60.0060269854873[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]73.0794642857143[/C][C]1.19983839332915[/C][C]60.9077561545127[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]73.0340740740741[/C][C]1.18641004687984[/C][C]61.5588803096768[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]72.9867307692308[/C][C]1.16989424439709[/C][C]62.3874603356517[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]72.9482[/C][C]1.15168227229845[/C][C]63.3405599396912[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]72.913125[/C][C]1.13015407834609[/C][C]64.5160924488311[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]72.8578260869565[/C][C]1.10609073161936[/C][C]65.8696651225798[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]72.7720454545454[/C][C]1.08036064859387[/C][C]67.3590301065304[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]72.7066666666667[/C][C]1.05512215973819[/C][C]68.9082927466027[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]72.6355[/C][C]1.02101532862247[/C][C]71.140459857736[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]72.5568421052632[/C][C]0.974421381013214[/C][C]74.461463509573[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]72.4833333333333[/C][C]0.918349364651359[/C][C]78.9278417597107[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]72.4388235294118[/C][C]0.857552352040073[/C][C]84.4716049779159[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]72.325625[/C][C]0.792927652180665[/C][C]91.213397339712[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]72.1883333333333[/C][C]0.716522907260021[/C][C]100.748116496905[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]71.9257142857143[/C][C]0.637081105983302[/C][C]112.89883440304[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]71.6226923076923[/C][C]0.500092470739103[/C][C]143.218897500774[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]71.48625[/C][C]0.464800803718842[/C][C]153.7997555685[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]71.325[/C][C]0.40262060923201[/C][C]177.151885334561[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]71.189[/C][C]0.334909964334486[/C][C]212.561606345344[/C][/ROW]
[ROW][C]Median[/C][C]71.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]75.415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]71.9635483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]72.1883333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]71.9635483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]72.1883333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]72.1883333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]71.9635483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]72.1883333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]72.325625[/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=163640&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163640&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 Mean73.23051.2496313450724558.6016830393723
Geometric Mean72.6132675530843
Harmonic Mean72.0107736925263
Quadratic Mean73.8568836444286
Winsorized Mean ( 1 / 20 )73.22583333333331.2342396797623359.3286980916333
Winsorized Mean ( 2 / 20 )73.16116666666671.2171641601483160.1078877131515
Winsorized Mean ( 3 / 20 )73.15716666666671.2147387269163860.2246104825985
Winsorized Mean ( 4 / 20 )73.11516666666671.2059878734637560.6267842948293
Winsorized Mean ( 5 / 20 )73.08851.1989676308989860.9595272769782
Winsorized Mean ( 6 / 20 )73.16751.1849448633147661.7475987830533
Winsorized Mean ( 7 / 20 )73.29816666666671.162999616024863.0250996274653
Winsorized Mean ( 8 / 20 )73.13816666666671.1310541928218264.6637156122445
Winsorized Mean ( 9 / 20 )73.13366666666671.1301786261163964.7098299124402
Winsorized Mean ( 10 / 20 )73.13366666666671.1301786261163964.7098299124402
Winsorized Mean ( 11 / 20 )73.0421.1039995036026166.161261632498
Winsorized Mean ( 12 / 20 )72.7861.0505111534942569.2862705530507
Winsorized Mean ( 13 / 20 )73.22366666666670.98019290637607774.7033223668041
Winsorized Mean ( 14 / 20 )73.28666666666670.92653283185877579.0977547116617
Winsorized Mean ( 15 / 20 )74.02666666666670.8081979908828391.5947175095104
Winsorized Mean ( 16 / 20 )74.02666666666670.8081979908828391.5947175095104
Winsorized Mean ( 17 / 20 )72.55050.486982953390214148.979547425485
Winsorized Mean ( 18 / 20 )72.55050.486982953390214148.979547425485
Winsorized Mean ( 19 / 20 )72.18633333333330.424018905256671170.243195382142
Winsorized Mean ( 20 / 20 )71.00633333333330.238422661146962297.817048898575
Trimmed Mean ( 1 / 20 )73.15517241379311.2191304122081960.0060269854873
Trimmed Mean ( 2 / 20 )73.07946428571431.1998383933291560.9077561545127
Trimmed Mean ( 3 / 20 )73.03407407407411.1864100468798461.5588803096768
Trimmed Mean ( 4 / 20 )72.98673076923081.1698942443970962.3874603356517
Trimmed Mean ( 5 / 20 )72.94821.1516822722984563.3405599396912
Trimmed Mean ( 6 / 20 )72.9131251.1301540783460964.5160924488311
Trimmed Mean ( 7 / 20 )72.85782608695651.1060907316193665.8696651225798
Trimmed Mean ( 8 / 20 )72.77204545454541.0803606485938767.3590301065304
Trimmed Mean ( 9 / 20 )72.70666666666671.0551221597381968.9082927466027
Trimmed Mean ( 10 / 20 )72.63551.0210153286224771.140459857736
Trimmed Mean ( 11 / 20 )72.55684210526320.97442138101321474.461463509573
Trimmed Mean ( 12 / 20 )72.48333333333330.91834936465135978.9278417597107
Trimmed Mean ( 13 / 20 )72.43882352941180.85755235204007384.4716049779159
Trimmed Mean ( 14 / 20 )72.3256250.79292765218066591.213397339712
Trimmed Mean ( 15 / 20 )72.18833333333330.716522907260021100.748116496905
Trimmed Mean ( 16 / 20 )71.92571428571430.637081105983302112.89883440304
Trimmed Mean ( 17 / 20 )71.62269230769230.500092470739103143.218897500774
Trimmed Mean ( 18 / 20 )71.486250.464800803718842153.7997555685
Trimmed Mean ( 19 / 20 )71.3250.40262060923201177.151885334561
Trimmed Mean ( 20 / 20 )71.1890.334909964334486212.561606345344
Median71.75
Midrange75.415
Midmean - Weighted Average at Xnp71.9635483870968
Midmean - Weighted Average at X(n+1)p72.1883333333333
Midmean - Empirical Distribution Function71.9635483870968
Midmean - Empirical Distribution Function - Averaging72.1883333333333
Midmean - Empirical Distribution Function - Interpolation72.1883333333333
Midmean - Closest Observation71.9635483870968
Midmean - True Basic - Statistics Graphics Toolkit72.1883333333333
Midmean - MS Excel (old versions)72.325625
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')