Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 08 Dec 2007 01:57:37 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/08/t1197103466262hzcsr860132b.htm/, Retrieved Mon, 29 Apr 2024 07:12:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2899, Retrieved Mon, 29 Apr 2024 07:12:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact245
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [PAPER echtscheidi...] [2007-12-08 08:57:37] [e0964b90cb3acfe235da067e79729c23] [Current]
Feedback Forum

Post a new message
Dataseries X:
2.293994811
117.7565127
124.0593836
-57.63118383
-148.4807117
2.067407253
302.1252747
308.9934276
7.711016284
-53.06218801
-215.8121082
-179.2793928
-36.66712334
-7.308481737
-133.1500993
93.76314183
206.619249
-229.5349296
259.0708568
-99.58126552
269.9669353
48.91481502
-29.12063
-61.5094603
57.5987677
-327.2439788
-50.22952022
-13.61930104
163.6860018
18.89331263
106.4302721
-70.56844503
-12.83994858
6.97089635
-167.8275625
-85.94257367
50.78900794
-117.6915576
-155.6069484
46.73153252
-286.1272517
-17.53192217
137.8713085
-115.515968
-126.7975933
-186.4451633
24.28894823
80.13347931
-238.2445942




Summary of compuational 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 compuational 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=2899&T=0

[TABLE]
[ROW][C]Summary of compuational 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=2899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2899&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 compuational 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 Mean-16.053762466714321.1780623659292-0.75803735909954
Geometric MeanNaN
Harmonic Mean57.6601369193282
Quadratic Mean147.601554588516
Winsorized Mean ( 1 / 16 )-15.354811972836720.8916351948538-0.734974157342123
Winsorized Mean ( 2 / 16 )-14.713003070795919.9966918642086-0.735771855200219
Winsorized Mean ( 3 / 16 )-14.846865146306119.6783120044965-0.754478592620832
Winsorized Mean ( 4 / 16 )-18.008398729979618.2520471922483-0.986650896762298
Winsorized Mean ( 5 / 16 )-19.392715291204116.5271937978279-1.17338221651112
Winsorized Mean ( 6 / 16 )-21.676256858551015.6412971376116-1.38583498976102
Winsorized Mean ( 7 / 16 )-22.013413229979614.891129753687-1.47829033754334
Winsorized Mean ( 8 / 16 )-21.047251074877614.2823053508178-1.47365922782714
Winsorized Mean ( 9 / 16 )-21.818680362632613.6120142859125-1.60289872640037
Winsorized Mean ( 10 / 16 )-21.27511258112.5154355910260-1.69990987738812
Winsorized Mean ( 11 / 16 )-22.908759963040811.6758064972816-1.96207088292998
Winsorized Mean ( 12 / 16 )-26.197415287938810.2842457602943-2.54733462215405
Winsorized Mean ( 13 / 16 )-27.42688900385719.8746272734525-2.77751131706947
Winsorized Mean ( 14 / 16 )-23.40960055814298.95817020160571-2.61321230020242
Winsorized Mean ( 15 / 16 )-19.90284259385718.12060329663829-2.45090689285319
Winsorized Mean ( 16 / 16 )-22.21090974487766.05867806253545-3.66596632394471
Trimmed Mean ( 1 / 16 )-16.053762466714319.8560636236708-0.808506800289274
Trimmed Mean ( 2 / 16 )-16.348591695085118.5065965714307-0.883392666608567
Trimmed Mean ( 3 / 16 )-18.979166831837217.3983214638353-1.09086194730267
Trimmed Mean ( 4 / 16 )-18.979166831837216.0965535069546-1.17908264173677
Trimmed Mean ( 5 / 16 )-21.447365173564115.0383694164905-1.42617624155753
Trimmed Mean ( 6 / 16 )-21.99156973714.333241442549-1.53430539945534
Trimmed Mean ( 7 / 16 )-22.065142741971413.7000491527326-1.6105885822731
Trimmed Mean ( 8 / 16 )-22.065142741971413.0831272357992-1.68653429293226
Trimmed Mean ( 9 / 16 )-22.27939939912.4161146673369-1.79439381770615
Trimmed Mean ( 10 / 16 )-22.365894543758611.6852999347808-1.91401972295016
Trimmed Mean ( 11 / 16 )-22.563851270333311.0112213749133-2.04916879808994
Trimmed Mean ( 12 / 16 )-22.5023948123610.3040349864538-2.18384301314414
Trimmed Mean ( 13 / 16 )-21.84639480039139.76166693518211-2.23797789306399
Trimmed Mean ( 14 / 16 )-20.84476763566679.01663178238908-2.3118131181069
Trimmed Mean ( 15 / 16 )-20.37229841310538.21419675096125-2.48013275439515
Trimmed Mean ( 16 / 16 )-20.37229841310537.24397625063828-2.81230883540103
Median-13.61930104
Midrange-9.12527559999998
Midmean - Weighted Average at Xnp-25.839943250375
Midmean - Weighted Average at X(n+1)p-22.50239481236
Midmean - Empirical Distribution Function-22.50239481236
Midmean - Empirical Distribution Function - Averaging-22.50239481236
Midmean - Empirical Distribution Function - Interpolation-22.50239481236
Midmean - Closest Observation-26.5137486003462
Midmean - True Basic - Statistics Graphics Toolkit-22.50239481236
Midmean - MS Excel (old versions)-22.50239481236
Number of observations49

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -16.0537624667143 & 21.1780623659292 & -0.75803735909954 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 57.6601369193282 &  &  \tabularnewline
Quadratic Mean & 147.601554588516 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & -15.3548119728367 & 20.8916351948538 & -0.734974157342123 \tabularnewline
Winsorized Mean ( 2 / 16 ) & -14.7130030707959 & 19.9966918642086 & -0.735771855200219 \tabularnewline
Winsorized Mean ( 3 / 16 ) & -14.8468651463061 & 19.6783120044965 & -0.754478592620832 \tabularnewline
Winsorized Mean ( 4 / 16 ) & -18.0083987299796 & 18.2520471922483 & -0.986650896762298 \tabularnewline
Winsorized Mean ( 5 / 16 ) & -19.3927152912041 & 16.5271937978279 & -1.17338221651112 \tabularnewline
Winsorized Mean ( 6 / 16 ) & -21.6762568585510 & 15.6412971376116 & -1.38583498976102 \tabularnewline
Winsorized Mean ( 7 / 16 ) & -22.0134132299796 & 14.891129753687 & -1.47829033754334 \tabularnewline
Winsorized Mean ( 8 / 16 ) & -21.0472510748776 & 14.2823053508178 & -1.47365922782714 \tabularnewline
Winsorized Mean ( 9 / 16 ) & -21.8186803626326 & 13.6120142859125 & -1.60289872640037 \tabularnewline
Winsorized Mean ( 10 / 16 ) & -21.275112581 & 12.5154355910260 & -1.69990987738812 \tabularnewline
Winsorized Mean ( 11 / 16 ) & -22.9087599630408 & 11.6758064972816 & -1.96207088292998 \tabularnewline
Winsorized Mean ( 12 / 16 ) & -26.1974152879388 & 10.2842457602943 & -2.54733462215405 \tabularnewline
Winsorized Mean ( 13 / 16 ) & -27.4268890038571 & 9.8746272734525 & -2.77751131706947 \tabularnewline
Winsorized Mean ( 14 / 16 ) & -23.4096005581429 & 8.95817020160571 & -2.61321230020242 \tabularnewline
Winsorized Mean ( 15 / 16 ) & -19.9028425938571 & 8.12060329663829 & -2.45090689285319 \tabularnewline
Winsorized Mean ( 16 / 16 ) & -22.2109097448776 & 6.05867806253545 & -3.66596632394471 \tabularnewline
Trimmed Mean ( 1 / 16 ) & -16.0537624667143 & 19.8560636236708 & -0.808506800289274 \tabularnewline
Trimmed Mean ( 2 / 16 ) & -16.3485916950851 & 18.5065965714307 & -0.883392666608567 \tabularnewline
Trimmed Mean ( 3 / 16 ) & -18.9791668318372 & 17.3983214638353 & -1.09086194730267 \tabularnewline
Trimmed Mean ( 4 / 16 ) & -18.9791668318372 & 16.0965535069546 & -1.17908264173677 \tabularnewline
Trimmed Mean ( 5 / 16 ) & -21.4473651735641 & 15.0383694164905 & -1.42617624155753 \tabularnewline
Trimmed Mean ( 6 / 16 ) & -21.991569737 & 14.333241442549 & -1.53430539945534 \tabularnewline
Trimmed Mean ( 7 / 16 ) & -22.0651427419714 & 13.7000491527326 & -1.6105885822731 \tabularnewline
Trimmed Mean ( 8 / 16 ) & -22.0651427419714 & 13.0831272357992 & -1.68653429293226 \tabularnewline
Trimmed Mean ( 9 / 16 ) & -22.279399399 & 12.4161146673369 & -1.79439381770615 \tabularnewline
Trimmed Mean ( 10 / 16 ) & -22.3658945437586 & 11.6852999347808 & -1.91401972295016 \tabularnewline
Trimmed Mean ( 11 / 16 ) & -22.5638512703333 & 11.0112213749133 & -2.04916879808994 \tabularnewline
Trimmed Mean ( 12 / 16 ) & -22.50239481236 & 10.3040349864538 & -2.18384301314414 \tabularnewline
Trimmed Mean ( 13 / 16 ) & -21.8463948003913 & 9.76166693518211 & -2.23797789306399 \tabularnewline
Trimmed Mean ( 14 / 16 ) & -20.8447676356667 & 9.01663178238908 & -2.3118131181069 \tabularnewline
Trimmed Mean ( 15 / 16 ) & -20.3722984131053 & 8.21419675096125 & -2.48013275439515 \tabularnewline
Trimmed Mean ( 16 / 16 ) & -20.3722984131053 & 7.24397625063828 & -2.81230883540103 \tabularnewline
Median & -13.61930104 &  &  \tabularnewline
Midrange & -9.12527559999998 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -25.839943250375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -22.50239481236 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -22.50239481236 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -22.50239481236 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -22.50239481236 &  &  \tabularnewline
Midmean - Closest Observation & -26.5137486003462 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -22.50239481236 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -22.50239481236 &  &  \tabularnewline
Number of observations & 49 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2899&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]-16.0537624667143[/C][C]21.1780623659292[/C][C]-0.75803735909954[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]57.6601369193282[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]147.601554588516[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]-15.3548119728367[/C][C]20.8916351948538[/C][C]-0.734974157342123[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]-14.7130030707959[/C][C]19.9966918642086[/C][C]-0.735771855200219[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]-14.8468651463061[/C][C]19.6783120044965[/C][C]-0.754478592620832[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]-18.0083987299796[/C][C]18.2520471922483[/C][C]-0.986650896762298[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]-19.3927152912041[/C][C]16.5271937978279[/C][C]-1.17338221651112[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]-21.6762568585510[/C][C]15.6412971376116[/C][C]-1.38583498976102[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]-22.0134132299796[/C][C]14.891129753687[/C][C]-1.47829033754334[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]-21.0472510748776[/C][C]14.2823053508178[/C][C]-1.47365922782714[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]-21.8186803626326[/C][C]13.6120142859125[/C][C]-1.60289872640037[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]-21.275112581[/C][C]12.5154355910260[/C][C]-1.69990987738812[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]-22.9087599630408[/C][C]11.6758064972816[/C][C]-1.96207088292998[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]-26.1974152879388[/C][C]10.2842457602943[/C][C]-2.54733462215405[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]-27.4268890038571[/C][C]9.8746272734525[/C][C]-2.77751131706947[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]-23.4096005581429[/C][C]8.95817020160571[/C][C]-2.61321230020242[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]-19.9028425938571[/C][C]8.12060329663829[/C][C]-2.45090689285319[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]-22.2109097448776[/C][C]6.05867806253545[/C][C]-3.66596632394471[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]-16.0537624667143[/C][C]19.8560636236708[/C][C]-0.808506800289274[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]-16.3485916950851[/C][C]18.5065965714307[/C][C]-0.883392666608567[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]-18.9791668318372[/C][C]17.3983214638353[/C][C]-1.09086194730267[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]-18.9791668318372[/C][C]16.0965535069546[/C][C]-1.17908264173677[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]-21.4473651735641[/C][C]15.0383694164905[/C][C]-1.42617624155753[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]-21.991569737[/C][C]14.333241442549[/C][C]-1.53430539945534[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]-22.0651427419714[/C][C]13.7000491527326[/C][C]-1.6105885822731[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]-22.0651427419714[/C][C]13.0831272357992[/C][C]-1.68653429293226[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]-22.279399399[/C][C]12.4161146673369[/C][C]-1.79439381770615[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]-22.3658945437586[/C][C]11.6852999347808[/C][C]-1.91401972295016[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]-22.5638512703333[/C][C]11.0112213749133[/C][C]-2.04916879808994[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]-22.50239481236[/C][C]10.3040349864538[/C][C]-2.18384301314414[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]-21.8463948003913[/C][C]9.76166693518211[/C][C]-2.23797789306399[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]-20.8447676356667[/C][C]9.01663178238908[/C][C]-2.3118131181069[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]-20.3722984131053[/C][C]8.21419675096125[/C][C]-2.48013275439515[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]-20.3722984131053[/C][C]7.24397625063828[/C][C]-2.81230883540103[/C][/ROW]
[ROW][C]Median[/C][C]-13.61930104[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-9.12527559999998[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-25.839943250375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-22.50239481236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-22.50239481236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-22.50239481236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-22.50239481236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-26.5137486003462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-22.50239481236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-22.50239481236[/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=2899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2899&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 Mean-16.053762466714321.1780623659292-0.75803735909954
Geometric MeanNaN
Harmonic Mean57.6601369193282
Quadratic Mean147.601554588516
Winsorized Mean ( 1 / 16 )-15.354811972836720.8916351948538-0.734974157342123
Winsorized Mean ( 2 / 16 )-14.713003070795919.9966918642086-0.735771855200219
Winsorized Mean ( 3 / 16 )-14.846865146306119.6783120044965-0.754478592620832
Winsorized Mean ( 4 / 16 )-18.008398729979618.2520471922483-0.986650896762298
Winsorized Mean ( 5 / 16 )-19.392715291204116.5271937978279-1.17338221651112
Winsorized Mean ( 6 / 16 )-21.676256858551015.6412971376116-1.38583498976102
Winsorized Mean ( 7 / 16 )-22.013413229979614.891129753687-1.47829033754334
Winsorized Mean ( 8 / 16 )-21.047251074877614.2823053508178-1.47365922782714
Winsorized Mean ( 9 / 16 )-21.818680362632613.6120142859125-1.60289872640037
Winsorized Mean ( 10 / 16 )-21.27511258112.5154355910260-1.69990987738812
Winsorized Mean ( 11 / 16 )-22.908759963040811.6758064972816-1.96207088292998
Winsorized Mean ( 12 / 16 )-26.197415287938810.2842457602943-2.54733462215405
Winsorized Mean ( 13 / 16 )-27.42688900385719.8746272734525-2.77751131706947
Winsorized Mean ( 14 / 16 )-23.40960055814298.95817020160571-2.61321230020242
Winsorized Mean ( 15 / 16 )-19.90284259385718.12060329663829-2.45090689285319
Winsorized Mean ( 16 / 16 )-22.21090974487766.05867806253545-3.66596632394471
Trimmed Mean ( 1 / 16 )-16.053762466714319.8560636236708-0.808506800289274
Trimmed Mean ( 2 / 16 )-16.348591695085118.5065965714307-0.883392666608567
Trimmed Mean ( 3 / 16 )-18.979166831837217.3983214638353-1.09086194730267
Trimmed Mean ( 4 / 16 )-18.979166831837216.0965535069546-1.17908264173677
Trimmed Mean ( 5 / 16 )-21.447365173564115.0383694164905-1.42617624155753
Trimmed Mean ( 6 / 16 )-21.99156973714.333241442549-1.53430539945534
Trimmed Mean ( 7 / 16 )-22.065142741971413.7000491527326-1.6105885822731
Trimmed Mean ( 8 / 16 )-22.065142741971413.0831272357992-1.68653429293226
Trimmed Mean ( 9 / 16 )-22.27939939912.4161146673369-1.79439381770615
Trimmed Mean ( 10 / 16 )-22.365894543758611.6852999347808-1.91401972295016
Trimmed Mean ( 11 / 16 )-22.563851270333311.0112213749133-2.04916879808994
Trimmed Mean ( 12 / 16 )-22.5023948123610.3040349864538-2.18384301314414
Trimmed Mean ( 13 / 16 )-21.84639480039139.76166693518211-2.23797789306399
Trimmed Mean ( 14 / 16 )-20.84476763566679.01663178238908-2.3118131181069
Trimmed Mean ( 15 / 16 )-20.37229841310538.21419675096125-2.48013275439515
Trimmed Mean ( 16 / 16 )-20.37229841310537.24397625063828-2.81230883540103
Median-13.61930104
Midrange-9.12527559999998
Midmean - Weighted Average at Xnp-25.839943250375
Midmean - Weighted Average at X(n+1)p-22.50239481236
Midmean - Empirical Distribution Function-22.50239481236
Midmean - Empirical Distribution Function - Averaging-22.50239481236
Midmean - Empirical Distribution Function - Interpolation-22.50239481236
Midmean - Closest Observation-26.5137486003462
Midmean - True Basic - Statistics Graphics Toolkit-22.50239481236
Midmean - MS Excel (old versions)-22.50239481236
Number of observations49



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')