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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Dec 2010 14:57:03 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/13/t1292252226zvp6r0dum0fjo5t.htm/, Retrieved Mon, 06 May 2024 11:11:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108957, Retrieved Mon, 06 May 2024 11:11:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Spectral Analysis] [Unemployment] [2010-11-29 09:27:34] [b98453cac15ba1066b407e146608df68]
-   PD    [Spectral Analysis] [Workshop 9 CP (1)] [2010-12-07 15:31:19] [a9e130f95bad0a0597234e75c6380c5a]
-           [Spectral Analysis] [] [2010-12-07 22:07:26] [afdb2fc47981b6a655b732edc8065db9]
- RMPD        [Standard Deviation-Mean Plot] [] [2010-12-12 13:55:03] [afdb2fc47981b6a655b732edc8065db9]
- RMPD            [Central Tendency] [] [2010-12-13 14:57:03] [297722d8c88c4886be8e106c47d8f3cc] [Current]
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Dataseries X:
-359.571607953986
-2313.40174157408
-458.909041234261
-1511.62520054540
-1412.05101907477
3230.73156376355
-3359.59417563836
-2541.21894821932
872.44414461875
-4810.24424730606
-1719.68834437048
-6765.69231129807
4349.73058653668
540.896815335916
-2779.55375248146
-1525.85298806976
1655.44443186453
2302.85011810251
-837.776439784218
1692.87048596592
-1059.92175870099
91.2248118790486
3701.24902827296
1277.781090107
3758.70389605239
927.892916117894
-968.46413469261
2612.52020748951
-67.9700052554981
-4137.99067058662
3239.07295330528
151.781042841903
597.433769339769
4088.59661045384
2965.97886009382
-404.462070874797
4261.25490001266
1607.61904941779
5571.51047223473
-4651.92096188192
-3206.29864576434
3397.26719770752
2004.89246118837
-2974.16877824417
-4061.09181487588
1539.20943989673
-2972.96243506618
7150.15243163015
167.131979535770




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108957&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108957&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean180.730819801464427.5378677444240.422724706831122
Geometric MeanNaN
Harmonic Mean9401.16914010495
Quadratic Mean2967.57776482565
Winsorized Mean ( 1 / 16 )188.420740303436405.6681006497030.464470191276238
Winsorized Mean ( 2 / 16 )145.014348455521391.518575384520.370389446562271
Winsorized Mean ( 3 / 16 )171.062589563967382.5983701903850.44710747063257
Winsorized Mean ( 4 / 16 )163.245492923307378.0368453337280.431824291569239
Winsorized Mean ( 5 / 16 )201.164362804539355.0413163381820.5665942343818
Winsorized Mean ( 6 / 16 )212.899954081427349.7028002244920.608802543030127
Winsorized Mean ( 7 / 16 )202.635387932103334.1989992073820.60633152227473
Winsorized Mean ( 8 / 16 )177.004710181205329.084233888380.537870526611864
Winsorized Mean ( 9 / 16 )210.996661964611321.8039933863070.65566825241762
Winsorized Mean ( 10 / 16 )205.605253922246302.0556100692170.680686757895776
Winsorized Mean ( 11 / 16 )177.400031360006277.6121045252920.639021240314267
Winsorized Mean ( 12 / 16 )246.961657764071237.635485644361.03924570480046
Winsorized Mean ( 13 / 16 )219.337373927858214.8662308310551.02080896136871
Winsorized Mean ( 14 / 16 )134.253320299832199.1714516570790.674059054060525
Winsorized Mean ( 15 / 16 )153.278257249599192.0923104502990.797940619748325
Winsorized Mean ( 16 / 16 )252.642788817612170.5171294211171.48162703462872
Trimmed Mean ( 1 / 16 )180.730819801464392.5139042055360.460444376275717
Trimmed Mean ( 2 / 16 )180.241490424248375.4585829639940.480056918665603
Trimmed Mean ( 3 / 16 )186.33195814782363.3138157541410.512867802070904
Trimmed Mean ( 4 / 16 )186.33195814782351.8939808871430.529511637789505
Trimmed Mean ( 5 / 16 )201.577055778263338.4934749145690.595512382710297
Trimmed Mean ( 6 / 16 )201.686363646979329.3332689505790.612408106504553
Trimmed Mean ( 7 / 16 )199.069859212274318.356751466110.625304342676916
Trimmed Mean ( 8 / 16 )199.069859212274308.2050101875160.64590078886504
Trimmed Mean ( 9 / 16 )202.523746281521295.1326074637510.686212709676262
Trimmed Mean ( 10 / 16 )200.933045636037278.4172496371360.721697545313425
Trimmed Mean ( 11 / 16 )200.085126354465260.8834174617680.76695225898667
Trimmed Mean ( 12 / 16 )204.127197826205243.7223928130110.837539774126604
Trimmed Mean ( 13 / 16 )196.522529214048233.2674278530040.842477370384898
Trimmed Mean ( 14 / 16 )192.427557085928225.1782216263710.85455669600773
Trimmed Mean ( 15 / 16 )203.143863862314217.2319918903220.93514708443533
Trimmed Mean ( 16 / 16 )203.143863862314204.8968373208240.991444604604778
Median151.781042841903
Midrange192.23006016604
Midmean - Weighted Average at Xnp116.680409481359
Midmean - Weighted Average at X(n+1)p204.127197826205
Midmean - Empirical Distribution Function204.127197826205
Midmean - Empirical Distribution Function - Averaging204.127197826205
Midmean - Empirical Distribution Function - Interpolation204.127197826205
Midmean - Closest Observation107.299161695425
Midmean - True Basic - Statistics Graphics Toolkit204.127197826205
Midmean - MS Excel (old versions)204.127197826205
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 180.730819801464 & 427.537867744424 & 0.422724706831122 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 9401.16914010495 &  &  \tabularnewline
Quadratic Mean & 2967.57776482565 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 188.420740303436 & 405.668100649703 & 0.464470191276238 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 145.014348455521 & 391.51857538452 & 0.370389446562271 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 171.062589563967 & 382.598370190385 & 0.44710747063257 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 163.245492923307 & 378.036845333728 & 0.431824291569239 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 201.164362804539 & 355.041316338182 & 0.5665942343818 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 212.899954081427 & 349.702800224492 & 0.608802543030127 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 202.635387932103 & 334.198999207382 & 0.60633152227473 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 177.004710181205 & 329.08423388838 & 0.537870526611864 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 210.996661964611 & 321.803993386307 & 0.65566825241762 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 205.605253922246 & 302.055610069217 & 0.680686757895776 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 177.400031360006 & 277.612104525292 & 0.639021240314267 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 246.961657764071 & 237.63548564436 & 1.03924570480046 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 219.337373927858 & 214.866230831055 & 1.02080896136871 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 134.253320299832 & 199.171451657079 & 0.674059054060525 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 153.278257249599 & 192.092310450299 & 0.797940619748325 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 252.642788817612 & 170.517129421117 & 1.48162703462872 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 180.730819801464 & 392.513904205536 & 0.460444376275717 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 180.241490424248 & 375.458582963994 & 0.480056918665603 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 186.33195814782 & 363.313815754141 & 0.512867802070904 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 186.33195814782 & 351.893980887143 & 0.529511637789505 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 201.577055778263 & 338.493474914569 & 0.595512382710297 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 201.686363646979 & 329.333268950579 & 0.612408106504553 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 199.069859212274 & 318.35675146611 & 0.625304342676916 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 199.069859212274 & 308.205010187516 & 0.64590078886504 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 202.523746281521 & 295.132607463751 & 0.686212709676262 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 200.933045636037 & 278.417249637136 & 0.721697545313425 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 200.085126354465 & 260.883417461768 & 0.76695225898667 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 204.127197826205 & 243.722392813011 & 0.837539774126604 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 196.522529214048 & 233.267427853004 & 0.842477370384898 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 192.427557085928 & 225.178221626371 & 0.85455669600773 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 203.143863862314 & 217.231991890322 & 0.93514708443533 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 203.143863862314 & 204.896837320824 & 0.991444604604778 \tabularnewline
Median & 151.781042841903 &  &  \tabularnewline
Midrange & 192.23006016604 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.680409481359 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 204.127197826205 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 204.127197826205 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 204.127197826205 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 204.127197826205 &  &  \tabularnewline
Midmean - Closest Observation & 107.299161695425 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 204.127197826205 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 204.127197826205 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108957&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]180.730819801464[/C][C]427.537867744424[/C][C]0.422724706831122[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9401.16914010495[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2967.57776482565[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]188.420740303436[/C][C]405.668100649703[/C][C]0.464470191276238[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]145.014348455521[/C][C]391.51857538452[/C][C]0.370389446562271[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]171.062589563967[/C][C]382.598370190385[/C][C]0.44710747063257[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]163.245492923307[/C][C]378.036845333728[/C][C]0.431824291569239[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]201.164362804539[/C][C]355.041316338182[/C][C]0.5665942343818[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]212.899954081427[/C][C]349.702800224492[/C][C]0.608802543030127[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]202.635387932103[/C][C]334.198999207382[/C][C]0.60633152227473[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]177.004710181205[/C][C]329.08423388838[/C][C]0.537870526611864[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]210.996661964611[/C][C]321.803993386307[/C][C]0.65566825241762[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]205.605253922246[/C][C]302.055610069217[/C][C]0.680686757895776[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]177.400031360006[/C][C]277.612104525292[/C][C]0.639021240314267[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]246.961657764071[/C][C]237.63548564436[/C][C]1.03924570480046[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]219.337373927858[/C][C]214.866230831055[/C][C]1.02080896136871[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]134.253320299832[/C][C]199.171451657079[/C][C]0.674059054060525[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]153.278257249599[/C][C]192.092310450299[/C][C]0.797940619748325[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]252.642788817612[/C][C]170.517129421117[/C][C]1.48162703462872[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]180.730819801464[/C][C]392.513904205536[/C][C]0.460444376275717[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]180.241490424248[/C][C]375.458582963994[/C][C]0.480056918665603[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]186.33195814782[/C][C]363.313815754141[/C][C]0.512867802070904[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]186.33195814782[/C][C]351.893980887143[/C][C]0.529511637789505[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]201.577055778263[/C][C]338.493474914569[/C][C]0.595512382710297[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]201.686363646979[/C][C]329.333268950579[/C][C]0.612408106504553[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]199.069859212274[/C][C]318.35675146611[/C][C]0.625304342676916[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]199.069859212274[/C][C]308.205010187516[/C][C]0.64590078886504[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]202.523746281521[/C][C]295.132607463751[/C][C]0.686212709676262[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]200.933045636037[/C][C]278.417249637136[/C][C]0.721697545313425[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]200.085126354465[/C][C]260.883417461768[/C][C]0.76695225898667[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]204.127197826205[/C][C]243.722392813011[/C][C]0.837539774126604[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]196.522529214048[/C][C]233.267427853004[/C][C]0.842477370384898[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]192.427557085928[/C][C]225.178221626371[/C][C]0.85455669600773[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]203.143863862314[/C][C]217.231991890322[/C][C]0.93514708443533[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]203.143863862314[/C][C]204.896837320824[/C][C]0.991444604604778[/C][/ROW]
[ROW][C]Median[/C][C]151.781042841903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]192.23006016604[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.680409481359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]204.127197826205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]204.127197826205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]204.127197826205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]204.127197826205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.299161695425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]204.127197826205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]204.127197826205[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]49[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108957&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 Mean180.730819801464427.5378677444240.422724706831122
Geometric MeanNaN
Harmonic Mean9401.16914010495
Quadratic Mean2967.57776482565
Winsorized Mean ( 1 / 16 )188.420740303436405.6681006497030.464470191276238
Winsorized Mean ( 2 / 16 )145.014348455521391.518575384520.370389446562271
Winsorized Mean ( 3 / 16 )171.062589563967382.5983701903850.44710747063257
Winsorized Mean ( 4 / 16 )163.245492923307378.0368453337280.431824291569239
Winsorized Mean ( 5 / 16 )201.164362804539355.0413163381820.5665942343818
Winsorized Mean ( 6 / 16 )212.899954081427349.7028002244920.608802543030127
Winsorized Mean ( 7 / 16 )202.635387932103334.1989992073820.60633152227473
Winsorized Mean ( 8 / 16 )177.004710181205329.084233888380.537870526611864
Winsorized Mean ( 9 / 16 )210.996661964611321.8039933863070.65566825241762
Winsorized Mean ( 10 / 16 )205.605253922246302.0556100692170.680686757895776
Winsorized Mean ( 11 / 16 )177.400031360006277.6121045252920.639021240314267
Winsorized Mean ( 12 / 16 )246.961657764071237.635485644361.03924570480046
Winsorized Mean ( 13 / 16 )219.337373927858214.8662308310551.02080896136871
Winsorized Mean ( 14 / 16 )134.253320299832199.1714516570790.674059054060525
Winsorized Mean ( 15 / 16 )153.278257249599192.0923104502990.797940619748325
Winsorized Mean ( 16 / 16 )252.642788817612170.5171294211171.48162703462872
Trimmed Mean ( 1 / 16 )180.730819801464392.5139042055360.460444376275717
Trimmed Mean ( 2 / 16 )180.241490424248375.4585829639940.480056918665603
Trimmed Mean ( 3 / 16 )186.33195814782363.3138157541410.512867802070904
Trimmed Mean ( 4 / 16 )186.33195814782351.8939808871430.529511637789505
Trimmed Mean ( 5 / 16 )201.577055778263338.4934749145690.595512382710297
Trimmed Mean ( 6 / 16 )201.686363646979329.3332689505790.612408106504553
Trimmed Mean ( 7 / 16 )199.069859212274318.356751466110.625304342676916
Trimmed Mean ( 8 / 16 )199.069859212274308.2050101875160.64590078886504
Trimmed Mean ( 9 / 16 )202.523746281521295.1326074637510.686212709676262
Trimmed Mean ( 10 / 16 )200.933045636037278.4172496371360.721697545313425
Trimmed Mean ( 11 / 16 )200.085126354465260.8834174617680.76695225898667
Trimmed Mean ( 12 / 16 )204.127197826205243.7223928130110.837539774126604
Trimmed Mean ( 13 / 16 )196.522529214048233.2674278530040.842477370384898
Trimmed Mean ( 14 / 16 )192.427557085928225.1782216263710.85455669600773
Trimmed Mean ( 15 / 16 )203.143863862314217.2319918903220.93514708443533
Trimmed Mean ( 16 / 16 )203.143863862314204.8968373208240.991444604604778
Median151.781042841903
Midrange192.23006016604
Midmean - Weighted Average at Xnp116.680409481359
Midmean - Weighted Average at X(n+1)p204.127197826205
Midmean - Empirical Distribution Function204.127197826205
Midmean - Empirical Distribution Function - Averaging204.127197826205
Midmean - Empirical Distribution Function - Interpolation204.127197826205
Midmean - Closest Observation107.299161695425
Midmean - True Basic - Statistics Graphics Toolkit204.127197826205
Midmean - MS Excel (old versions)204.127197826205
Number of observations49



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
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')