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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Dec 2007 03:12:06 -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/17/t1197886712p3ipoj8jb299cps.htm/, Retrieved Sat, 04 May 2024 04:20:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4327, Retrieved Sat, 04 May 2024 04:20:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper G30 Back-to...] [2007-12-17 10:12:06] [44e3ac4f32e975b756edf7d4f50e5cb3] [Current]
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Dataseries X:
121,7
113,3
112,9
127,0
116,8
112,0
129,7
113,6
115,7
119,5
125,8
129,6
128,0
112,8
101,6
123,9
118,8
109,1
130,6
112,4
111,0
116,2
119,8
117,2
127,3
107,7
97,5
120,1
110,6
111,3
119,8
105,5
108,7
128,7
119,5
121,1
128,4
108,8
107,5
125,6
102,9
107,5
120,4
104,3
100,6
121,9
112,7
124,9
123,9
102,2
104,9
109,8
98,9
107,3
112,6
104,0
110,6
100,8
103,8
117,0




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=4327&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=4327&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4327&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 Mean114.6351.1612063301769198.720612367429
Geometric Mean114.287330476032
Harmonic Mean113.939507748940
Quadratic Mean114.981471695806
Winsorized Mean ( 1 / 20 )114.6433333333331.1521764388058699.50154288188
Winsorized Mean ( 2 / 20 )114.6966666666671.13892844541107100.705770523862
Winsorized Mean ( 3 / 20 )114.6616666666671.12709589239742101.731953279301
Winsorized Mean ( 4 / 20 )114.6951.11201304965314103.141775211879
Winsorized Mean ( 5 / 20 )114.7116666666671.09527256279765104.733443129133
Winsorized Mean ( 6 / 20 )114.7116666666671.06773717027339107.434366677799
Winsorized Mean ( 7 / 20 )114.7816666666671.04152889484389110.204975814782
Winsorized Mean ( 8 / 20 )114.6483333333331.00579813900297113.987418436648
Winsorized Mean ( 9 / 20 )114.6633333333330.992155579045955115.569912375630
Winsorized Mean ( 10 / 20 )114.6466666666670.953093288889288120.289029419432
Winsorized Mean ( 11 / 20 )114.5733333333330.901363896449695127.111074433552
Winsorized Mean ( 12 / 20 )114.9333333333330.842922232932629136.351052140915
Winsorized Mean ( 13 / 20 )114.5433333333330.76147851525188150.422278552987
Winsorized Mean ( 14 / 20 )114.4966666666670.753878733623264151.876769512223
Winsorized Mean ( 15 / 20 )114.3966666666670.722061419154918158.430659265182
Winsorized Mean ( 16 / 20 )114.4766666666670.651956493412867175.589426324145
Winsorized Mean ( 17 / 20 )114.420.634710664097149180.271116387745
Winsorized Mean ( 18 / 20 )114.420.607699189636407188.283943686775
Winsorized Mean ( 19 / 20 )114.6416666666670.575430527433218199.227641220289
Winsorized Mean ( 20 / 20 )114.8083333333330.522992755060311219.521842745400
Trimmed Mean ( 1 / 20 )114.6551724137931.13045390348817101.424013893896
Trimmed Mean ( 2 / 20 )114.6678571428571.10345416096149103.917191306743
Trimmed Mean ( 3 / 20 )114.6518518518521.07856227497418106.300632343734
Trimmed Mean ( 4 / 20 )114.6480769230771.05292270949083108.885558160787
Trimmed Mean ( 5 / 20 )114.6341.02633729587205111.692326159304
Trimmed Mean ( 6 / 20 )114.6145833333330.998109869658137114.831630081556
Trimmed Mean ( 7 / 20 )114.5934782608700.970409556318531118.087747090626
Trimmed Mean ( 8 / 20 )114.5568181818180.941981839368763121.612554928431
Trimmed Mean ( 9 / 20 )114.5404761904760.914765060778204125.212998508092
Trimmed Mean ( 10 / 20 )114.520.882073605859424129.830435055837
Trimmed Mean ( 11 / 20 )114.50.849005777843008134.863628715107
Trimmed Mean ( 12 / 20 )114.4888888888890.818484641018861139.879092595276
Trimmed Mean ( 13 / 20 )114.4235294117650.79194990325195144.483292367247
Trimmed Mean ( 14 / 20 )114.406250.777622222267674147.123174626328
Trimmed Mean ( 15 / 20 )114.3933333333330.757308199356286151.052548263135
Trimmed Mean ( 16 / 20 )114.3928571428570.73569116930859155.490322454685
Trimmed Mean ( 17 / 20 )114.3807692307690.723963858655288157.992374706693
Trimmed Mean ( 18 / 20 )114.3750.708162809823696161.509469875260
Trimmed Mean ( 19 / 20 )114.3681818181820.689387279355109165.898305993067
Trimmed Mean ( 20 / 20 )114.3250.667196609545847171.351290405717
Median113.1
Midrange114.05
Midmean - Weighted Average at Xnp113.9625
Midmean - Weighted Average at X(n+1)p114.393333333333
Midmean - Empirical Distribution Function113.9625
Midmean - Empirical Distribution Function - Averaging114.393333333333
Midmean - Empirical Distribution Function - Interpolation114.393333333333
Midmean - Closest Observation113.9625
Midmean - True Basic - Statistics Graphics Toolkit114.393333333333
Midmean - MS Excel (old versions)114.196969696970
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 114.635 & 1.16120633017691 & 98.720612367429 \tabularnewline
Geometric Mean & 114.287330476032 &  &  \tabularnewline
Harmonic Mean & 113.939507748940 &  &  \tabularnewline
Quadratic Mean & 114.981471695806 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 114.643333333333 & 1.15217643880586 & 99.50154288188 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 114.696666666667 & 1.13892844541107 & 100.705770523862 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 114.661666666667 & 1.12709589239742 & 101.731953279301 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.695 & 1.11201304965314 & 103.141775211879 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 114.711666666667 & 1.09527256279765 & 104.733443129133 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 114.711666666667 & 1.06773717027339 & 107.434366677799 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 114.781666666667 & 1.04152889484389 & 110.204975814782 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 114.648333333333 & 1.00579813900297 & 113.987418436648 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 114.663333333333 & 0.992155579045955 & 115.569912375630 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 114.646666666667 & 0.953093288889288 & 120.289029419432 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.573333333333 & 0.901363896449695 & 127.111074433552 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 114.933333333333 & 0.842922232932629 & 136.351052140915 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 114.543333333333 & 0.76147851525188 & 150.422278552987 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 114.496666666667 & 0.753878733623264 & 151.876769512223 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 114.396666666667 & 0.722061419154918 & 158.430659265182 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 114.476666666667 & 0.651956493412867 & 175.589426324145 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 114.42 & 0.634710664097149 & 180.271116387745 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.42 & 0.607699189636407 & 188.283943686775 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.641666666667 & 0.575430527433218 & 199.227641220289 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.808333333333 & 0.522992755060311 & 219.521842745400 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 114.655172413793 & 1.13045390348817 & 101.424013893896 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 114.667857142857 & 1.10345416096149 & 103.917191306743 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 114.651851851852 & 1.07856227497418 & 106.300632343734 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 114.648076923077 & 1.05292270949083 & 108.885558160787 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 114.634 & 1.02633729587205 & 111.692326159304 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.614583333333 & 0.998109869658137 & 114.831630081556 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 114.593478260870 & 0.970409556318531 & 118.087747090626 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 114.556818181818 & 0.941981839368763 & 121.612554928431 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 114.540476190476 & 0.914765060778204 & 125.212998508092 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 114.52 & 0.882073605859424 & 129.830435055837 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 114.5 & 0.849005777843008 & 134.863628715107 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 114.488888888889 & 0.818484641018861 & 139.879092595276 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 114.423529411765 & 0.79194990325195 & 144.483292367247 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.40625 & 0.777622222267674 & 147.123174626328 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.393333333333 & 0.757308199356286 & 151.052548263135 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.392857142857 & 0.73569116930859 & 155.490322454685 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.380769230769 & 0.723963858655288 & 157.992374706693 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.375 & 0.708162809823696 & 161.509469875260 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.368181818182 & 0.689387279355109 & 165.898305993067 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.325 & 0.667196609545847 & 171.351290405717 \tabularnewline
Median & 113.1 &  &  \tabularnewline
Midrange & 114.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 113.9625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.393333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 113.9625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.393333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.393333333333 &  &  \tabularnewline
Midmean - Closest Observation & 113.9625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.393333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.196969696970 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4327&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]114.635[/C][C]1.16120633017691[/C][C]98.720612367429[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.287330476032[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.939507748940[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.981471695806[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]114.643333333333[/C][C]1.15217643880586[/C][C]99.50154288188[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]114.696666666667[/C][C]1.13892844541107[/C][C]100.705770523862[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]114.661666666667[/C][C]1.12709589239742[/C][C]101.731953279301[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.695[/C][C]1.11201304965314[/C][C]103.141775211879[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]114.711666666667[/C][C]1.09527256279765[/C][C]104.733443129133[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]114.711666666667[/C][C]1.06773717027339[/C][C]107.434366677799[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]114.781666666667[/C][C]1.04152889484389[/C][C]110.204975814782[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]114.648333333333[/C][C]1.00579813900297[/C][C]113.987418436648[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]114.663333333333[/C][C]0.992155579045955[/C][C]115.569912375630[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]114.646666666667[/C][C]0.953093288889288[/C][C]120.289029419432[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.573333333333[/C][C]0.901363896449695[/C][C]127.111074433552[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]114.933333333333[/C][C]0.842922232932629[/C][C]136.351052140915[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]114.543333333333[/C][C]0.76147851525188[/C][C]150.422278552987[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]114.496666666667[/C][C]0.753878733623264[/C][C]151.876769512223[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]114.396666666667[/C][C]0.722061419154918[/C][C]158.430659265182[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]114.476666666667[/C][C]0.651956493412867[/C][C]175.589426324145[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]114.42[/C][C]0.634710664097149[/C][C]180.271116387745[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.42[/C][C]0.607699189636407[/C][C]188.283943686775[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.641666666667[/C][C]0.575430527433218[/C][C]199.227641220289[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.808333333333[/C][C]0.522992755060311[/C][C]219.521842745400[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]114.655172413793[/C][C]1.13045390348817[/C][C]101.424013893896[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]114.667857142857[/C][C]1.10345416096149[/C][C]103.917191306743[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]114.651851851852[/C][C]1.07856227497418[/C][C]106.300632343734[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]114.648076923077[/C][C]1.05292270949083[/C][C]108.885558160787[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]114.634[/C][C]1.02633729587205[/C][C]111.692326159304[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.614583333333[/C][C]0.998109869658137[/C][C]114.831630081556[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]114.593478260870[/C][C]0.970409556318531[/C][C]118.087747090626[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]114.556818181818[/C][C]0.941981839368763[/C][C]121.612554928431[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]114.540476190476[/C][C]0.914765060778204[/C][C]125.212998508092[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]114.52[/C][C]0.882073605859424[/C][C]129.830435055837[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]114.5[/C][C]0.849005777843008[/C][C]134.863628715107[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]114.488888888889[/C][C]0.818484641018861[/C][C]139.879092595276[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]114.423529411765[/C][C]0.79194990325195[/C][C]144.483292367247[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.40625[/C][C]0.777622222267674[/C][C]147.123174626328[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.393333333333[/C][C]0.757308199356286[/C][C]151.052548263135[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.392857142857[/C][C]0.73569116930859[/C][C]155.490322454685[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.380769230769[/C][C]0.723963858655288[/C][C]157.992374706693[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.375[/C][C]0.708162809823696[/C][C]161.509469875260[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.368181818182[/C][C]0.689387279355109[/C][C]165.898305993067[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.325[/C][C]0.667196609545847[/C][C]171.351290405717[/C][/ROW]
[ROW][C]Median[/C][C]113.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]113.9625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.393333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]113.9625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.393333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.393333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.9625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.393333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.196969696970[/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=4327&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4327&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 Mean114.6351.1612063301769198.720612367429
Geometric Mean114.287330476032
Harmonic Mean113.939507748940
Quadratic Mean114.981471695806
Winsorized Mean ( 1 / 20 )114.6433333333331.1521764388058699.50154288188
Winsorized Mean ( 2 / 20 )114.6966666666671.13892844541107100.705770523862
Winsorized Mean ( 3 / 20 )114.6616666666671.12709589239742101.731953279301
Winsorized Mean ( 4 / 20 )114.6951.11201304965314103.141775211879
Winsorized Mean ( 5 / 20 )114.7116666666671.09527256279765104.733443129133
Winsorized Mean ( 6 / 20 )114.7116666666671.06773717027339107.434366677799
Winsorized Mean ( 7 / 20 )114.7816666666671.04152889484389110.204975814782
Winsorized Mean ( 8 / 20 )114.6483333333331.00579813900297113.987418436648
Winsorized Mean ( 9 / 20 )114.6633333333330.992155579045955115.569912375630
Winsorized Mean ( 10 / 20 )114.6466666666670.953093288889288120.289029419432
Winsorized Mean ( 11 / 20 )114.5733333333330.901363896449695127.111074433552
Winsorized Mean ( 12 / 20 )114.9333333333330.842922232932629136.351052140915
Winsorized Mean ( 13 / 20 )114.5433333333330.76147851525188150.422278552987
Winsorized Mean ( 14 / 20 )114.4966666666670.753878733623264151.876769512223
Winsorized Mean ( 15 / 20 )114.3966666666670.722061419154918158.430659265182
Winsorized Mean ( 16 / 20 )114.4766666666670.651956493412867175.589426324145
Winsorized Mean ( 17 / 20 )114.420.634710664097149180.271116387745
Winsorized Mean ( 18 / 20 )114.420.607699189636407188.283943686775
Winsorized Mean ( 19 / 20 )114.6416666666670.575430527433218199.227641220289
Winsorized Mean ( 20 / 20 )114.8083333333330.522992755060311219.521842745400
Trimmed Mean ( 1 / 20 )114.6551724137931.13045390348817101.424013893896
Trimmed Mean ( 2 / 20 )114.6678571428571.10345416096149103.917191306743
Trimmed Mean ( 3 / 20 )114.6518518518521.07856227497418106.300632343734
Trimmed Mean ( 4 / 20 )114.6480769230771.05292270949083108.885558160787
Trimmed Mean ( 5 / 20 )114.6341.02633729587205111.692326159304
Trimmed Mean ( 6 / 20 )114.6145833333330.998109869658137114.831630081556
Trimmed Mean ( 7 / 20 )114.5934782608700.970409556318531118.087747090626
Trimmed Mean ( 8 / 20 )114.5568181818180.941981839368763121.612554928431
Trimmed Mean ( 9 / 20 )114.5404761904760.914765060778204125.212998508092
Trimmed Mean ( 10 / 20 )114.520.882073605859424129.830435055837
Trimmed Mean ( 11 / 20 )114.50.849005777843008134.863628715107
Trimmed Mean ( 12 / 20 )114.4888888888890.818484641018861139.879092595276
Trimmed Mean ( 13 / 20 )114.4235294117650.79194990325195144.483292367247
Trimmed Mean ( 14 / 20 )114.406250.777622222267674147.123174626328
Trimmed Mean ( 15 / 20 )114.3933333333330.757308199356286151.052548263135
Trimmed Mean ( 16 / 20 )114.3928571428570.73569116930859155.490322454685
Trimmed Mean ( 17 / 20 )114.3807692307690.723963858655288157.992374706693
Trimmed Mean ( 18 / 20 )114.3750.708162809823696161.509469875260
Trimmed Mean ( 19 / 20 )114.3681818181820.689387279355109165.898305993067
Trimmed Mean ( 20 / 20 )114.3250.667196609545847171.351290405717
Median113.1
Midrange114.05
Midmean - Weighted Average at Xnp113.9625
Midmean - Weighted Average at X(n+1)p114.393333333333
Midmean - Empirical Distribution Function113.9625
Midmean - Empirical Distribution Function - Averaging114.393333333333
Midmean - Empirical Distribution Function - Interpolation114.393333333333
Midmean - Closest Observation113.9625
Midmean - True Basic - Statistics Graphics Toolkit114.393333333333
Midmean - MS Excel (old versions)114.196969696970
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')