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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Oct 2009 10:10:01 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/21/t125614152442wz6fv4at5lg46.htm/, Retrieved Thu, 02 May 2024 08:51:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49471, Retrieved Thu, 02 May 2024 08:51:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMean and Median
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [WS 2 - Tijdreeks 1] [2009-10-13 19:32:15] [b00a5c3d5f6ccb867aa9e2de58adfa61]
-   PD  [Univariate Data Series] [WS 2 - Tijdreeks 2] [2009-10-13 19:35:52] [b00a5c3d5f6ccb867aa9e2de58adfa61]
- RMPD    [Univariate Explorative Data Analysis] [WS 3 - Part2: EDA] [2009-10-21 15:35:04] [b00a5c3d5f6ccb867aa9e2de58adfa61]
- RMP         [Central Tendency] [WS 3 - Part 3: Ce...] [2009-10-21 16:10:01] [63d6214c2814604a6f6cfa44dba5912e] [Current]
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Dataseries X:
1.35
1.30
1.23
1.21
1.22
1.23
1.22
1.21
1.19
1.27
1.35
1.37
1.34
1.25
1.19
1.18
1.16
1.15
1.12
1.10
1.14
1.23
1.42
1.51
1.46
1.35
1.29
1.27
1.26
1.28
1.32
1.31
1.29
1.30
1.25
1.23
1.20
1.25
1.27
1.23
1.16
1.12
1.11
1.11
1.12
1.13
1.14
1.19
1.20
1.30
1.29
1.26
1.17
1.09
1.03
1.00
0.97
0.97
1.01
1.05




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49471&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49471&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.215333333333330.014519549779534483.703238171088
Geometric Mean1.21015134358475
Harmonic Mean1.20489061256561
Quadratic Mean1.22043981143411
Winsorized Mean ( 1 / 20 )1.21450.014254397676062885.201776153579
Winsorized Mean ( 2 / 20 )1.214166666666670.01360934305746489.215670553676
Winsorized Mean ( 3 / 20 )1.212166666666670.012894819322053394.0041606161603
Winsorized Mean ( 4 / 20 )1.212166666666670.012284507874147198.6744181439853
Winsorized Mean ( 5 / 20 )1.213833333333330.0118800304044454102.174261513601
Winsorized Mean ( 6 / 20 )1.217833333333330.0110164019131072110.547286032146
Winsorized Mean ( 7 / 20 )1.217833333333330.0105581298278338115.345553918349
Winsorized Mean ( 8 / 20 )1.21650.00980840467455778124.026285656372
Winsorized Mean ( 9 / 20 )1.2150.00954767993233935127.256046349503
Winsorized Mean ( 10 / 20 )1.2150.00896792778815481135.482803686803
Winsorized Mean ( 11 / 20 )1.2150.00896792778815481135.482803686803
Winsorized Mean ( 12 / 20 )1.2150.00896792778815481135.482803686803
Winsorized Mean ( 13 / 20 )1.2150.00824244218101315147.407767421021
Winsorized Mean ( 14 / 20 )1.217333333333330.00784333416170242155.206103455002
Winsorized Mean ( 15 / 20 )1.217333333333330.00784333416170242155.206103455002
Winsorized Mean ( 16 / 20 )1.217333333333330.00699017335553917174.149233705154
Winsorized Mean ( 17 / 20 )1.217333333333330.00611040913619343199.222884458387
Winsorized Mean ( 18 / 20 )1.217333333333330.00611040913619343199.222884458386
Winsorized Mean ( 19 / 20 )1.22050.00561688837598262217.291126029630
Winsorized Mean ( 20 / 20 )1.22050.00462384509935453263.957804332670
Trimmed Mean ( 1 / 20 )1.214482758620690.013463158966315390.207859957631
Trimmed Mean ( 2 / 20 )1.214464285714290.012473139043084897.3663711692202
Trimmed Mean ( 3 / 20 )1.214629629629630.0116875015008402103.925516462377
Trimmed Mean ( 4 / 20 )1.215576923076920.0110681880151199109.826190286645
Trimmed Mean ( 5 / 20 )1.21660.0105428571428571115.395663956640
Trimmed Mean ( 6 / 20 )1.217291666666670.0100254091342794121.420647313479
Trimmed Mean ( 7 / 20 )1.217173913043480.00965423009826108126.076745701629
Trimmed Mean ( 8 / 20 )1.217045454545450.0093135398121447130.674853932384
Trimmed Mean ( 9 / 20 )1.217142857142860.00908269988490592134.006724054107
Trimmed Mean ( 10 / 20 )1.21750.00884155398802026137.702037633841
Trimmed Mean ( 11 / 20 )1.217894736842110.0086677070650931140.509448196150
Trimmed Mean ( 12 / 20 )1.218333333333330.00841861127936288144.719038913213
Trimmed Mean ( 13 / 20 )1.218823529411760.00806352569794048151.152681230131
Trimmed Mean ( 14 / 20 )1.2193750.00777632754976862156.806023434067
Trimmed Mean ( 15 / 20 )1.219666666666670.00748152257743225163.023856981432
Trimmed Mean ( 16 / 20 )1.220.0070335552511443173.454242760305
Trimmed Mean ( 17 / 20 )1.220384615384620.00666750487827157183.034679038882
Trimmed Mean ( 18 / 20 )1.220833333333330.00642449644636621190.027863432605
Trimmed Mean ( 19 / 20 )1.221363636363640.00600488453938672203.395024226123
Trimmed Mean ( 20 / 20 )1.22150.00553814523388282220.561207482744
Median1.225
Midrange1.24
Midmean - Weighted Average at Xnp1.22151515151515
Midmean - Weighted Average at X(n+1)p1.22151515151515
Midmean - Empirical Distribution Function1.22151515151515
Midmean - Empirical Distribution Function - Averaging1.22151515151515
Midmean - Empirical Distribution Function - Interpolation1.22151515151515
Midmean - Closest Observation1.22151515151515
Midmean - True Basic - Statistics Graphics Toolkit1.22151515151515
Midmean - MS Excel (old versions)1.22151515151515
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.21533333333333 & 0.0145195497795344 & 83.703238171088 \tabularnewline
Geometric Mean & 1.21015134358475 &  &  \tabularnewline
Harmonic Mean & 1.20489061256561 &  &  \tabularnewline
Quadratic Mean & 1.22043981143411 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.2145 & 0.0142543976760628 & 85.201776153579 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.21416666666667 & 0.013609343057464 & 89.215670553676 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.21216666666667 & 0.0128948193220533 & 94.0041606161603 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.21216666666667 & 0.0122845078741471 & 98.6744181439853 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.21383333333333 & 0.0118800304044454 & 102.174261513601 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.21783333333333 & 0.0110164019131072 & 110.547286032146 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.21783333333333 & 0.0105581298278338 & 115.345553918349 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.2165 & 0.00980840467455778 & 124.026285656372 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.215 & 0.00954767993233935 & 127.256046349503 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.215 & 0.00896792778815481 & 135.482803686803 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.215 & 0.00896792778815481 & 135.482803686803 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.215 & 0.00896792778815481 & 135.482803686803 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.215 & 0.00824244218101315 & 147.407767421021 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.21733333333333 & 0.00784333416170242 & 155.206103455002 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.21733333333333 & 0.00784333416170242 & 155.206103455002 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.21733333333333 & 0.00699017335553917 & 174.149233705154 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.21733333333333 & 0.00611040913619343 & 199.222884458387 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.21733333333333 & 0.00611040913619343 & 199.222884458386 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.2205 & 0.00561688837598262 & 217.291126029630 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.2205 & 0.00462384509935453 & 263.957804332670 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.21448275862069 & 0.0134631589663153 & 90.207859957631 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.21446428571429 & 0.0124731390430848 & 97.3663711692202 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.21462962962963 & 0.0116875015008402 & 103.925516462377 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.21557692307692 & 0.0110681880151199 & 109.826190286645 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.2166 & 0.0105428571428571 & 115.395663956640 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.21729166666667 & 0.0100254091342794 & 121.420647313479 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.21717391304348 & 0.00965423009826108 & 126.076745701629 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.21704545454545 & 0.0093135398121447 & 130.674853932384 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.21714285714286 & 0.00908269988490592 & 134.006724054107 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.2175 & 0.00884155398802026 & 137.702037633841 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.21789473684211 & 0.0086677070650931 & 140.509448196150 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.21833333333333 & 0.00841861127936288 & 144.719038913213 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.21882352941176 & 0.00806352569794048 & 151.152681230131 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.219375 & 0.00777632754976862 & 156.806023434067 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.21966666666667 & 0.00748152257743225 & 163.023856981432 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.22 & 0.0070335552511443 & 173.454242760305 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.22038461538462 & 0.00666750487827157 & 183.034679038882 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.22083333333333 & 0.00642449644636621 & 190.027863432605 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.22136363636364 & 0.00600488453938672 & 203.395024226123 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.2215 & 0.00553814523388282 & 220.561207482744 \tabularnewline
Median & 1.225 &  &  \tabularnewline
Midrange & 1.24 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.22151515151515 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.22151515151515 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.22151515151515 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.22151515151515 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.22151515151515 &  &  \tabularnewline
Midmean - Closest Observation & 1.22151515151515 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.22151515151515 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.22151515151515 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49471&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]1.21533333333333[/C][C]0.0145195497795344[/C][C]83.703238171088[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.21015134358475[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.20489061256561[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.22043981143411[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.2145[/C][C]0.0142543976760628[/C][C]85.201776153579[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.21416666666667[/C][C]0.013609343057464[/C][C]89.215670553676[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.21216666666667[/C][C]0.0128948193220533[/C][C]94.0041606161603[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.21216666666667[/C][C]0.0122845078741471[/C][C]98.6744181439853[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.21383333333333[/C][C]0.0118800304044454[/C][C]102.174261513601[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.21783333333333[/C][C]0.0110164019131072[/C][C]110.547286032146[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.21783333333333[/C][C]0.0105581298278338[/C][C]115.345553918349[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.2165[/C][C]0.00980840467455778[/C][C]124.026285656372[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.215[/C][C]0.00954767993233935[/C][C]127.256046349503[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.215[/C][C]0.00896792778815481[/C][C]135.482803686803[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.215[/C][C]0.00896792778815481[/C][C]135.482803686803[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.215[/C][C]0.00896792778815481[/C][C]135.482803686803[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.215[/C][C]0.00824244218101315[/C][C]147.407767421021[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.21733333333333[/C][C]0.00784333416170242[/C][C]155.206103455002[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.21733333333333[/C][C]0.00784333416170242[/C][C]155.206103455002[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.21733333333333[/C][C]0.00699017335553917[/C][C]174.149233705154[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.21733333333333[/C][C]0.00611040913619343[/C][C]199.222884458387[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.21733333333333[/C][C]0.00611040913619343[/C][C]199.222884458386[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.2205[/C][C]0.00561688837598262[/C][C]217.291126029630[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.2205[/C][C]0.00462384509935453[/C][C]263.957804332670[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.21448275862069[/C][C]0.0134631589663153[/C][C]90.207859957631[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.21446428571429[/C][C]0.0124731390430848[/C][C]97.3663711692202[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.21462962962963[/C][C]0.0116875015008402[/C][C]103.925516462377[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.21557692307692[/C][C]0.0110681880151199[/C][C]109.826190286645[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.2166[/C][C]0.0105428571428571[/C][C]115.395663956640[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.21729166666667[/C][C]0.0100254091342794[/C][C]121.420647313479[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.21717391304348[/C][C]0.00965423009826108[/C][C]126.076745701629[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.21704545454545[/C][C]0.0093135398121447[/C][C]130.674853932384[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.21714285714286[/C][C]0.00908269988490592[/C][C]134.006724054107[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.2175[/C][C]0.00884155398802026[/C][C]137.702037633841[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.21789473684211[/C][C]0.0086677070650931[/C][C]140.509448196150[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.21833333333333[/C][C]0.00841861127936288[/C][C]144.719038913213[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.21882352941176[/C][C]0.00806352569794048[/C][C]151.152681230131[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.219375[/C][C]0.00777632754976862[/C][C]156.806023434067[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.21966666666667[/C][C]0.00748152257743225[/C][C]163.023856981432[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.22[/C][C]0.0070335552511443[/C][C]173.454242760305[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.22038461538462[/C][C]0.00666750487827157[/C][C]183.034679038882[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.22083333333333[/C][C]0.00642449644636621[/C][C]190.027863432605[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.22136363636364[/C][C]0.00600488453938672[/C][C]203.395024226123[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.2215[/C][C]0.00553814523388282[/C][C]220.561207482744[/C][/ROW]
[ROW][C]Median[/C][C]1.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.22151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.22151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.22151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.22151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.22151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.22151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.22151515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.22151515151515[/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=49471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49471&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 Mean1.215333333333330.014519549779534483.703238171088
Geometric Mean1.21015134358475
Harmonic Mean1.20489061256561
Quadratic Mean1.22043981143411
Winsorized Mean ( 1 / 20 )1.21450.014254397676062885.201776153579
Winsorized Mean ( 2 / 20 )1.214166666666670.01360934305746489.215670553676
Winsorized Mean ( 3 / 20 )1.212166666666670.012894819322053394.0041606161603
Winsorized Mean ( 4 / 20 )1.212166666666670.012284507874147198.6744181439853
Winsorized Mean ( 5 / 20 )1.213833333333330.0118800304044454102.174261513601
Winsorized Mean ( 6 / 20 )1.217833333333330.0110164019131072110.547286032146
Winsorized Mean ( 7 / 20 )1.217833333333330.0105581298278338115.345553918349
Winsorized Mean ( 8 / 20 )1.21650.00980840467455778124.026285656372
Winsorized Mean ( 9 / 20 )1.2150.00954767993233935127.256046349503
Winsorized Mean ( 10 / 20 )1.2150.00896792778815481135.482803686803
Winsorized Mean ( 11 / 20 )1.2150.00896792778815481135.482803686803
Winsorized Mean ( 12 / 20 )1.2150.00896792778815481135.482803686803
Winsorized Mean ( 13 / 20 )1.2150.00824244218101315147.407767421021
Winsorized Mean ( 14 / 20 )1.217333333333330.00784333416170242155.206103455002
Winsorized Mean ( 15 / 20 )1.217333333333330.00784333416170242155.206103455002
Winsorized Mean ( 16 / 20 )1.217333333333330.00699017335553917174.149233705154
Winsorized Mean ( 17 / 20 )1.217333333333330.00611040913619343199.222884458387
Winsorized Mean ( 18 / 20 )1.217333333333330.00611040913619343199.222884458386
Winsorized Mean ( 19 / 20 )1.22050.00561688837598262217.291126029630
Winsorized Mean ( 20 / 20 )1.22050.00462384509935453263.957804332670
Trimmed Mean ( 1 / 20 )1.214482758620690.013463158966315390.207859957631
Trimmed Mean ( 2 / 20 )1.214464285714290.012473139043084897.3663711692202
Trimmed Mean ( 3 / 20 )1.214629629629630.0116875015008402103.925516462377
Trimmed Mean ( 4 / 20 )1.215576923076920.0110681880151199109.826190286645
Trimmed Mean ( 5 / 20 )1.21660.0105428571428571115.395663956640
Trimmed Mean ( 6 / 20 )1.217291666666670.0100254091342794121.420647313479
Trimmed Mean ( 7 / 20 )1.217173913043480.00965423009826108126.076745701629
Trimmed Mean ( 8 / 20 )1.217045454545450.0093135398121447130.674853932384
Trimmed Mean ( 9 / 20 )1.217142857142860.00908269988490592134.006724054107
Trimmed Mean ( 10 / 20 )1.21750.00884155398802026137.702037633841
Trimmed Mean ( 11 / 20 )1.217894736842110.0086677070650931140.509448196150
Trimmed Mean ( 12 / 20 )1.218333333333330.00841861127936288144.719038913213
Trimmed Mean ( 13 / 20 )1.218823529411760.00806352569794048151.152681230131
Trimmed Mean ( 14 / 20 )1.2193750.00777632754976862156.806023434067
Trimmed Mean ( 15 / 20 )1.219666666666670.00748152257743225163.023856981432
Trimmed Mean ( 16 / 20 )1.220.0070335552511443173.454242760305
Trimmed Mean ( 17 / 20 )1.220384615384620.00666750487827157183.034679038882
Trimmed Mean ( 18 / 20 )1.220833333333330.00642449644636621190.027863432605
Trimmed Mean ( 19 / 20 )1.221363636363640.00600488453938672203.395024226123
Trimmed Mean ( 20 / 20 )1.22150.00553814523388282220.561207482744
Median1.225
Midrange1.24
Midmean - Weighted Average at Xnp1.22151515151515
Midmean - Weighted Average at X(n+1)p1.22151515151515
Midmean - Empirical Distribution Function1.22151515151515
Midmean - Empirical Distribution Function - Averaging1.22151515151515
Midmean - Empirical Distribution Function - Interpolation1.22151515151515
Midmean - Closest Observation1.22151515151515
Midmean - True Basic - Statistics Graphics Toolkit1.22151515151515
Midmean - MS Excel (old versions)1.22151515151515
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')