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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Dec 2007 04:21:46 -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/16/t1197803917lgtxwn0db53wv4w.htm/, Retrieved Thu, 02 May 2024 09:05:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4135, Retrieved Thu, 02 May 2024 09:05:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact219
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency ...] [2007-12-16 11:21:46] [908a52009ae83f013a8231794220d3ac] [Current]
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Dataseries X:
108,1
105,4
114,6
106,9
115,9
109,8
101,8
114,2
110,8
108,4
127,5
128,6
116,6
127,4
105,0
108,3
125,0
111,6
106,5
130,3
115,0
116,1
134,0
126,5
125,8
136,4
114,9
110,9
125,5
116,8
116,8
125,5
104,2
115,1
132,8
123,3
124,8
122,0
117,4
117,9
137,4
114,6
124,7
129,6
109,4
120,9
134,9
136,3
133,2
127,2
122,7
120,5
137,8
119,1
124,3
134,4
121,1
121,0
127,0
133,4




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4135&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4135&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4135&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.5651.24601245334896.7606701490383
Geometric Mean120.183291711816
Harmonic Mean119.800303025193
Quadratic Mean120.94428262634
Winsorized Mean ( 1 / 20 )120.5983333333331.2348528393456197.662109597806
Winsorized Mean ( 2 / 20 )120.5916666666671.2214659426133198.7269988131331
Winsorized Mean ( 3 / 20 )120.6066666666671.2160877037457199.1759609896412
Winsorized Mean ( 4 / 20 )120.5866666666671.18109751379800102.097130218234
Winsorized Mean ( 5 / 20 )120.5783333333331.16594834625697103.416531032807
Winsorized Mean ( 6 / 20 )120.6583333333331.13474975878645106.330344993746
Winsorized Mean ( 7 / 20 )120.6116666666671.11661082160721108.015849687954
Winsorized Mean ( 8 / 20 )120.5983333333331.10896575134888108.748474140563
Winsorized Mean ( 9 / 20 )120.6883333333331.07002849021331112.789831707448
Winsorized Mean ( 10 / 20 )120.3383333333330.982045287789369122.538476412041
Winsorized Mean ( 11 / 20 )120.3933333333330.927449776813947129.811162116960
Winsorized Mean ( 12 / 20 )120.2133333333330.891131657436275134.899632764904
Winsorized Mean ( 13 / 20 )120.1266666666670.82740103157013145.185541331398
Winsorized Mean ( 14 / 20 )120.710.724165992145994166.688302556556
Winsorized Mean ( 15 / 20 )120.760.701295008727096172.195721482731
Winsorized Mean ( 16 / 20 )120.7066666666670.693039920531346174.169861058108
Winsorized Mean ( 17 / 20 )120.650.658836073504944183.125977541202
Winsorized Mean ( 18 / 20 )120.470.62335115839041193.261853095889
Winsorized Mean ( 19 / 20 )120.4066666666670.604978715910181199.026285553727
Winsorized Mean ( 20 / 20 )120.6733333333330.566074133546511213.175847794533
Trimmed Mean ( 1 / 20 )120.5913793103451.2108110616433799.5955381731258
Trimmed Mean ( 2 / 20 )120.5839285714291.18096311340868102.106430931091
Trimmed Mean ( 3 / 20 )120.5796296296301.15266949190977104.609023207382
Trimmed Mean ( 4 / 20 )120.5692307692311.11972422557472107.677612054295
Trimmed Mean ( 5 / 20 )120.5641.09203334029989110.403222640521
Trimmed Mean ( 6 / 20 )120.5604166666671.06182441844070113.540821413498
Trimmed Mean ( 7 / 20 )120.5391304347831.03271827539601116.720245304617
Trimmed Mean ( 8 / 20 )120.5251.00012221768998120.510271512997
Trimmed Mean ( 9 / 20 )120.5119047619050.959330985314184125.620778028385
Trimmed Mean ( 10 / 20 )120.48250.916472386171774131.463317190899
Trimmed Mean ( 11 / 20 )120.5052631578950.884414983473927136.254208046722
Trimmed Mean ( 12 / 20 )120.5222222222220.855812165186455140.827890891179
Trimmed Mean ( 13 / 20 )120.5676470588240.825687425894622146.020931502245
Trimmed Mean ( 14 / 20 )120.631250.800912250791397150.617311547928
Trimmed Mean ( 15 / 20 )120.620.794483856161439151.821838876346
Trimmed Mean ( 16 / 20 )120.60.788139594972884153.018577888032
Trimmed Mean ( 17 / 20 )120.5846153846150.777207868594958155.151048074962
Trimmed Mean ( 18 / 20 )120.5750.767695827823736157.06090306861
Trimmed Mean ( 19 / 20 )120.5909090909090.760123853285586158.646395017947
Trimmed Mean ( 20 / 20 )120.620.748106381402229161.23375364599
Median120.95
Midrange119.8
Midmean - Weighted Average at Xnp120.412903225806
Midmean - Weighted Average at X(n+1)p120.62
Midmean - Empirical Distribution Function120.412903225806
Midmean - Empirical Distribution Function - Averaging120.62
Midmean - Empirical Distribution Function - Interpolation120.62
Midmean - Closest Observation120.412903225806
Midmean - True Basic - Statistics Graphics Toolkit120.62
Midmean - MS Excel (old versions)120.63125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.565 & 1.246012453348 & 96.7606701490383 \tabularnewline
Geometric Mean & 120.183291711816 &  &  \tabularnewline
Harmonic Mean & 119.800303025193 &  &  \tabularnewline
Quadratic Mean & 120.94428262634 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 120.598333333333 & 1.23485283934561 & 97.662109597806 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 120.591666666667 & 1.22146594261331 & 98.7269988131331 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 120.606666666667 & 1.21608770374571 & 99.1759609896412 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 120.586666666667 & 1.18109751379800 & 102.097130218234 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 120.578333333333 & 1.16594834625697 & 103.416531032807 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 120.658333333333 & 1.13474975878645 & 106.330344993746 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 120.611666666667 & 1.11661082160721 & 108.015849687954 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 120.598333333333 & 1.10896575134888 & 108.748474140563 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 120.688333333333 & 1.07002849021331 & 112.789831707448 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 120.338333333333 & 0.982045287789369 & 122.538476412041 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 120.393333333333 & 0.927449776813947 & 129.811162116960 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 120.213333333333 & 0.891131657436275 & 134.899632764904 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 120.126666666667 & 0.82740103157013 & 145.185541331398 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 120.71 & 0.724165992145994 & 166.688302556556 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 120.76 & 0.701295008727096 & 172.195721482731 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 120.706666666667 & 0.693039920531346 & 174.169861058108 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 120.65 & 0.658836073504944 & 183.125977541202 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 120.47 & 0.62335115839041 & 193.261853095889 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 120.406666666667 & 0.604978715910181 & 199.026285553727 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 120.673333333333 & 0.566074133546511 & 213.175847794533 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 120.591379310345 & 1.21081106164337 & 99.5955381731258 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 120.583928571429 & 1.18096311340868 & 102.106430931091 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 120.579629629630 & 1.15266949190977 & 104.609023207382 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 120.569230769231 & 1.11972422557472 & 107.677612054295 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 120.564 & 1.09203334029989 & 110.403222640521 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 120.560416666667 & 1.06182441844070 & 113.540821413498 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 120.539130434783 & 1.03271827539601 & 116.720245304617 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 120.525 & 1.00012221768998 & 120.510271512997 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 120.511904761905 & 0.959330985314184 & 125.620778028385 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 120.4825 & 0.916472386171774 & 131.463317190899 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 120.505263157895 & 0.884414983473927 & 136.254208046722 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 120.522222222222 & 0.855812165186455 & 140.827890891179 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 120.567647058824 & 0.825687425894622 & 146.020931502245 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 120.63125 & 0.800912250791397 & 150.617311547928 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 120.62 & 0.794483856161439 & 151.821838876346 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 120.6 & 0.788139594972884 & 153.018577888032 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 120.584615384615 & 0.777207868594958 & 155.151048074962 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 120.575 & 0.767695827823736 & 157.06090306861 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 120.590909090909 & 0.760123853285586 & 158.646395017947 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 120.62 & 0.748106381402229 & 161.23375364599 \tabularnewline
Median & 120.95 &  &  \tabularnewline
Midrange & 119.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 120.412903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 120.62 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 120.412903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 120.62 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 120.62 &  &  \tabularnewline
Midmean - Closest Observation & 120.412903225806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 120.62 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 120.63125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4135&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]120.565[/C][C]1.246012453348[/C][C]96.7606701490383[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]120.183291711816[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]119.800303025193[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.94428262634[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]120.598333333333[/C][C]1.23485283934561[/C][C]97.662109597806[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]120.591666666667[/C][C]1.22146594261331[/C][C]98.7269988131331[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]120.606666666667[/C][C]1.21608770374571[/C][C]99.1759609896412[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]120.586666666667[/C][C]1.18109751379800[/C][C]102.097130218234[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]120.578333333333[/C][C]1.16594834625697[/C][C]103.416531032807[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]120.658333333333[/C][C]1.13474975878645[/C][C]106.330344993746[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]120.611666666667[/C][C]1.11661082160721[/C][C]108.015849687954[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]120.598333333333[/C][C]1.10896575134888[/C][C]108.748474140563[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]120.688333333333[/C][C]1.07002849021331[/C][C]112.789831707448[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]120.338333333333[/C][C]0.982045287789369[/C][C]122.538476412041[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]120.393333333333[/C][C]0.927449776813947[/C][C]129.811162116960[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]120.213333333333[/C][C]0.891131657436275[/C][C]134.899632764904[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]120.126666666667[/C][C]0.82740103157013[/C][C]145.185541331398[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]120.71[/C][C]0.724165992145994[/C][C]166.688302556556[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]120.76[/C][C]0.701295008727096[/C][C]172.195721482731[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]120.706666666667[/C][C]0.693039920531346[/C][C]174.169861058108[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]120.65[/C][C]0.658836073504944[/C][C]183.125977541202[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]120.47[/C][C]0.62335115839041[/C][C]193.261853095889[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]120.406666666667[/C][C]0.604978715910181[/C][C]199.026285553727[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]120.673333333333[/C][C]0.566074133546511[/C][C]213.175847794533[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]120.591379310345[/C][C]1.21081106164337[/C][C]99.5955381731258[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]120.583928571429[/C][C]1.18096311340868[/C][C]102.106430931091[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]120.579629629630[/C][C]1.15266949190977[/C][C]104.609023207382[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]120.569230769231[/C][C]1.11972422557472[/C][C]107.677612054295[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]120.564[/C][C]1.09203334029989[/C][C]110.403222640521[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]120.560416666667[/C][C]1.06182441844070[/C][C]113.540821413498[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]120.539130434783[/C][C]1.03271827539601[/C][C]116.720245304617[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]120.525[/C][C]1.00012221768998[/C][C]120.510271512997[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]120.511904761905[/C][C]0.959330985314184[/C][C]125.620778028385[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]120.4825[/C][C]0.916472386171774[/C][C]131.463317190899[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]120.505263157895[/C][C]0.884414983473927[/C][C]136.254208046722[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]120.522222222222[/C][C]0.855812165186455[/C][C]140.827890891179[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]120.567647058824[/C][C]0.825687425894622[/C][C]146.020931502245[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]120.63125[/C][C]0.800912250791397[/C][C]150.617311547928[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]120.62[/C][C]0.794483856161439[/C][C]151.821838876346[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]120.6[/C][C]0.788139594972884[/C][C]153.018577888032[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]120.584615384615[/C][C]0.777207868594958[/C][C]155.151048074962[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]120.575[/C][C]0.767695827823736[/C][C]157.06090306861[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]120.590909090909[/C][C]0.760123853285586[/C][C]158.646395017947[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]120.62[/C][C]0.748106381402229[/C][C]161.23375364599[/C][/ROW]
[ROW][C]Median[/C][C]120.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]119.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]120.412903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]120.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]120.412903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]120.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]120.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]120.412903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]120.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]120.63125[/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=4135&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4135&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 Mean120.5651.24601245334896.7606701490383
Geometric Mean120.183291711816
Harmonic Mean119.800303025193
Quadratic Mean120.94428262634
Winsorized Mean ( 1 / 20 )120.5983333333331.2348528393456197.662109597806
Winsorized Mean ( 2 / 20 )120.5916666666671.2214659426133198.7269988131331
Winsorized Mean ( 3 / 20 )120.6066666666671.2160877037457199.1759609896412
Winsorized Mean ( 4 / 20 )120.5866666666671.18109751379800102.097130218234
Winsorized Mean ( 5 / 20 )120.5783333333331.16594834625697103.416531032807
Winsorized Mean ( 6 / 20 )120.6583333333331.13474975878645106.330344993746
Winsorized Mean ( 7 / 20 )120.6116666666671.11661082160721108.015849687954
Winsorized Mean ( 8 / 20 )120.5983333333331.10896575134888108.748474140563
Winsorized Mean ( 9 / 20 )120.6883333333331.07002849021331112.789831707448
Winsorized Mean ( 10 / 20 )120.3383333333330.982045287789369122.538476412041
Winsorized Mean ( 11 / 20 )120.3933333333330.927449776813947129.811162116960
Winsorized Mean ( 12 / 20 )120.2133333333330.891131657436275134.899632764904
Winsorized Mean ( 13 / 20 )120.1266666666670.82740103157013145.185541331398
Winsorized Mean ( 14 / 20 )120.710.724165992145994166.688302556556
Winsorized Mean ( 15 / 20 )120.760.701295008727096172.195721482731
Winsorized Mean ( 16 / 20 )120.7066666666670.693039920531346174.169861058108
Winsorized Mean ( 17 / 20 )120.650.658836073504944183.125977541202
Winsorized Mean ( 18 / 20 )120.470.62335115839041193.261853095889
Winsorized Mean ( 19 / 20 )120.4066666666670.604978715910181199.026285553727
Winsorized Mean ( 20 / 20 )120.6733333333330.566074133546511213.175847794533
Trimmed Mean ( 1 / 20 )120.5913793103451.2108110616433799.5955381731258
Trimmed Mean ( 2 / 20 )120.5839285714291.18096311340868102.106430931091
Trimmed Mean ( 3 / 20 )120.5796296296301.15266949190977104.609023207382
Trimmed Mean ( 4 / 20 )120.5692307692311.11972422557472107.677612054295
Trimmed Mean ( 5 / 20 )120.5641.09203334029989110.403222640521
Trimmed Mean ( 6 / 20 )120.5604166666671.06182441844070113.540821413498
Trimmed Mean ( 7 / 20 )120.5391304347831.03271827539601116.720245304617
Trimmed Mean ( 8 / 20 )120.5251.00012221768998120.510271512997
Trimmed Mean ( 9 / 20 )120.5119047619050.959330985314184125.620778028385
Trimmed Mean ( 10 / 20 )120.48250.916472386171774131.463317190899
Trimmed Mean ( 11 / 20 )120.5052631578950.884414983473927136.254208046722
Trimmed Mean ( 12 / 20 )120.5222222222220.855812165186455140.827890891179
Trimmed Mean ( 13 / 20 )120.5676470588240.825687425894622146.020931502245
Trimmed Mean ( 14 / 20 )120.631250.800912250791397150.617311547928
Trimmed Mean ( 15 / 20 )120.620.794483856161439151.821838876346
Trimmed Mean ( 16 / 20 )120.60.788139594972884153.018577888032
Trimmed Mean ( 17 / 20 )120.5846153846150.777207868594958155.151048074962
Trimmed Mean ( 18 / 20 )120.5750.767695827823736157.06090306861
Trimmed Mean ( 19 / 20 )120.5909090909090.760123853285586158.646395017947
Trimmed Mean ( 20 / 20 )120.620.748106381402229161.23375364599
Median120.95
Midrange119.8
Midmean - Weighted Average at Xnp120.412903225806
Midmean - Weighted Average at X(n+1)p120.62
Midmean - Empirical Distribution Function120.412903225806
Midmean - Empirical Distribution Function - Averaging120.62
Midmean - Empirical Distribution Function - Interpolation120.62
Midmean - Closest Observation120.412903225806
Midmean - True Basic - Statistics Graphics Toolkit120.62
Midmean - MS Excel (old versions)120.63125
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')