Free Statistics

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, 22 Dec 2008 13:07:10 -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/2008/Dec/22/t1229976478crxfcg0o8qlvxa4.htm/, Retrieved Sat, 20 Apr 2024 05:42:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36199, Retrieved Sat, 20 Apr 2024 05:42:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-    D  [Central Tendency] [Arithmetic mean -...] [2008-12-21 10:09:47] [33f4701c7363e8b81858dafbf0350eed]
-    D      [Central Tendency] [Arithmetic mean -...] [2008-12-22 20:07:10] [9d7d6e0b01d5647e3f5dd21d8ef8600e] [Current]
Feedback Forum

Post a new message
Dataseries X:
101.1
100.7
100
100
100.8
101.9
102.7
103.1
103.5
103.9
104.4
105.2
106
107
108.2
109
109.1
109.3
110.1
110.7
110.8
110.7
110.9
111.3
111.6
111.8
112.1
112.3
112.5
113
113.6
114.4
114.9
115.2
116
117
118
119.4
121.1
123.1
125
126.3
127.4
129
131
133.3
135.9
138.4
140.3
141.7
143.1
144.5
146
147.7
149
149.7
150.2
150.5
150.7
150.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36199&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36199&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36199&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean119.952.1070268500644856.9285578854057
Geometric Mean118.913183447844
Harmonic Mean117.935241252939
Quadratic Mean121.036922741231
Winsorized Mean ( 1 / 20 )119.9466666666672.1061994404287856.9493393475823
Winsorized Mean ( 2 / 20 )119.9633333333332.1008674112072657.1018107536813
Winsorized Mean ( 3 / 20 )119.9533333333332.0964099885100457.2184515389504
Winsorized Mean ( 4 / 20 )119.942.0852226913009557.5190364560873
Winsorized Mean ( 5 / 20 )119.9483333333332.0611464799174558.1949582438884
Winsorized Mean ( 6 / 20 )119.8983333333332.0187279818696359.3930110496068
Winsorized Mean ( 7 / 20 )119.7466666666671.966413562186760.8959727339886
Winsorized Mean ( 8 / 20 )119.61.914100222302162.4836665324433
Winsorized Mean ( 9 / 20 )119.451.8597817440746264.2279667388797
Winsorized Mean ( 10 / 20 )119.31.7982383092763766.3427085189879
Winsorized Mean ( 11 / 20 )119.191.7241123156094469.1312270789437
Winsorized Mean ( 12 / 20 )118.971.6242987187348373.2439166686445
Winsorized Mean ( 13 / 20 )118.6451.4869952735307679.7884176983872
Winsorized Mean ( 14 / 20 )118.3183333333331.3328159130216688.7731997925285
Winsorized Mean ( 15 / 20 )117.9433333333331.1993862994431498.3364020316834
Winsorized Mean ( 16 / 20 )117.4366666666671.09916498010262106.841710564416
Winsorized Mean ( 17 / 20 )117.041.01206339543735115.644929485294
Winsorized Mean ( 18 / 20 )116.950.924489475851646126.502251301741
Winsorized Mean ( 19 / 20 )116.7283333333330.830815716738019140.498465522098
Winsorized Mean ( 20 / 20 )116.0950.725443269906825160.033189107828
Trimmed Mean ( 1 / 20 )119.7603448275862.0839938790534157.4667449992625
Trimmed Mean ( 2 / 20 )119.5607142857142.0550929428399558.1777650019528
Trimmed Mean ( 3 / 20 )119.3370370370372.0212382065123859.0415502005335
Trimmed Mean ( 4 / 20 )119.11.9796628138932960.1617604594858
Trimmed Mean ( 5 / 20 )118.8481.9304038701890461.566391279749
Trimmed Mean ( 6 / 20 )118.5729166666671.8748303459495763.2446113979511
Trimmed Mean ( 7 / 20 )118.2847826086961.815879945039165.1390985025437
Trimmed Mean ( 8 / 20 )1181.7543934581272467.2597127248532
Trimmed Mean ( 9 / 20 )117.7142857142861.6881515481664969.7296909404467
Trimmed Mean ( 10 / 20 )117.4251.6150007938396172.7089425887068
Trimmed Mean ( 11 / 20 )117.1289473684211.5335457472660776.377863247466
Trimmed Mean ( 12 / 20 )116.8166666666671.4430649701023580.9503862174556
Trimmed Mean ( 13 / 20 )116.51.3476129288711286.4491557658106
Trimmed Mean ( 14 / 20 )116.1906251.2572159412300992.4189880111735
Trimmed Mean ( 15 / 20 )115.8866666666671.1786387368615898.3224656057413
Trimmed Mean ( 16 / 20 )115.5928571428571.10932708249809104.200879043315
Trimmed Mean ( 17 / 20 )115.3269230769231.04262328460929110.612265023546
Trimmed Mean ( 18 / 20 )115.0750.973363546781416118.224069907399
Trimmed Mean ( 19 / 20 )114.7909090909090.895464983348311128.191399133983
Trimmed Mean ( 20 / 20 )114.4850.807245967863314141.821705598640
Median113.3
Midrange125.45
Midmean - Weighted Average at Xnp115.638709677419
Midmean - Weighted Average at X(n+1)p115.886666666667
Midmean - Empirical Distribution Function115.638709677419
Midmean - Empirical Distribution Function - Averaging115.886666666667
Midmean - Empirical Distribution Function - Interpolation115.886666666667
Midmean - Closest Observation115.638709677419
Midmean - True Basic - Statistics Graphics Toolkit115.886666666667
Midmean - MS Excel (old versions)116.190625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 119.95 & 2.10702685006448 & 56.9285578854057 \tabularnewline
Geometric Mean & 118.913183447844 &  &  \tabularnewline
Harmonic Mean & 117.935241252939 &  &  \tabularnewline
Quadratic Mean & 121.036922741231 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 119.946666666667 & 2.10619944042878 & 56.9493393475823 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 119.963333333333 & 2.10086741120726 & 57.1018107536813 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 119.953333333333 & 2.09640998851004 & 57.2184515389504 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 119.94 & 2.08522269130095 & 57.5190364560873 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 119.948333333333 & 2.06114647991745 & 58.1949582438884 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 119.898333333333 & 2.01872798186963 & 59.3930110496068 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 119.746666666667 & 1.9664135621867 & 60.8959727339886 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 119.6 & 1.9141002223021 & 62.4836665324433 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 119.45 & 1.85978174407462 & 64.2279667388797 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 119.3 & 1.79823830927637 & 66.3427085189879 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 119.19 & 1.72411231560944 & 69.1312270789437 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 118.97 & 1.62429871873483 & 73.2439166686445 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 118.645 & 1.48699527353076 & 79.7884176983872 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 118.318333333333 & 1.33281591302166 & 88.7731997925285 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 117.943333333333 & 1.19938629944314 & 98.3364020316834 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 117.436666666667 & 1.09916498010262 & 106.841710564416 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 117.04 & 1.01206339543735 & 115.644929485294 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 116.95 & 0.924489475851646 & 126.502251301741 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.728333333333 & 0.830815716738019 & 140.498465522098 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 116.095 & 0.725443269906825 & 160.033189107828 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 119.760344827586 & 2.08399387905341 & 57.4667449992625 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 119.560714285714 & 2.05509294283995 & 58.1777650019528 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 119.337037037037 & 2.02123820651238 & 59.0415502005335 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 119.1 & 1.97966281389329 & 60.1617604594858 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 118.848 & 1.93040387018904 & 61.566391279749 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 118.572916666667 & 1.87483034594957 & 63.2446113979511 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 118.284782608696 & 1.8158799450391 & 65.1390985025437 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 118 & 1.75439345812724 & 67.2597127248532 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 117.714285714286 & 1.68815154816649 & 69.7296909404467 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 117.425 & 1.61500079383961 & 72.7089425887068 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 117.128947368421 & 1.53354574726607 & 76.377863247466 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.816666666667 & 1.44306497010235 & 80.9503862174556 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.5 & 1.34761292887112 & 86.4491557658106 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.190625 & 1.25721594123009 & 92.4189880111735 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 115.886666666667 & 1.17863873686158 & 98.3224656057413 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 115.592857142857 & 1.10932708249809 & 104.200879043315 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 115.326923076923 & 1.04262328460929 & 110.612265023546 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 115.075 & 0.973363546781416 & 118.224069907399 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.790909090909 & 0.895464983348311 & 128.191399133983 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.485 & 0.807245967863314 & 141.821705598640 \tabularnewline
Median & 113.3 &  &  \tabularnewline
Midrange & 125.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.638709677419 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 115.886666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.638709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 115.886666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.886666666667 &  &  \tabularnewline
Midmean - Closest Observation & 115.638709677419 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 115.886666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.190625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36199&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]119.95[/C][C]2.10702685006448[/C][C]56.9285578854057[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]118.913183447844[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]117.935241252939[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]121.036922741231[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]119.946666666667[/C][C]2.10619944042878[/C][C]56.9493393475823[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]119.963333333333[/C][C]2.10086741120726[/C][C]57.1018107536813[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]119.953333333333[/C][C]2.09640998851004[/C][C]57.2184515389504[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]119.94[/C][C]2.08522269130095[/C][C]57.5190364560873[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]119.948333333333[/C][C]2.06114647991745[/C][C]58.1949582438884[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]119.898333333333[/C][C]2.01872798186963[/C][C]59.3930110496068[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]119.746666666667[/C][C]1.9664135621867[/C][C]60.8959727339886[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]119.6[/C][C]1.9141002223021[/C][C]62.4836665324433[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]119.45[/C][C]1.85978174407462[/C][C]64.2279667388797[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]119.3[/C][C]1.79823830927637[/C][C]66.3427085189879[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]119.19[/C][C]1.72411231560944[/C][C]69.1312270789437[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]118.97[/C][C]1.62429871873483[/C][C]73.2439166686445[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]118.645[/C][C]1.48699527353076[/C][C]79.7884176983872[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]118.318333333333[/C][C]1.33281591302166[/C][C]88.7731997925285[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]117.943333333333[/C][C]1.19938629944314[/C][C]98.3364020316834[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]117.436666666667[/C][C]1.09916498010262[/C][C]106.841710564416[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]117.04[/C][C]1.01206339543735[/C][C]115.644929485294[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]116.95[/C][C]0.924489475851646[/C][C]126.502251301741[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.728333333333[/C][C]0.830815716738019[/C][C]140.498465522098[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]116.095[/C][C]0.725443269906825[/C][C]160.033189107828[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]119.760344827586[/C][C]2.08399387905341[/C][C]57.4667449992625[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]119.560714285714[/C][C]2.05509294283995[/C][C]58.1777650019528[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]119.337037037037[/C][C]2.02123820651238[/C][C]59.0415502005335[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]119.1[/C][C]1.97966281389329[/C][C]60.1617604594858[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]118.848[/C][C]1.93040387018904[/C][C]61.566391279749[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]118.572916666667[/C][C]1.87483034594957[/C][C]63.2446113979511[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]118.284782608696[/C][C]1.8158799450391[/C][C]65.1390985025437[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]118[/C][C]1.75439345812724[/C][C]67.2597127248532[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]117.714285714286[/C][C]1.68815154816649[/C][C]69.7296909404467[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]117.425[/C][C]1.61500079383961[/C][C]72.7089425887068[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]117.128947368421[/C][C]1.53354574726607[/C][C]76.377863247466[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.816666666667[/C][C]1.44306497010235[/C][C]80.9503862174556[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.5[/C][C]1.34761292887112[/C][C]86.4491557658106[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.190625[/C][C]1.25721594123009[/C][C]92.4189880111735[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]115.886666666667[/C][C]1.17863873686158[/C][C]98.3224656057413[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]115.592857142857[/C][C]1.10932708249809[/C][C]104.200879043315[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]115.326923076923[/C][C]1.04262328460929[/C][C]110.612265023546[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]115.075[/C][C]0.973363546781416[/C][C]118.224069907399[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.790909090909[/C][C]0.895464983348311[/C][C]128.191399133983[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.485[/C][C]0.807245967863314[/C][C]141.821705598640[/C][/ROW]
[ROW][C]Median[/C][C]113.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]125.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.638709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]115.886666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.638709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]115.886666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.886666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.638709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]115.886666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.190625[/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=36199&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36199&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 Mean119.952.1070268500644856.9285578854057
Geometric Mean118.913183447844
Harmonic Mean117.935241252939
Quadratic Mean121.036922741231
Winsorized Mean ( 1 / 20 )119.9466666666672.1061994404287856.9493393475823
Winsorized Mean ( 2 / 20 )119.9633333333332.1008674112072657.1018107536813
Winsorized Mean ( 3 / 20 )119.9533333333332.0964099885100457.2184515389504
Winsorized Mean ( 4 / 20 )119.942.0852226913009557.5190364560873
Winsorized Mean ( 5 / 20 )119.9483333333332.0611464799174558.1949582438884
Winsorized Mean ( 6 / 20 )119.8983333333332.0187279818696359.3930110496068
Winsorized Mean ( 7 / 20 )119.7466666666671.966413562186760.8959727339886
Winsorized Mean ( 8 / 20 )119.61.914100222302162.4836665324433
Winsorized Mean ( 9 / 20 )119.451.8597817440746264.2279667388797
Winsorized Mean ( 10 / 20 )119.31.7982383092763766.3427085189879
Winsorized Mean ( 11 / 20 )119.191.7241123156094469.1312270789437
Winsorized Mean ( 12 / 20 )118.971.6242987187348373.2439166686445
Winsorized Mean ( 13 / 20 )118.6451.4869952735307679.7884176983872
Winsorized Mean ( 14 / 20 )118.3183333333331.3328159130216688.7731997925285
Winsorized Mean ( 15 / 20 )117.9433333333331.1993862994431498.3364020316834
Winsorized Mean ( 16 / 20 )117.4366666666671.09916498010262106.841710564416
Winsorized Mean ( 17 / 20 )117.041.01206339543735115.644929485294
Winsorized Mean ( 18 / 20 )116.950.924489475851646126.502251301741
Winsorized Mean ( 19 / 20 )116.7283333333330.830815716738019140.498465522098
Winsorized Mean ( 20 / 20 )116.0950.725443269906825160.033189107828
Trimmed Mean ( 1 / 20 )119.7603448275862.0839938790534157.4667449992625
Trimmed Mean ( 2 / 20 )119.5607142857142.0550929428399558.1777650019528
Trimmed Mean ( 3 / 20 )119.3370370370372.0212382065123859.0415502005335
Trimmed Mean ( 4 / 20 )119.11.9796628138932960.1617604594858
Trimmed Mean ( 5 / 20 )118.8481.9304038701890461.566391279749
Trimmed Mean ( 6 / 20 )118.5729166666671.8748303459495763.2446113979511
Trimmed Mean ( 7 / 20 )118.2847826086961.815879945039165.1390985025437
Trimmed Mean ( 8 / 20 )1181.7543934581272467.2597127248532
Trimmed Mean ( 9 / 20 )117.7142857142861.6881515481664969.7296909404467
Trimmed Mean ( 10 / 20 )117.4251.6150007938396172.7089425887068
Trimmed Mean ( 11 / 20 )117.1289473684211.5335457472660776.377863247466
Trimmed Mean ( 12 / 20 )116.8166666666671.4430649701023580.9503862174556
Trimmed Mean ( 13 / 20 )116.51.3476129288711286.4491557658106
Trimmed Mean ( 14 / 20 )116.1906251.2572159412300992.4189880111735
Trimmed Mean ( 15 / 20 )115.8866666666671.1786387368615898.3224656057413
Trimmed Mean ( 16 / 20 )115.5928571428571.10932708249809104.200879043315
Trimmed Mean ( 17 / 20 )115.3269230769231.04262328460929110.612265023546
Trimmed Mean ( 18 / 20 )115.0750.973363546781416118.224069907399
Trimmed Mean ( 19 / 20 )114.7909090909090.895464983348311128.191399133983
Trimmed Mean ( 20 / 20 )114.4850.807245967863314141.821705598640
Median113.3
Midrange125.45
Midmean - Weighted Average at Xnp115.638709677419
Midmean - Weighted Average at X(n+1)p115.886666666667
Midmean - Empirical Distribution Function115.638709677419
Midmean - Empirical Distribution Function - Averaging115.886666666667
Midmean - Empirical Distribution Function - Interpolation115.886666666667
Midmean - Closest Observation115.638709677419
Midmean - True Basic - Statistics Graphics Toolkit115.886666666667
Midmean - MS Excel (old versions)116.190625
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')